Daily Papers

Despite significant progress in Natural Language Generation for Indian languages (IndicNLP), there is a lack of datasets around complex structured tasks such as semantic parsing. One reason for this imminent gap is the complexity of the logical form, which makes English to multilingual translation difficult. The process involves alignment of logical forms, intents and slots with translated unstructured utterance. To address this, we propose an Inter-bilingual Seq2seq Semantic parsing dataset IE-SEMPARSE for 11 distinct Indian languages. We highlight the proposed task's practicality, and evaluate existing multilingual seq2seq models across several train-test strategies. Our experiment reveals a high correlation across performance of original multilingual semantic parsing datasets (such as mTOP, multilingual TOP and multiATIS++) and our proposed IE-SEMPARSE suite.

Answering natural language questions over tables is usually seen as a semantic parsing task. To alleviate the collection cost of full logical forms, one popular approach focuses on weak supervision consisting of denotations instead of logical forms. However, training semantic parsers from weak supervision poses difficulties, and in addition, the generated logical forms are only used as an intermediate step prior to retrieving the denotation. In this paper, we present TAPAS, an approach to question answering over tables without generating logical forms. TAPAS trains from weak supervision, and predicts the denotation by selecting table cells and optionally applying a corresponding aggregation operator to such selection. TAPAS extends BERT's architecture to encode tables as input, initializes from an effective joint pre-training of text segments and tables crawled from Wikipedia, and is trained end-to-end. We experiment with three different semantic parsing datasets, and find that TAPAS outperforms or rivals semantic parsing models by improving state-of-the-art accuracy on SQA from 55.1 to 67.2 and performing on par with the state-of-the-art on WIKISQL and WIKITQ, but with a simpler model architecture. We additionally find that transfer learning, which is trivial in our setting, from WIKISQL to WIKITQ, yields 48.7 accuracy, 4.2 points above the state-of-the-art.

Large language models (LLMs) face challenges in solving complex mathematical problems that require comprehensive capacities to parse the statements, associate domain knowledge, perform compound logical reasoning, and integrate the intermediate rationales. Tackling all these problems once could be arduous for LLMs, thus leading to confusion in generation. In this work, we explore the potential of enhancing LLMs with agents by meticulous decomposition and modeling of mathematical reasoning process. Specifically, we propose a formal description of the mathematical solving and extend LLMs with an agent-based zero-shot framework named Planner-Reasoner-Executor-Reflector (PRER). We further provide and implement two MathAgents that define the logical forms and inherent relations via a pool of actions in different grains and orientations: MathAgent-M adapts its actions to LLMs, while MathAgent-H aligns with humankind. Experiments on miniF2F and MATH have demonstrated the effectiveness of PRER and proposed MathAgents, achieving an increase of 12.3%(53.9%66.2%) on the MiniF2F, 9.2% (49.8%59.0%) on MATH, and 13.2%(23.2%35.4%) for level-5 problems of MATH against GPT-4. Further analytical results provide more insightful perspectives on exploiting the behaviors of LLMs as agents.

The task of Question Generation over Knowledge Bases (KBQG) aims to convert a logical form into a natural language question. For the sake of expensive cost of large-scale question annotation, the methods of KBQG under low-resource scenarios urgently need to be developed. However, current methods heavily rely on annotated data for fine-tuning, which is not well-suited for few-shot question generation. The emergence of Large Language Models (LLMs) has shown their impressive generalization ability in few-shot tasks. Inspired by Chain-of-Thought (CoT) prompting, which is an in-context learning strategy for reasoning, we formulate KBQG task as a reasoning problem, where the generation of a complete question is splitted into a series of sub-question generation. Our proposed prompting method KQG-CoT first retrieves supportive logical forms from the unlabeled data pool taking account of the characteristics of the logical form. Then, we write a prompt to explicit the reasoning chain of generating complicated questions based on the selected demonstrations. To further ensure prompt quality, we extend KQG-CoT into KQG-CoT+ via sorting the logical forms by their complexity. We conduct extensive experiments over three public KBQG datasets. The results demonstrate that our prompting method consistently outperforms other prompting baselines on the evaluated datasets. Remarkably, our KQG-CoT+ method could surpass existing few-shot SoTA results of the PathQuestions dataset by 18.25, 10.72, and 10.18 absolute points on BLEU-4, METEOR, and ROUGE-L, respectively.

Domain-general semantic parsing is a long-standing goal in natural language processing, where the semantic parser is capable of robustly parsing sentences from domains outside of which it was trained. Current approaches largely rely on additional supervision from new domains in order to generalize to those domains. We present a generative model of natural language utterances and logical forms and demonstrate its application to semantic parsing. Our approach relies on domain-independent supervision to generalize to new domains. We derive and implement efficient algorithms for training, parsing, and sentence generation. The work relies on a novel application of hierarchical Dirichlet processes (HDPs) for structured prediction, which we also present in this manuscript. This manuscript is an excerpt of chapter 4 from the Ph.D. thesis of Saparov (2022), where the model plays a central role in a larger natural language understanding system. This manuscript provides a new simplified and more complete presentation of the work first introduced in Saparov, Saraswat, and Mitchell (2017). The description and proofs of correctness of the training algorithm, parsing algorithm, and sentence generation algorithm are much simplified in this new presentation. We also describe the novel application of hierarchical Dirichlet processes for structured prediction. In addition, we extend the earlier work with a new model of word morphology, which utilizes the comprehensive morphological data from Wiktionary.

Temporal Knowledge Graph Question Answering (TKGQA) aims to answer questions with temporal intent over Temporal Knowledge Graphs (TKGs). The core challenge of this task lies in understanding the complex semantic information regarding multiple types of time constraints (e.g., before, first) in questions. Existing end-to-end methods implicitly model the time constraints by learning time-aware embeddings of questions and candidate answers, which is far from understanding the question comprehensively. Motivated by semantic-parsing-based approaches that explicitly model constraints in questions by generating logical forms with symbolic operators, we design fundamental temporal operators for time constraints and introduce a novel self-improvement Programming method for TKGQA (Prog-TQA). Specifically, Prog-TQA leverages the in-context learning ability of Large Language Models (LLMs) to understand the combinatory time constraints in the questions and generate corresponding program drafts with a few examples given. Then, it aligns these drafts to TKGs with the linking module and subsequently executes them to generate the answers. To enhance the ability to understand questions, Prog-TQA is further equipped with a self-improvement strategy to effectively bootstrap LLMs using high-quality self-generated drafts. Extensive experiments demonstrate the superiority of the proposed Prog-TQA on MultiTQ and CronQuestions datasets, especially in the Hits@1 metric.

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

Most available semantic parsing datasets, comprising of pairs of natural utterances and logical forms, were collected solely for the purpose of training and evaluation of natural language understanding systems. As a result, they do not contain any of the richness and variety of natural-occurring utterances, where humans ask about data they need or are curious about. In this work, we release SEDE, a dataset with 12,023 pairs of utterances and SQL queries collected from real usage on the Stack Exchange website. We show that these pairs contain a variety of real-world challenges which were rarely reflected so far in any other semantic parsing dataset, propose an evaluation metric based on comparison of partial query clauses that is more suitable for real-world queries, and conduct experiments with strong baselines, showing a large gap between the performance on SEDE compared to other common datasets.

Pre-trained language models (PLMs) have shown their effectiveness in multiple scenarios. However, KBQA remains challenging, especially regarding coverage and generalization settings. This is due to two main factors: i) understanding the semantics of both questions and relevant knowledge from the KB; ii) generating executable logical forms with both semantic and syntactic correctness. In this paper, we present a new KBQA model, TIARA, which addresses those issues by applying multi-grained retrieval to help the PLM focus on the most relevant KB contexts, viz., entities, exemplary logical forms, and schema items. Moreover, constrained decoding is used to control the output space and reduce generation errors. Experiments over important benchmarks demonstrate the effectiveness of our approach. TIARA outperforms previous SOTA, including those using PLMs or oracle entity annotations, by at least 4.1 and 1.1 F1 points on GrailQA and WebQuestionsSP, respectively.

Recent advancement in the capabilities of large language models (LLMs) has triggered a new surge in LLMs' evaluation. Most recent evaluation works tends to evaluate the comprehensive ability of LLMs over series of tasks. However, the deep structure understanding of natural language is rarely explored. In this work, we examine the ability of LLMs to deal with structured semantics on the tasks of question answering with the help of the human-constructed formal language. Specifically, we implement the inter-conversion of natural and formal language through in-context learning of LLMs to verify their ability to understand and generate the structured logical forms. Extensive experiments with models of different sizes and in different formal languages show that today's state-of-the-art LLMs' understanding of the logical forms can approach human level overall, but there still are plenty of room in generating correct logical forms, which suggest that it is more effective to use LLMs to generate more natural language training data to reinforce a small model than directly answering questions with LLMs. Moreover, our results also indicate that models exhibit considerable sensitivity to different formal languages. In general, the formal language with the lower the formalization level, i.e. the more similar it is to natural language, is more LLMs-friendly.

Two important aspects of semantic parsing for question answering are the breadth of the knowledge source and the depth of logical compositionality. While existing work trades off one aspect for another, this paper simultaneously makes progress on both fronts through a new task: answering complex questions on semi-structured tables using question-answer pairs as supervision. The central challenge arises from two compounding factors: the broader domain results in an open-ended set of relations, and the deeper compositionality results in a combinatorial explosion in the space of logical forms. We propose a logical-form driven parsing algorithm guided by strong typing constraints and show that it obtains significant improvements over natural baselines. For evaluation, we created a new dataset of 22,033 complex questions on Wikipedia tables, which is made publicly available.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

Intermediate reasoning or acting steps have successfully improved large language models (LLMs) for handling various downstream natural language processing (NLP) tasks. When applying LLMs for code generation, recent works mainly focus on directing the models to articulate intermediate natural-language reasoning steps, as in chain-of-thought (CoT) prompting, and then output code with the natural language or other structured intermediate steps. However, such output is not suitable for code translation or generation tasks since the standard CoT has different logical structures and forms of expression with the code. In this work, we introduce the universal code (UniCode) as the intermediate representation. It is a description of algorithm steps using a mix of conventions of programming languages, such as assignment operator, conditional operator, and loop. Hence, we collect an instruction dataset UniCoder-Instruct to train our model UniCoder on multi-task learning objectives. UniCoder-Instruct comprises natural-language questions, code solutions, and the corresponding universal code. The alignment between the intermediate universal code representation and the final code solution significantly improves the quality of the generated code. The experimental results demonstrate that UniCoder with the universal code significantly outperforms the previous prompting methods by a large margin, showcasing the effectiveness of the structural clues in pseudo-code.

Semantic parsing is the task of mapping natural language to logic form. In question answering, semantic parsing can be used to map the question to logic form and execute the logic form to get the answer. One key problem for semantic parsing is the hard label work. We study this problem in another way: we do not use the logic form any more. Instead we only use the schema and answer info. We think that the logic form step can be injected into the deep model. The reason why we think removing the logic form step is possible is that human can do the task without explicit logic form. We use BERT-based model and do the experiment in the WikiSQL dataset, which is a large natural language to SQL dataset. Our experimental evaluations that show that our model can achieves the baseline results in WikiSQL dataset.

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP), exhibiting impressive achievements across various classic NLP tasks. However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include three representative LLMs (i.e., text-davinci-003, ChatGPT and BARD) and evaluate them on all selected datasets under zero-shot, one-shot and three-shot settings. Secondly, different from previous evaluations relying only on simple metrics (e.g., accuracy), we propose fine-level evaluations from objective and subjective manners, covering both answers and explanations. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., evidence selection process and reasoning process. Thirdly, to avoid the influences of knowledge bias and purely focus on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. It contains 3,000 samples and covers deductive, inductive and abductive settings. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions. It reflects the pros and cons of LLMs and gives guiding directions for future works.

Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to their occasionally wrong predictions. In this study, we introduce a generative neural model, the "Circuit Transformer", which eliminates such wrong predictions and produces logic circuits strictly equivalent to given Boolean functions. The main idea is a carefully designed decoding mechanism that builds a circuit step-by-step by generating tokens, which has beneficial "cutoff properties" that block a candidate token once it invalidate equivalence. In such a way, the proposed model works similar to typical LLMs while logical equivalence is strictly preserved. A Markov decision process formulation is also proposed for optimizing certain objectives of circuits. Experimentally, we trained an 88-million-parameter Circuit Transformer to generate equivalent yet more compact forms of input circuits, outperforming existing neural approaches on both synthetic and real world benchmarks, without any violation of equivalence constraints.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

In this thesis, I evaluate the performance of Large Language Models (LLMs) on the Law School Admissions Test (LSAT), specifically the Logic Games section of the test. I focus on this section because it presents a complex logical reasoning task and thus is a valuable source of data for evaluating how modern, increasingly capable LLMs can handle hard logical reasoning tasks. I construct a dataset of LSAT logic games and their associated metadata, and extensively evaluate LLMs' performance in a Chain-of-Thought prompting setting. Given the weak performance in this setting, I explore other prompting frameworks on a smaller subset of the dataset, adapting ideas from Reflexion to this task. This results in a substantially improved accuracy of 70 percent for GPT-4 and 46 percent for GPT-3.5 on this data subset, highlighting the capacity of LLMs to revise their logical errors, despite initially weak performance. Finally, I analyze the types of logic games that models perform better or worse on, as well as the types of logical errors I observe from human annotation, providing detailed insights on the logical reasoning capabilities of LLMs.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer language models (LMs) can reason according to logical rules. We ask whether those LMs can deduce theorems in propositional calculus and first-order logic; if their relative success in these problems reflects general logical capabilities; and which layers contribute the most to the task. First, we show for several encoder-only LMs that they can be trained, to a reasonable degree, to determine logical validity on various datasets. Next, by cross-probing fine-tuned models on these datasets, we show that LMs have difficulty in transferring their putative logical reasoning ability, which suggests that they may have learned dataset-specific features, instead of a general capability. Finally, we conduct a layerwise probing experiment, which shows that the hypothesis classification task is mostly solved through higher layers.

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain of large language models (LLMs) has showcased their capability in executing deductive reasoning tasks. Nonetheless, a significant portion of research primarily assesses the accuracy of LLMs in solving such tasks, often overlooking a deeper analysis of their reasoning behavior. In this study, we draw upon principles from cognitive psychology to examine inferential strategies employed by LLMs, through a detailed evaluation of their responses to propositional logic problems. Our findings indicate that LLMs display reasoning patterns akin to those observed in humans, including strategies like supposition following or chain construction. Moreover, our research demonstrates that the architecture and scale of the model significantly affect its preferred method of reasoning, with more advanced models tending to adopt strategies more frequently than less sophisticated ones. Importantly, we assert that a model's accuracy, that is the correctness of its final conclusion, does not necessarily reflect the validity of its reasoning process. This distinction underscores the necessity for more nuanced evaluation procedures in the field.

Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required non trivial manual effort. Recently, the emergence of large language models (LLMs) has demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. Consequently, there is a growing interest in using LLMs for logical reasoning via natural language. This work strives to understand the proficiency of LLMs in logical reasoning by offering a brief review of the latest progress in this area; with a focus on the logical reasoning datasets, tasks, and the methods adopted to utilize LLMs for reasoning. To offer a thorough analysis, we have compiled a benchmark titled LogiGLUE. This includes 24 varied datasets encompassing deductive, abductive, and inductive reasoning. We have standardized these datasets into Seq2Seq tasks to facilitate straightforward training and evaluation for future research. Utilizing LogiGLUE as a foundation, we have trained an instruction fine tuned language model, resulting in LogiT5. We study single task training, multi task training, and a chain of thought knowledge distillation fine tuning technique to assess the performance of model across the different logical reasoning categories. By this comprehensive process, we aim to shed light on the capabilities and potential pathways for enhancing logical reasoning proficiency in LLMs, paving the way for more advanced and nuanced developments in this critical field.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving. Our method first utilizes LLMs to translate a natural language problem into a symbolic formulation. Afterward, a deterministic symbolic solver performs inference on the formulated problem. We also introduce a self-refinement module, which utilizes the symbolic solver's error messages to revise symbolic formalizations. We demonstrate Logic-LM's effectiveness on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. On average, Logic-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-of-thought prompting. Our findings suggest that Logic-LM, by combining LLMs with symbolic logic, offers a promising avenue for faithful logical reasoning. Code and data are publicly available at https://github.com/teacherpeterpan/Logic-LLM.

Recent advancements in large language models (LLMs) have propelled Artificial Intelligence (AI) to new heights, enabling breakthroughs in various tasks such as writing assistance, code generation, and machine translation. A significant distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to "reason." However, evaluating the reasoning ability of LLMs remains a challenge as most existing evaluations focus on their accuracy on the downstream tasks rather than directly assessing their reasoning processes. Efforts have been made to develop benchmarks and metrics to assess reasoning in LLMs, but they suffer from data leakage or limited scope. In this paper, we introduce LogicAsker, an automatic approach that comprehensively evaluates and improves the logical reasoning abilities of LLMs under a set of atomic reasoning skills based on propositional and predicate logic. The results provide insights into LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3, ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases from LogicAsker can find logical reasoning failures in different LLMs with a rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further used to design demonstration examples for in-context learning, which effectively improves the logical reasoning ability of LLMs, e.g., 10\% for GPT-4. As far as we know, our work is the first to create prompts based on testing results to improve LLMs' formal reasoning ability effectively. All the code, data, and results will be released for reproduction and future research.

Language serves as a vehicle for conveying thought, enabling communication among individuals. The ability to distinguish between diverse concepts, identify fairness and injustice, and comprehend a range of legal notions fundamentally relies on logical reasoning. Large Language Models (LLMs) attempt to emulate human language understanding and generation, but their competency in logical reasoning remains limited. This paper seeks to address the philosophical question: How can we effectively teach logical reasoning to LLMs while maintaining a deep understanding of the intricate relationship between language and logic? By focusing on bolstering LLMs' capabilities in logical reasoning, we aim to expand their applicability in law and other logic-intensive disciplines. To this end, we propose a Reinforcement Learning from Logical Feedback (RLLF) approach, which serves as a potential framework for refining LLMs' reasoning capacities. Through RLLF and a revised evaluation methodology, we explore new avenues for research in this domain and contribute to the development of LLMs capable of handling complex legal reasoning tasks while acknowledging the fundamental connection between language and logic.

Studies have underscored how, regardless of the recent breakthrough and swift advances in AI research, even state-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning. The results seem to suggest that LLMs still work as (highly advanced) data pattern identifiers, scoring poorly when attempting to generalise and solve reasoning problems the models have never previously seen or that are not close to samples presented in their training data. To address this compelling concern, this paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation. We show that employing these critical questions can improve the reasoning capabilities of LLMs. By probing the rationale behind the models' reasoning process, the LLM can assess whether some logical mistake is occurring and correct it before providing the final reply to the user prompt. The underlying idea is drawn from the gold standard of any valid argumentative procedure: the conclusion is valid if it is entailed by accepted premises. Or, to paraphrase such Aristotelian principle in a real-world approximation, characterised by incomplete information and presumptive logic, the conclusion is valid if not proved otherwise. This approach successfully steers the models' output through a reasoning pipeline, resulting in better performance against the baseline and its Chain-of-Thought (CoT) implementation. To this end, an extensive evaluation of the proposed approach on the MT-Bench Reasoning and Math tasks across a range of LLMs is provided.

Natural language (NL) has long been the predominant format for human cognition and communication, and by extension, has been similarly pivotal in the development and application of Large Language Models (LLMs). Yet, besides NL, LLMs have seen various non-NL formats during pre-training, such as code and logical expression. NL's status as the optimal format for LLMs, particularly in single-LLM reasoning and multi-agent communication, has not been thoroughly examined. In this work, we challenge the default use of NL by exploring the utility of non-NL formats in these contexts. We show that allowing LLMs to autonomously select the most suitable format before reasoning or communicating leads to a 3.3 to 5.7\% improvement in reasoning efficiency for different LLMs, and up to a 72.7\% reduction in token usage in multi-agent communication, all while maintaining communicative effectiveness. Our comprehensive analysis further reveals that LLMs can devise a format from limited task instructions and that the devised format is effectively transferable across different LLMs. Intriguingly, the structured communication format decided by LLMs exhibits notable parallels with established agent communication languages, suggesting a natural evolution towards efficient, structured communication in agent communication. Our code is released at https://github.com/thunlp/AutoForm.

We propose LogicVista, an evaluation benchmark that assesses the integrated logical reasoning capabilities of multimodal large language models (MLLMs) in Visual contexts. Recent advancements in MLLMs have demonstrated various fascinating abilities, from crafting poetry based on an image to performing mathematical reasoning. However, there is still a lack of systematic evaluation of MLLMs' proficiency in logical reasoning tasks, which are essential for activities like navigation and puzzle-solving. Thus we evaluate general logical cognition abilities across 5 logical reasoning tasks encompassing 9 different capabilities, using a sample of 448 multiple-choice questions. Each question is annotated with the correct answer and the human-written reasoning behind the selection, enabling both open-ended and multiple-choice evaluation. A total of 8 MLLMs are comprehensively evaluated using LogicVista. Code and Data Available at https://github.com/Yijia-Xiao/LogicVista.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks. In particular, the LoT enhances Chain-of-Thought's performance on the ReClor dataset by +4.35%; moreover, it improves Chain-of-Thought with Self-Consistency's performance on LogiQA by +5%; additionally, it boosts performance of Tree-of-Thoughts on ProofWriter dataset by +8%.

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary, limiting the generalizability of acquired reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. Then, using the proposed corpora, which we name FLD (Formal Logic Deduction), we first evaluate and analyze the logical reasoning ability of the latest LLMs. Even GPT-4 can solve only half of the problems, suggesting that pure logical reasoning isolated from knowledge is still challenging for the LLMs, and additional training specialized in logical reasoning is indeed essential. We next empirically verify that LMs trained on FLD corpora acquire more generalizable reasoning ability. Furthermore, we identify the aspects of reasoning ability on which deduction corpora can enhance LMs and those on which they cannot, and discuss future directions on each aspect. The released corpora serve both as learning resources and as challenging benchmarks.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for large language models (LLMs), even though they have demonstrated promising performance in other reasoning tasks. Within this context, some recent studies use programming languages (e.g., Python) to express the necessary logic for solving a given instance/question (e.g., Program-of-Thought) as inspired by their strict and precise syntaxes. However, it is non-trivial to write an executable code that expresses the correct logic on the fly within a single inference call. Also, the code generated specifically for an instance cannot be reused for others, even if they are from the same task and might require identical logic to solve. This paper presents Think-and-Execute, a novel framework that decomposes the reasoning process of language models into two steps. (1) In Think, we discover a task-level logic that is shared across all instances for solving a given task and then express the logic with pseudocode; (2) In Execute, we further tailor the generated pseudocode to each instance and simulate the execution of the code. With extensive experiments on seven algorithmic reasoning tasks, we demonstrate the effectiveness of Think-and-Execute. Our approach better improves LMs' reasoning compared to several strong baselines performing instance-specific reasoning (e.g., CoT and PoT), suggesting the helpfulness of discovering task-level logic. Also, we show that compared to natural language, pseudocode can better guide the reasoning of LMs, even though they are trained to follow natural language instructions.

We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague semantics based on a lambda calculus where the primitives act on string diagrams rather than logical formulae. As a special case, we show how to translate from the Lambek calculus into Peirce's system beta for first-order logic. This allows us to give a purely diagrammatic treatment of higher-order and non-linear processes in natural language semantics: adverbs, prepositions, negation and quantifiers. The theoretical definition presented in this article comes with a proof-of-concept implementation in DisCoPy, the Python library for string diagrams.

Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs' suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. To evaluate LLMs' capability of logical fallacy understanding (LFU), we propose five concrete tasks from three cognitive dimensions of WHAT, WHY, and HOW in this paper. Towards these LFU tasks, we have successfully constructed a new dataset LFUD based on GPT-4 accompanied by a little human effort. Our extensive experiments justify that our LFUD can be used not only to evaluate LLMs' LFU capability, but also to fine-tune LLMs to obtain significantly enhanced performance on logical reasoning.

This paper investigates the rational thinking capability of Large Language Models (LLMs) in multi-round argumentative debates by exploring the impact of fallacious arguments on their logical reasoning performance. More specifically, we present Logic Competence Measurement Benchmark (LOGICOM), a diagnostic benchmark to assess the robustness of LLMs against logical fallacies. LOGICOM involves two agents: a persuader and a debater engaging in a multi-round debate on a controversial topic, where the persuader tries to convince the debater of the correctness of its claim. First, LOGICOM assesses the potential of LLMs to change their opinions through reasoning. Then, it evaluates the debater's performance in logical reasoning by contrasting the scenario where the persuader employs logical fallacies against one where logical reasoning is used. We use this benchmark to evaluate the performance of GPT-3.5 and GPT-4 using a dataset containing controversial topics, claims, and reasons supporting them. Our findings indicate that both GPT-3.5 and GPT-4 can adjust their opinion through reasoning. However, when presented with logical fallacies, GPT-3.5 and GPT-4 are erroneously convinced 41% and 69% more often, respectively, compared to when logical reasoning is used. Finally, we introduce a new dataset containing over 5k pairs of logical vs. fallacious arguments. The source code and dataset of this work are made publicly available.

Logical reasoning is of vital importance to natural language understanding. Previous studies either employ graph-based models to incorporate prior knowledge about logical relations, or introduce symbolic logic into neural models through data augmentation. These methods, however, heavily depend on annotated training data, and thus suffer from over-fitting and poor generalization problems due to the dataset sparsity. To address these two problems, in this paper, we propose MERIt, a MEta-path guided contrastive learning method for logical ReasonIng of text, to perform self-supervised pre-training on abundant unlabeled text data. Two novel strategies serve as indispensable components of our method. In particular, a strategy based on meta-path is devised to discover the logical structure in natural texts, followed by a counterfactual data augmentation strategy to eliminate the information shortcut induced by pre-training. The experimental results on two challenging logical reasoning benchmarks, i.e., ReClor and LogiQA, demonstrate that our method outperforms the SOTA baselines with significant improvements.

Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning capabilities, but complex logical reasoning remains a challenge. The state-of-the-art, solver-augmented language models, use LLMs to parse natural language logical questions into symbolic representations first and then adopt external logical solvers to take in the symbolic representations and output the answers. Despite their impressive performance, any parsing errors will inevitably result in the failure of the execution of the external logical solver and no answer to the logical questions. In this paper, we introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers and bypasses the parsing errors by learning to strict adherence to solver syntax and grammar. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers. Experimental results on two public deductive reasoning datasets demonstrate that LoGiPT outperforms state-of-the-art solver-augmented LMs and few-shot prompting methods on competitive LLMs like ChatGPT or GPT-4.

Logical reasoning task has attracted great interest since it was proposed. Faced with such a task, current competitive models, even large language models (e.g., ChatGPT and PaLM 2), still perform badly. Previous promising LMs struggle in logical consistency modeling and logical structure perception. To this end, we model the logical reasoning task by transforming each logical sample into reasoning paths and propose an architecture PathReasoner. It addresses the task from the views of both data and model. To expand the diversity of the logical samples, we propose an atom extension strategy supported by equivalent logical formulas, to form new reasoning paths. From the model perspective, we design a stack of transformer-style blocks. In particular, we propose a path-attention module to joint model in-atom and cross-atom relations with the high-order diffusion strategy. Experiments show that PathReasoner achieves competitive performances on two logical reasoning benchmarks and great generalization abilities.

Pre-trained large language model (LLM) is under exploration to perform NLP tasks that may require logical reasoning. Logic-driven data augmentation for representation learning has been shown to improve the performance of tasks requiring logical reasoning, but most of these data rely on designed templates and therefore lack generalization. In this regard, we propose an AMR-based logical equivalence-driven data augmentation method (AMR-LE) for generating logically equivalent data. Specifically, we first parse a text into the form of an AMR graph, next apply four logical equivalence laws (contraposition, double negation, commutative and implication laws) on the AMR graph to construct a logically equivalent/inequivalent AMR graph, and then convert it into a logically equivalent/inequivalent sentence. To help the model to better learn these logical equivalence laws, we propose a logical equivalence-driven contrastive learning training paradigm, which aims to distinguish the difference between logical equivalence and inequivalence. Our AMR-LE (Ensemble) achieves #2 on the ReClor leaderboard https://eval.ai/web/challenges/challenge-page/503/leaderboard/1347 . Our model shows better performance on seven downstream tasks, including ReClor, LogiQA, MNLI, MRPC, RTE, QNLI, and QQP. The source code and dataset are public at https://github.com/Strong-AI-Lab/Logical-Equivalence-driven-AMR-Data-Augmentation-for-Representation-Learning .

Large language models (LLMs) have gained enormous attention from both academia and industry, due to their exceptional ability in language generation and extremely powerful generalization. However, current LLMs still output unreliable content in practical reasoning tasks due to their inherent issues (e.g., hallucination). To better disentangle this problem, in this paper, we conduct an in-depth investigation to systematically explore the capability of LLMs in logical reasoning. More in detail, we first investigate the deficiency of LLMs in logical reasoning on different tasks, including event relation extraction and deductive reasoning. Our study demonstrates that LLMs are not good reasoners in solving tasks with rigorous reasoning and will produce counterfactual answers, which require us to iteratively refine. Therefore, we comprehensively explore different strategies to endow LLMs with logical reasoning ability, and thus enable them to generate more logically consistent answers across different scenarios. Based on our approach, we also contribute a synthesized dataset (LLM-LR) involving multi-hop reasoning for evaluation and pre-training. Extensive quantitative and qualitative analyses on different tasks also validate the effectiveness and necessity of teaching LLMs with logic and provide insights for solving practical tasks with LLMs in future work.

Multi-hop query answering over a Knowledge Graph (KG) involves traversing one or more hops from the start node to answer a query. Path-based and logic-based methods are state-of-the-art for multi-hop question answering. The former is used in link prediction tasks. The latter is for answering complex logical queries. The logical multi-hop querying technique embeds the KG and queries in the same embedding space. The existing work incorporates First Order Logic (FOL) operators, such as conjunction (wedge), disjunction (vee), and negation (neg), in queries. Though current models have most of the building blocks to execute the FOL queries, they cannot use the dense information of multi-modal entities in the case of Multi-Modal Knowledge Graphs (MMKGs). We propose RConE, an embedding method to capture the multi-modal information needed to answer a query. The model first shortlists candidate (multi-modal) entities containing the answer. It then finds the solution (sub-entities) within those entities. Several existing works tackle path-based question-answering in MMKGs. However, to our knowledge, we are the first to introduce logical constructs in querying MMKGs and to answer queries that involve sub-entities of multi-modal entities as the answer. Extensive evaluation of four publicly available MMKGs indicates that RConE outperforms the current state-of-the-art.

In large language models (LLMs), code and reasoning reinforce each other: code offers an abstract, modular, and logic-driven structure that supports reasoning, while reasoning translates high-level goals into smaller, executable steps that drive more advanced code intelligence. In this study, we examine how code serves as a structured medium for enhancing reasoning: it provides verifiable execution paths, enforces logical decomposition, and enables runtime validation. We also explore how improvements in reasoning have transformed code intelligence from basic completion to advanced capabilities, enabling models to address complex software engineering tasks through planning and debugging. Finally, we identify key challenges and propose future research directions to strengthen this synergy, ultimately improving LLM's performance in both areas.

Extensive studies have been devoted to privatizing general-domain Large Language Models (LLMs) as Domain-Specific LLMs via feeding specific-domain data. However, these privatization efforts often ignored a critical aspect: Dual Logic Ability, which is a core reasoning ability for LLMs. The dual logic ability of LLMs ensures that they can maintain a consistent stance when confronted with both positive and negative statements about the same fact. Our study focuses on how the dual logic ability of LLMs is affected during the privatization process in the medical domain. We conduct several experiments to analyze the dual logic ability of LLMs by examining the consistency of the stance in responses to paired questions about the same fact. In our experiments, interestingly, we observed a significant decrease in the dual logic ability of existing LLMs after privatization. Besides, our results indicate that incorporating general domain dual logic data into LLMs not only enhances LLMs' dual logic ability but also further improves their accuracy. These findings underscore the importance of prioritizing LLMs' dual logic ability during the privatization process. Our study establishes a benchmark for future research aimed at exploring LLMs' dual logic ability during the privatization process and offers valuable guidance for privatization efforts in real-world applications.

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, their reasoning can be unsound, inconsistent, or rely on undesirable prior assumptions. To tackle these issues, we introduce a class of tools for language models called guides that use state and incremental constraints to guide generation. A guide can be invoked by the model to constrain its own generation to a set of valid statements given by the tool. In turn, the model's choices can change the guide's state. We show how a general system for logical reasoning can be used as a guide, which we call LogicGuide. Given a reasoning problem in natural language, a model can formalize its assumptions for LogicGuide and then guarantee that its reasoning steps are sound. In experiments with the PrOntoQA and ProofWriter reasoning datasets, LogicGuide significantly improves the performance of GPT-3, GPT-3.5 Turbo and LLaMA (accuracy gains up to 35%). LogicGuide also drastically reduces content effects: the interference of prior and current assumptions that both humans and language models have been shown to suffer from. Finally, we explore bootstrapping LLaMA 13B from its own reasoning and find that LogicGuide is critical: by training only on certified self-generated reasoning, LLaMA can self-improve, avoiding learning from its own hallucinations.

Abstract reasoning is a key ability for an intelligent system. Large language models achieve above-chance performance on abstract reasoning tasks, but exhibit many imperfections. However, human abstract reasoning is also imperfect, and depends on our knowledge and beliefs about the content of the reasoning problem. For example, humans reason much more reliably about logical rules that are grounded in everyday situations than arbitrary rules about abstract attributes. The training experiences of language models similarly endow them with prior expectations that reflect human knowledge and beliefs. We therefore hypothesized that language models would show human-like content effects on abstract reasoning problems. We explored this hypothesis across three logical reasoning tasks: natural language inference, judging the logical validity of syllogisms, and the Wason selection task (Wason, 1968). We find that state of the art large language models (with 7 or 70 billion parameters; Hoffman et al., 2022) reflect many of the same patterns observed in humans across these tasks -- like humans, models reason more effectively about believable situations than unrealistic or abstract ones. Our findings have implications for understanding both these cognitive effects, and the factors that contribute to language model performance.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

We present FOLIO, a human-annotated, open-domain, and logically complex and diverse dataset for reasoning in natural language (NL), equipped with first order logic (FOL) annotations. FOLIO consists of 1,435 examples (unique conclusions), each paired with one of 487 sets of premises which serve as rules to be used to deductively reason for the validity of each conclusion. The logical correctness of premises and conclusions is ensured by their parallel FOL annotations, which are automatically verified by our FOL inference engine. In addition to the main NL reasoning task, NL-FOL pairs in FOLIO automatically constitute a new NL-FOL translation dataset using FOL as the logical form. Our experiments on FOLIO systematically evaluate the FOL reasoning ability of supervised fine-tuning on medium-sized language models (BERT, RoBERTa) and few-shot prompting on large language models (GPT-NeoX, OPT, GPT-3, Codex). For NL-FOL translation, we experiment with GPT-3 and Codex. Our results show that one of the most capable Large Language Model (LLM) publicly available, GPT-3 davinci, achieves only slightly better than random results with few-shot prompting on a subset of FOLIO, and the model is especially bad at predicting the correct truth values for False and Unknown conclusions. Our dataset and code are available at https://github.com/Yale-LILY/FOLIO.

Scientific documents record research findings and valuable human knowledge, comprising a vast corpus of high-quality data. Leveraging multi-modality data extracted from these documents and assessing large models' abilities to handle scientific document-oriented tasks is therefore meaningful. Despite promising advancements, large models still perform poorly on multi-page scientific document extraction and understanding tasks, and their capacity to process within-document data formats such as charts and equations remains under-explored. To address these issues, we present DocGenome, a structured document benchmark constructed by annotating 500K scientific documents from 153 disciplines in the arXiv open-access community, using our custom auto-labeling pipeline. DocGenome features four key characteristics: 1) Completeness: It is the first dataset to structure data from all modalities including 13 layout attributes along with their LaTeX source codes. 2) Logicality: It provides 6 logical relationships between different entities within each scientific document. 3) Diversity: It covers various document-oriented tasks, including document classification, visual grounding, document layout detection, document transformation, open-ended single-page QA and multi-page QA. 4) Correctness: It undergoes rigorous quality control checks conducted by a specialized team. We conduct extensive experiments to demonstrate the advantages of DocGenome and objectively evaluate the performance of large models on our benchmark.

Reasoning is central to human intelligence. However, fallacious arguments are common, and some exacerbate problems such as spreading misinformation about climate change. In this paper, we propose the task of logical fallacy detection, and provide a new dataset (Logic) of logical fallacies generally found in text, together with an additional challenge set for detecting logical fallacies in climate change claims (LogicClimate). Detecting logical fallacies is a hard problem as the model must understand the underlying logical structure of the argument. We find that existing pretrained large language models perform poorly on this task. In contrast, we show that a simple structure-aware classifier outperforms the best language model by 5.46% on Logic and 4.51% on LogicClimate. We encourage future work to explore this task as (a) it can serve as a new reasoning challenge for language models, and (b) it can have potential applications in tackling the spread of misinformation. Our dataset and code are available at https://github.com/causalNLP/logical-fallacy

This article reports the results of a study examining the ability of legal and non-legal Large Language Models to perform legal analysis using the Issue-Rule-Application-Conclusion framework. LLMs were tested on legal reasoning tasks involving rule analysis and analogical reasoning. The results show that LLMs can conduct basic IRAC analysis, but are limited by brief responses lacking detail, an inability to commit to answers, false confidence, and hallucinations. The study compares legal and nonlegal LLMs, identifies shortcomings, and explores traits that may hinder their ability to think like a lawyer. It also discusses the implications for legal education and practice, highlighting the need for critical thinking skills in future lawyers and the potential pitfalls of overreliance on artificial intelligence AI resulting in a loss of logic, reasoning, and critical thinking skills.

We examine how well the state-of-the-art (SOTA) models used in legal reasoning support abductive reasoning tasks. Abductive reasoning is a form of logical inference in which a hypothesis is formulated from a set of observations, and that hypothesis is used to explain the observations. The ability to formulate such hypotheses is important for lawyers and legal scholars as it helps them articulate logical arguments, interpret laws, and develop legal theories. Our motivation is to consider the belief that deep learning models, especially large language models (LLMs), will soon replace lawyers because they perform well on tasks related to legal text processing. But to do so, we believe, requires some form of abductive hypothesis formation. In other words, while LLMs become more popular and powerful, we want to investigate their capacity for abductive reasoning. To pursue this goal, we start by building a logic-augmented dataset for abductive reasoning with 498,697 samples and then use it to evaluate the performance of a SOTA model in the legal field. Our experimental results show that although these models can perform well on tasks related to some aspects of legal text processing, they still fall short in supporting abductive reasoning tasks.

Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being learned in these studies and introduce a simple domain specific language and a systematic translation from this language to first-order logic. By recasting the target representations in terms of classical logic, we aim to broaden the applicability of existing code datasets for investigating more complex natural language understanding and reasoning problems in the software domain.

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

Machine reading is a fundamental task for testing the capability of natural language understanding, which is closely related to human cognition in many aspects. With the rising of deep learning techniques, algorithmic models rival human performances on simple QA, and thus increasingly challenging machine reading datasets have been proposed. Though various challenges such as evidence integration and commonsense knowledge have been integrated, one of the fundamental capabilities in human reading, namely logical reasoning, is not fully investigated. We build a comprehensive dataset, named LogiQA, which is sourced from expert-written questions for testing human Logical reasoning. It consists of 8,678 QA instances, covering multiple types of deductive reasoning. Results show that state-of-the-art neural models perform by far worse than human ceiling. Our dataset can also serve as a benchmark for reinvestigating logical AI under the deep learning NLP setting. The dataset is freely available at https://github.com/lgw863/LogiQA-dataset

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between inductive and deductive reasoning, leading to a blending of the two. This raises an essential question: In LLM reasoning, which poses a greater challenge - deductive or inductive reasoning? While the deductive reasoning capabilities of LLMs, (i.e. their capacity to follow instructions in reasoning tasks), have received considerable attention, their abilities in true inductive reasoning remain largely unexplored. To investigate into the true inductive reasoning capabilities of LLMs, we propose a novel framework, SolverLearner. This framework enables LLMs to learn the underlying function (i.e., y = f_w(x)), that maps input data points (x) to their corresponding output values (y), using only in-context examples. By focusing on inductive reasoning and separating it from LLM-based deductive reasoning, we can isolate and investigate inductive reasoning of LLMs in its pure form via SolverLearner. Our observations reveal that LLMs demonstrate remarkable inductive reasoning capabilities through SolverLearner, achieving near-perfect performance with ACC of 1 in most cases. Surprisingly, despite their strong inductive reasoning abilities, LLMs tend to relatively lack deductive reasoning capabilities, particularly in tasks involving ``counterfactual'' reasoning.

Many believe that Large Language Models (LLMs) open the era of Artificial Intelligence (AI). Some see opportunities while others see dangers. Yet both proponents and opponents grasp AI through the imagery popularised by science fiction. Will the machine become sentient and rebel against its creators? Will we experience a paperclip apocalypse? Before answering such questions, we should first ask whether this mental imagery provides a good description of the phenomenon at hand. Understanding weather patterns through the moods of the gods only goes so far. The present paper instead advocates understanding LLMs and their connection to AI through the imagery of Jorge Luis Borges, a master of 20th century literature, forerunner of magical realism, and precursor to postmodern literature. This exercise leads to a new perspective that illuminates the relation between language modelling and artificial intelligence.

Assurance cases can be used to argue for the safety of products in safety engineering. In safety-critical areas, the construction of assurance cases is indispensable. Trustworthiness Derivation Trees (TDTs) enhance assurance cases by incorporating formal methods, rendering it possible for automatic reasoning about assurance cases. We present Trustworthiness Derivation Tree Analyzer (Trusta), a desktop application designed to automatically construct and verify TDTs. The tool has a built-in Prolog interpreter in its backend, and is supported by the constraint solvers Z3 and MONA. Therefore, it can solve constraints about logical formulas involving arithmetic, sets, Horn clauses etc. Trusta also utilizes large language models to make the creation and evaluation of assurance cases more convenient. It allows for interactive human examination and modification. We evaluated top language models like ChatGPT-3.5, ChatGPT-4, and PaLM 2 for generating assurance cases. Our tests showed a 50%-80% similarity between machine-generated and human-created cases. In addition, Trusta can extract formal constraints from text in natural languages, facilitating an easier interpretation and validation process. This extraction is subject to human review and correction, blending the best of automated efficiency with human insight. To our knowledge, this marks the first integration of large language models in automatic creating and reasoning about assurance cases, bringing a novel approach to a traditional challenge. Through several industrial case studies, Trusta has proven to quickly find some subtle issues that are typically missed in manual inspection, demonstrating its practical value in enhancing the assurance case development process.

Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously. The source code and dataset is available at https://github.com/yangzhch6/InterMWP.

We present a new logic-based inference engine for natural language inference (NLI) called MonaLog, which is based on natural logic and the monotonicity calculus. In contrast to existing logic-based approaches, our system is intentionally designed to be as lightweight as possible, and operates using a small set of well-known (surface-level) monotonicity facts about quantifiers, lexical items and tokenlevel polarity information. Despite its simplicity, we find our approach to be competitive with other logic-based NLI models on the SICK benchmark. We also use MonaLog in combination with the current state-of-the-art model BERT in a variety of settings, including for compositional data augmentation. We show that MonaLog is capable of generating large amounts of high-quality training data for BERT, improving its accuracy on SICK.

Logical reasoning is a critical component of Large Language Models (LLMs), and substantial research efforts in recent years have aimed to enhance their deductive reasoning capabilities. However, existing deductive reasoning benchmarks, which are crucial for evaluating and advancing LLMs, are inadequate due to their lack of task complexity, presence of prior knowledge as a confounder, and superficial error analysis. To address these deficiencies, we introduce JustLogic, a synthetically generated deductive reasoning benchmark designed for rigorous evaluation of LLMs. JustLogic is (i) highly complex, capable of generating a diverse range of linguistic patterns, vocabulary, and argument structures; (ii) prior knowledge independent, eliminating the advantage of models possessing prior knowledge and ensuring that only deductive reasoning is used to answer questions; and (iii) capable of in-depth error analysis on the heterogeneous effects of reasoning depth and argument form on model accuracy. Our experimental results on JustLogic reveal that most state-of-the-art (SOTA) LLMs perform significantly worse than the human average, demonstrating substantial room for model improvement. All code and data are available at https://github.com/michaelchen-lab/JustLogic

Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose Additional Logic Training (ALT), which aims to enhance LLMs' reasoning capabilities by program-generated logical reasoning samples. We first establish principles for designing high-quality samples by integrating symbolic logic theory and previous empirical insights. Then, based on these principles, we construct a synthetic corpus named Formal Logic Deduction Diverse (FLD^{times 2}), comprising numerous samples of multi-step deduction with unknown facts, diverse reasoning rules, diverse linguistic expressions, and challenging distractors. Finally, we empirically show that ALT on FLD^{times2} substantially enhances the reasoning capabilities of state-of-the-art LLMs, including LLaMA-3.1-70B. Improvements include gains of up to 30 points on logical reasoning benchmarks, up to 10 points on math and coding benchmarks, and 5 points on the benchmark suite BBH.

Large language models (LLMs) have shown remarkable performance in reasoning tasks but face limitations in mathematical and complex logical reasoning. Existing methods to improve LLMs' logical capabilities either involve traceable or verifiable logical sequences that generate more reliable responses by constructing logical structures yet increase computational costs, or introduces rigid logic template rules, reducing flexibility. In this paper, we propose Reversal of Thought (RoT), a novel framework aimed at enhancing the logical reasoning abilities of LLMs. RoT utilizes a Preference-Guided Reverse Reasoning warm-up strategy, which integrates logical symbols for pseudocode planning through meta-cognitive mechanisms and pairwise preference self-evaluation to generate task-specific prompts solely through demonstrations, aligning with LLMs' cognitive preferences shaped by Reinforcement Learning with Human Feedback (RLHF). Through reverse reasoning, we ultilize a Cognitive Preference Manager to assess knowledge boundaries and further expand LLMs' reasoning capabilities by aggregating solution logic for known tasks and stylistic templates for unknown tasks. Experiments across various tasks demonstrate that RoT surpasses existing baselines in both reasoning accuracy and efficiency.

Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However, formal language can cause systematic problems for inductive reasoning such as disability of handling raw input such as natural language, sensitiveness to mislabeled data, and incapacity to handle ambiguous input. To this end, we propose a new paradigm (task) for inductive reasoning, which is to induce natural language rules from natural language facts, and create a dataset termed DEER containing 1.2k rule-fact pairs for the task, where rules and facts are written in natural language. New automatic metrics are also proposed and analysed for the evaluation of this task. With DEER, we investigate a modern approach for inductive reasoning where we use natural language as representation for knowledge instead of formal language and use pretrained language models as ''reasoners''. Moreover, we provide the first and comprehensive analysis of how well pretrained language models can induce natural language rules from natural language facts. We also propose a new framework drawing insights from philosophy literature for this task, which we show in the experiment section that surpasses baselines in both automatic and human evaluations. We discuss about our future perspectives for inductive reasoning in Section 7. Dataset and code are available at https://github.com/ZonglinY/Inductive_Reasoning.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

Reasoning is an essential component of human intelligence as it plays a fundamental role in our ability to think critically, support responsible decisions, and solve challenging problems. Traditionally, AI has addressed reasoning in the context of logic-based representations of knowledge. However, the recent leap forward in natural language processing, with the emergence of language models based on transformers, is hinting at the possibility that these models exhibit reasoning abilities, particularly as they grow in size and are trained on more data. Despite ongoing discussions about what reasoning is in language models, it is still not easy to pin down to what extent these models are actually capable of reasoning. The goal of this workshop is to create a platform for researchers from different disciplines and/or AI perspectives, to explore approaches and techniques with the aim to reconcile reasoning between language models using transformers and using logic-based representations. The specific objectives include analyzing the reasoning abilities of language models measured alongside KR methods, injecting KR-style reasoning abilities into language models (including by neuro-symbolic means), and formalizing the kind of reasoning language models carry out. This exploration aims to uncover how language models can effectively integrate and leverage knowledge and reasoning with it, thus improving their application and utility in areas where precision and reliability are a key requirement.

Existing efforts to improve logical reasoning ability of language models have predominantly relied on supervised fine-tuning, hindering generalization to new domains and/or tasks. The development of Large Langauge Models (LLMs) has demonstrated the capacity of compressing abundant knowledge into a single proxy, enabling them to tackle multiple tasks effectively. Our preliminary experiments, nevertheless, show that LLMs do not show capability on logical reasoning. The performance of LLMs on logical reasoning benchmarks is far behind the existing state-of-the-art baselines. In this paper, we make the first attempt to investigate the feasibility of incorporating logical knowledge through self-supervised post-training, and activating it via in-context learning, which we termed as LogicLLM. Specifically, we devise an auto-regressive objective variant of MERIt and integrate it with two LLM series, i.e., FLAN-T5 and LLaMA, with parameter size ranging from 3 billion to 13 billion. The results on two challenging logical reasoning benchmarks demonstrate the effectiveness of LogicLLM. Besides, we conduct extensive ablation studies to analyze the key factors in designing logic-oriented proxy tasks.

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive reasoning over formal logical theories expressed in natural language. A shortcoming of these studies, however, is that they do not take into account that logical theories, when sampled uniformly at random, do not necessarily lead to hard instances. We propose a new methodology for creating challenging algorithmic reasoning datasets that focus on natural language satisfiability (NLSat) problems. The key idea is to draw insights from empirical sampling of hard propositional SAT problems and from complexity-theoretic studies of language. This methodology allows us to distinguish easy from hard instances, and to systematically increase the complexity of existing reasoning benchmarks such as RuleTaker. We find that current transformers, given sufficient training data, are surprisingly robust at solving the resulting NLSat problems of substantially increased difficulty. They also exhibit some degree of scale-invariance - the ability to generalize to problems of larger size and scope. Our results, however, reveal important limitations too: a careful sampling of training data is crucial for building models that generalize to larger problems, and transformer models' limited scale-invariance suggests they are far from learning robust deductive reasoning algorithms.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Background. Due to the widespread adoption of Artificial Intelligence (AI) and Machine Learning (ML) for building software applications, companies are struggling to recruit employees with a deep understanding of such technologies. In this scenario, AutoML is soaring as a promising solution to fill the AI/ML skills gap since it promises to automate the building of end-to-end AI/ML pipelines that would normally be engineered by specialized team members. Aims. Despite the growing interest and high expectations, there is a dearth of information about the extent to which AutoML is currently adopted by teams developing AI/ML-enabled systems and how it is perceived by practitioners and researchers. Method. To fill these gaps, in this paper, we present a mixed-method study comprising a benchmark of 12 end-to-end AutoML tools on two SE datasets and a user survey with follow-up interviews to further our understanding of AutoML adoption and perception. Results. We found that AutoML solutions can generate models that outperform those trained and optimized by researchers to perform classification tasks in the SE domain. Also, our findings show that the currently available AutoML solutions do not live up to their names as they do not equally support automation across the stages of the ML development workflow and for all the team members. Conclusions. We derive insights to inform the SE research community on how AutoML can facilitate their activities and tool builders on how to design the next generation of AutoML technologies.

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.

Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional (DisCoCat) model of meaning of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) combines aspected of both to provide a general framework in which meanings of words, obtained distributionally, are composed using methods from the logical setting to form sentence meaning. Concrete consequences of this general abstract setting and applications to empirical data are under active study (Grefenstette et al., arxiv:1101.0309; Grefenstette and Sadrzadeh, arXiv:1106.4058v1 [cs.CL]). . In this paper, we extend this study by examining transitive verbs, represented as matrices in a DisCoCat. We discuss three ways of constructing such matrices, and evaluate each method in a disambiguation task developed by Grefenstette and Sadrzadeh (arXiv:1106.4058v1 [cs.CL]).

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis, and artificial intelligence. While the long-term goal of autoformalization seemed elusive for a long time, we show large language models provide new prospects towards this goal. We make the surprising observation that LLMs can correctly translate a significant portion (25.3%) of mathematical competition problems perfectly to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover via training on these autoformalized theorems. Our methodology results in a new state-of-the-art result on the MiniF2F theorem proving benchmark, improving the proof rate from 29.6% to 35.2%.

Thanks to rapid progress in artificial intelligence, we have entered an era when technology and philosophy intersect in interesting ways. Sitting squarely at the centre of this intersection are large language models (LLMs). The more adept LLMs become at mimicking human language, the more vulnerable we become to anthropomorphism, to seeing the systems in which they are embedded as more human-like than they really are. This trend is amplified by the natural tendency to use philosophically loaded terms, such as "knows", "believes", and "thinks", when describing these systems. To mitigate this trend, this paper advocates the practice of repeatedly stepping back to remind ourselves of how LLMs, and the systems of which they form a part, actually work. The hope is that increased scientific precision will encourage more philosophical nuance in the discourse around artificial intelligence, both within the field and in the public sphere.

We investigate the mathematical capabilities of ChatGPT by testing it on publicly available datasets, as well as hand-crafted ones, and measuring its performance against other models trained on a mathematical corpus, such as Minerva. We also test whether ChatGPT can be a useful assistant to professional mathematicians by emulating various use cases that come up in the daily professional activities of mathematicians (question answering, theorem searching). In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, only cover elementary mathematics. We address this issue by introducing a new dataset: GHOSTS. It is the first natural-language dataset made and curated by working researchers in mathematics that (1) aims to cover graduate-level mathematics and (2) provides a holistic overview of the mathematical capabilities of language models. We benchmark ChatGPT on GHOSTS and evaluate performance against fine-grained criteria. We make this new dataset publicly available to assist a community-driven comparison of ChatGPT with (future) large language models in terms of advanced mathematical comprehension. We conclude that contrary to many positive reports in the media (a potential case of selection bias), ChatGPT's mathematical abilities are significantly below those of an average mathematics graduate student. Our results show that ChatGPT often understands the question but fails to provide correct solutions. Hence, if your goal is to use it to pass a university exam, you would be better off copying from your average peer!

We introduce Goedel-Prover, an open-source large language model (LLM) that achieves the state-of-the-art (SOTA) performance in automated formal proof generation for mathematical problems. The key challenge in this field is the scarcity of formalized math statements and proofs, which we tackle in the following ways. We train statement formalizers to translate the natural language math problems from Numina into formal language (Lean 4), creating a dataset of 1.64 million formal statements. LLMs are used to check that the formal statements accurately preserve the content of the original natural language problems. We then iteratively build a large dataset of formal proofs by training a series of provers. Each prover succeeds in proving many statements that the previous ones could not, and these new proofs are added to the training set for the next prover. The final prover outperforms all existing open-source models in whole-proof generation. On the miniF2F benchmark, it achieves a 57.6% success rate (Pass@32), exceeding the previous best open-source model by 7.6%. On PutnamBench, Goedel-Prover successfully solves 7 problems (Pass@512), ranking first on the leaderboard. Furthermore, it generates 29.7K formal proofs for Lean Workbook problems, nearly doubling the 15.7K produced by earlier works.

Language models can store vast amounts of factual knowledge, but their ability to use this knowledge for logical reasoning remains questionable. This paper explores a language model's ability to manipulate its stored knowledge during inference. We focus on four manipulation types: retrieval (e.g., "What is person A's attribute X"), classification (e.g., "Is A's attribute X even or odd?"), comparison (e.g., "Is A greater than B in attribute X?") and inverse search (e.g., "Which person's attribute X equals T?") We observe that pre-trained language models like GPT2/3/4 excel in knowledge retrieval but struggle with simple classification or comparison tasks unless Chain of Thoughts (CoTs) are employed during both training and inference. They also perform poorly in inverse knowledge search, irrespective of the prompts. Our primary contribution is a synthetic dataset for a controlled experiment that confirms these inherent weaknesses: a language model cannot efficiently manipulate knowledge from pre-training data, even when such knowledge is perfectly stored and fully extractable in the models, and despite adequate instruct fine-tuning.

Deductive coding is a widely used qualitative research method for determining the prevalence of themes across documents. While useful, deductive coding is often burdensome and time consuming since it requires researchers to read, interpret, and reliably categorize a large body of unstructured text documents. Large language models (LLMs), like ChatGPT, are a class of quickly evolving AI tools that can perform a range of natural language processing and reasoning tasks. In this study, we explore the use of LLMs to reduce the time it takes for deductive coding while retaining the flexibility of a traditional content analysis. We outline the proposed approach, called LLM-assisted content analysis (LACA), along with an in-depth case study using GPT-3.5 for LACA on a publicly available deductive coding data set. Additionally, we conduct an empirical benchmark using LACA on 4 publicly available data sets to assess the broader question of how well GPT-3.5 performs across a range of deductive coding tasks. Overall, we find that GPT-3.5 can often perform deductive coding at levels of agreement comparable to human coders. Additionally, we demonstrate that LACA can help refine prompts for deductive coding, identify codes for which an LLM is randomly guessing, and help assess when to use LLMs vs. human coders for deductive coding. We conclude with several implications for future practice of deductive coding and related research methods.

In the last decade, several organizations have produced documents intended to standardize, in the normative sense, and promote guidance to our recent and rapid AI development. However, the full spectrum of ideas presented in these documents has not yet been analyzed, except for a few meta-analyses and critical reviews of the field. In this work, we seek to expand on the work done by past researchers and create a tool for better data visualization of the contents and nature of these documents, to understand whether there is consensus or similarity between the principles espoused by various institutions, which may inspire debates on future regulations. We also provide some preliminary thoughts and questions that could guide the continuity of the research through a critical analysis of the results acquired by our methodology into a sample size of 200 documents.

While pre-trained language models (PLMs) are the go-to solution to tackle many natural language processing problems, they are still very limited in their ability to capture and to use common-sense knowledge. In fact, even if information is available in the form of approximate (soft) logical rules, it is not clear how to transfer it to a PLM in order to improve its performance for deductive reasoning tasks. Here, we aim to bridge this gap by teaching PLMs how to reason with soft Horn rules. We introduce a classification task where, given facts and soft rules, the PLM should return a prediction with a probability for a given hypothesis. We release the first dataset for this task, and we propose a revised loss function that enables the PLM to learn how to predict precise probabilities for the task. Our evaluation results show that the resulting fine-tuned models achieve very high performance, even on logical rules that were unseen at training. Moreover, we demonstrate that logical notions expressed by the rules are transferred to the fine-tuned model, yielding state-of-the-art results on external datasets.

Neural natural language generation (NLG) models have recently shown remarkable progress in fluency and coherence. However, existing studies on neural NLG are primarily focused on surface-level realizations with limited emphasis on logical inference, an important aspect of human thinking and language. In this paper, we suggest a new NLG task where a model is tasked with generating natural language statements that can be logically entailed by the facts in an open-domain semi-structured table. To facilitate the study of the proposed logical NLG problem, we use the existing TabFact dataset chen2019tabfact featured with a wide range of logical/symbolic inferences as our testbed, and propose new automatic metrics to evaluate the fidelity of generation models w.r.t.\ logical inference. The new task poses challenges to the existing monotonic generation frameworks due to the mismatch between sequence order and logical order. In our experiments, we comprehensively survey different generation architectures (LSTM, Transformer, Pre-Trained LM) trained with different algorithms (RL, Adversarial Training, Coarse-to-Fine) on the dataset and made following observations: 1) Pre-Trained LM can significantly boost both the fluency and logical fidelity metrics, 2) RL and Adversarial Training are trading fluency for fidelity, 3) Coarse-to-Fine generation can help partially alleviate the fidelity issue while maintaining high language fluency. The code and data are available at https://github.com/wenhuchen/LogicNLG.

Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging, as these scenarios are often expressed in natural language. To address this, we introduce a framework for the autoformalization of game-theoretic scenarios, which translates natural language descriptions into formal logic representations suitable for formal solvers. Our approach utilizes one-shot prompting and a solver that provides feedback on syntactic correctness to allow LLMs to refine the code. We evaluate the framework using GPT-4o and a dataset of natural language problem descriptions, achieving 98% syntactic correctness and 88% semantic correctness. These results show the potential of LLMs to bridge the gap between real-life strategic interactions and formal reasoning.

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

We introduce the AutoGRAMS framework for programming multi-step interactions with language models. AutoGRAMS represents AI agents as a graph, where each node can execute either a language modeling instruction or traditional code. Likewise, transitions in the graph can be governed by either language modeling decisions or traditional branch logic. AutoGRAMS supports using variables as memory and allows nodes to call other AutoGRAMS graphs as functions. We show how AutoGRAMS can be used to design highly sophisticated agents, including self-referential agents that can modify their own graph. AutoGRAMS's graph-centric approach aids interpretability, controllability, and safety during the design, development, and deployment of AI agents. We provide our framework as open source at https://github.com/autograms/autograms .

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Enabling Large Language Models (LLMs) to handle a wider range of complex tasks (e.g., coding, math) has drawn great attention from many researchers. As LLMs continue to evolve, merely increasing the number of model parameters yields diminishing performance improvements and heavy computational costs. Recently, OpenAI's o1 model has shown that inference strategies (i.e., Test-time Compute methods) can also significantly enhance the reasoning capabilities of LLMs. However, the mechanisms behind these methods are still unexplored. In our work, to investigate the reasoning patterns of o1, we compare o1 with existing Test-time Compute methods (BoN, Step-wise BoN, Agent Workflow, and Self-Refine) by using OpenAI's GPT-4o as a backbone on general reasoning benchmarks in three domains (i.e., math, coding, commonsense reasoning). Specifically, first, our experiments show that the o1 model has achieved the best performance on most datasets. Second, as for the methods of searching diverse responses (e.g., BoN), we find the reward models' capability and the search space both limit the upper boundary of these methods. Third, as for the methods that break the problem into many sub-problems, the Agent Workflow has achieved better performance than Step-wise BoN due to the domain-specific system prompt for planning better reasoning processes. Fourth, it is worth mentioning that we have summarized six reasoning patterns of o1, and provided a detailed analysis on several reasoning benchmarks.

Causal reasoning, the ability to identify cause-and-effect relationship, is crucial in human thinking. Although large language models (LLMs) succeed in many NLP tasks, it is still challenging for them to conduct complex causal reasoning like abductive reasoning and counterfactual reasoning. Given the fact that programming code may express causal relations more often and explicitly with conditional statements like ``if``, we want to explore whether Code-LLMs acquire better causal reasoning abilities. Our experiments show that compared to text-only LLMs, Code-LLMs with code prompts are significantly better in causal reasoning. We further intervene on the prompts from different aspects, and discover that the programming structure is crucial in code prompt design, while Code-LLMs are robust towards format perturbations.

Human intelligence, the most evident and accessible form of source of reasoning, hosted by biological hardware, has evolved and been refined over thousands of years, positioning itself today to create new artificial forms and preparing to self--design their evolutionary path forward. Beginning with the advent of foundation models, the rate at which human and artificial intelligence interact with each other has surpassed any anticipated quantitative figures. The close engagement led to both bits of intelligence to be impacted in various ways, which naturally resulted in complex confluences that warrant close scrutiny. In the sequel, we shall explore the interplay between human and machine intelligence, focusing on the crucial role humans play in developing ethical, responsible, and robust intelligent systems. We slightly delve into interesting aspects of implementation inspired by the mechanisms underlying neuroscience and human cognition. Additionally, we propose future perspectives, capitalizing on the advantages of symbiotic designs to suggest a human-centered direction for next-generation AI development. We finalize this evolving document with a few thoughts and open questions yet to be addressed by the broader community.

Large Language Models (LLMs) have demonstrated notable capabilities across various tasks, showcasing complex problem-solving abilities. Understanding and executing complex rules, along with multi-step planning, are fundamental to logical reasoning and critical for practical LLM agents and decision-making systems. However, evaluating LLMs as effective rule-based executors and planners remains underexplored. In this paper, we introduce LogicGame, a novel benchmark designed to evaluate the comprehensive rule understanding, execution, and planning capabilities of LLMs. Unlike traditional benchmarks, LogicGame provides diverse games that contain a series of rules with an initial state, requiring models to comprehend and apply predefined regulations to solve problems. We create simulated scenarios in which models execute or plan operations to achieve specific outcomes. These game scenarios are specifically designed to distinguish logical reasoning from mere knowledge by relying exclusively on predefined rules. This separation allows for a pure assessment of rule-based reasoning capabilities. The evaluation considers not only final outcomes but also intermediate steps, providing a comprehensive assessment of model performance. Moreover, these intermediate steps are deterministic and can be automatically verified. LogicGame defines game scenarios with varying difficulty levels, from simple rule applications to complex reasoning chains, in order to offer a precise evaluation of model performance on rule understanding and multi-step execution. Utilizing LogicGame, we test various LLMs and identify notable shortcomings in their rule-based logical reasoning abilities.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate implications of a theory has not yet been demonstrated, and methods for reconstructing proofs of answers are imperfect. In this work we show that a generative model, called ProofWriter, can reliably generate both implications of a theory and the natural language proof(s) that support them. In particular, iterating a 1-step implication generator results in proofs that are highly reliable, and represent actual model decisions (rather than post-hoc rationalizations). On the RuleTaker dataset, the accuracy of ProofWriter's proofs exceed previous methods by +9% absolute, and in a way that generalizes to proof depths unseen in training and on out-of-domain problems. We also show that generative techniques can perform a type of abduction with high precision: Given a theory and an unprovable conclusion, identify a missing fact that allows the conclusion to be proved, along with a proof. These results significantly improve the viability of neural methods for systematically reasoning over natural language.

Compositional AI systems, which combine multiple artificial intelligence components together with other application components to solve a larger problem, have no known pattern of development and are often approached in a bespoke and ad hoc style. This makes development slower and harder to reuse for future applications. To support the full rapid development cycle of compositional AI applications, we have developed a novel framework called (Bee)* (written as a regular expression and pronounced as "beestar"). We illustrate how (Bee)* supports building integrated, scalable, and interactive compositional AI applications with a simplified developer experience.

Legislation can be viewed as a body of prescriptive rules expressed in natural language. The application of legislation to facts of a case we refer to as statutory reasoning, where those facts are also expressed in natural language. Computational statutory reasoning is distinct from most existing work in machine reading, in that much of the information needed for deciding a case is declared exactly once (a law), while the information needed in much of machine reading tends to be learned through distributional language statistics. To investigate the performance of natural language understanding approaches on statutory reasoning, we introduce a dataset, together with a legal-domain text corpus. Straightforward application of machine reading models exhibits low out-of-the-box performance on our questions, whether or not they have been fine-tuned to the legal domain. We contrast this with a hand-constructed Prolog-based system, designed to fully solve the task. These experiments support a discussion of the challenges facing statutory reasoning moving forward, which we argue is an interesting real-world task that can motivate the development of models able to utilize prescriptive rules specified in natural language.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Large language models (LLMs) are becoming increasingly important for machine learning applications. However, it can be challenging to align LLMs with our intent, particularly when we want to generate content that is preferable over others or when we want the LLM to respond in a certain style or tone that is hard to describe. To address this challenge, we propose an approach that uses contrastive examples to better describe our intent. This involves providing positive examples that illustrate the true intent, along with negative examples that show what characteristics we want LLMs to avoid. The negative examples can be retrieved from labeled data, written by a human, or generated by the LLM itself. Before generating an answer, we ask the model to analyze the examples to teach itself what to avoid. This reasoning step provides the model with the appropriate articulation of the user's need and guides it towards generting a better answer. We tested our approach on both synthesized and real-world datasets, including StackExchange and Reddit, and found that it significantly improves performance compared to standard few-shot prompting

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Of primary importance in formulating a response to the increasing prevalence and power of artificial intelligence (AI) applications in society are questions of ontology. Questions such as: What "are" these systems? How are they to be regarded? How does an algorithm come to be regarded as an agent? We discuss three factors which hinder discussion and obscure attempts to form a clear ontology of AI: (1) the various and evolving definitions of AI, (2) the tendency for pre-existing technologies to be assimilated and regarded as "normal," and (3) the tendency of human beings to anthropomorphize. This list is not intended as exhaustive, nor is it seen to preclude entirely a clear ontology, however, these challenges are a necessary set of topics for consideration. Each of these factors is seen to present a 'moving target' for discussion, which poses a challenge for both technical specialists and non-practitioners of AI systems development (e.g., philosophers and theologians) to speak meaningfully given that the corpus of AI structures and capabilities evolves at a rapid pace. Finally, we present avenues for moving forward, including opportunities for collaborative synthesis for scholars in philosophy and science.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

The recent development on large language models makes automatically constructing small programs possible. It thus has the potential to free software engineers from low-level coding and allow us to focus on the perhaps more interesting parts of software development, such as requirement engineering and system testing. In this project, we develop a prototype named AISD (AI-aided Software Development), which is capable of taking high-level (potentially vague) user requirements as inputs, generates detailed use cases, prototype system designs, and subsequently system implementation. Different from existing attempts, AISD is designed to keep the user in the loop, i.e., by repeatedly taking user feedback on use cases, high-level system designs, and prototype implementations through system testing. AISD has been evaluated with a novel benchmark of non-trivial software projects. The experimental results suggest that it might be possible to imagine a future where software engineering is reduced to requirement engineering and system testing only.

In this paper, we explore a new way for user targeting, where non-expert marketers could select their target users solely given demands in natural language form. The key to this issue is how to transform natural languages into practical structured logical languages, i.e., the structured understanding of marketer demands. Considering the impressive natural language processing ability of large language models (LLMs), we try to leverage LLMs to solve this issue. Past research indicates that the reasoning ability of LLMs can be effectively enhanced through chain-of-thought (CoT) prompting. But existing methods still have some limitations: (1) Previous methods either use simple "Let's think step by step" spells or provide fixed examples in demonstrations without considering compatibility between prompts and questions, making LLMs ineffective in some complex reasoning tasks such as structured language transformation. (2) Previous methods are often implemented in closed-source models or excessively large models, which is not suitable in industrial practical scenarios. Based on these, we propose ARALLM (i.e., Analogical Reasoning Augmented Large Language Models) consisting of two modules: Analogical Reasoning based Prompting and Reasoning-Augmented Multi-Task Model Distillation.

Are LLMs cultural technologies like photocopiers or printing presses, which transmit information but cannot create new content? A challenge for this idea, which we call bibliotechnism, is that LLMs often do generate entirely novel text. We begin by defending bibliotechnism against this challenge, showing how novel text may be meaningful only in a derivative sense, so that the content of this generated text depends in an important sense on the content of original human text. We go on to present a different, novel challenge for bibliotechnism, stemming from examples in which LLMs generate "novel reference", using novel names to refer to novel entities. Such examples could be smoothly explained if LLMs were not cultural technologies but possessed a limited form of agency (beliefs, desires, and intentions). According to interpretationism in the philosophy of mind, a system has beliefs, desires and intentions if and only if its behavior is well-explained by the hypothesis that it has such states. In line with this view, we argue that cases of novel reference provide evidence that LLMs do in fact have beliefs, desires, and intentions, and thus have a limited form of agency.

We introduce the concept and a default implementation of Guided Reasoning. A multi-agent system is a Guided Reasoning system iff one agent (the guide) primarily interacts with other agents in order to improve reasoning quality. We describe Logikon's default implementation of Guided Reasoning in non-technical terms. This is a living document we'll gradually enrich with more detailed information and examples. Code: https://github.com/logikon-ai/logikon

With the web getting bigger and assimilating knowledge about different concepts and domains, it is becoming very difficult for simple database driven applications to capture the data for a domain. Thus developers have come out with ontology based systems which can store large amount of information and can apply reasoning and produce timely information. Thus facilitating effective knowledge management. Though this approach has made our lives easier, but at the same time has given rise to another problem. Two different ontologies assimilating same knowledge tend to use different terms for the same concepts. This creates confusion among knowledge engineers and workers, as they do not know which is a better term then the other. Thus we need to merge ontologies working on same domain so that the engineers can develop a better application over it. This paper shows the development of one such matcher which merges the concepts available in two ontologies at two levels; 1) at string level and 2) at semantic level; thus producing better merged ontologies. We have used a graph matching technique which works at the core of the system. We have also evaluated the system and have tested its performance with its predecessor which works only on string matching. Thus current approach produces better results.

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation of LLMs on 50 tasks that probe different aspects of logical reasoning. We show that language models tend to perform fairly well at single step inference or entailment tasks, but struggle to chain together multiple reasoning steps to solve more complex problems. In light of this, we propose a Selection-Inference (SI) framework that exploits pre-trained LLMs as general processing modules, and alternates between selection and inference to generate a series of interpretable, casual reasoning steps leading to the final answer. We show that a 7B parameter LLM used within the SI framework in a 5-shot generalisation setting, with no fine-tuning, yields a performance improvement of over 100% compared to an equivalent vanilla baseline on a suite of 10 logical reasoning tasks. The same model in the same setting even outperforms a significantly larger 280B parameter baseline on the same suite of tasks. Moreover, answers produced by the SI framework are accompanied by a causal natural-language-based reasoning trace, which has important implications for the safety and trustworthiness of the system.

This technical report presents AutoGen, a new framework that enables development of LLM applications using multiple agents that can converse with each other to solve tasks. AutoGen agents are customizable, conversable, and seamlessly allow human participation. They can operate in various modes that employ combinations of LLMs, human inputs, and tools. AutoGen's design offers multiple advantages: a) it gracefully navigates the strong but imperfect generation and reasoning abilities of these LLMs; b) it leverages human understanding and intelligence, while providing valuable automation through conversations between agents; c) it simplifies and unifies the implementation of complex LLM workflows as automated agent chats. We provide many diverse examples of how developers can easily use AutoGen to effectively solve tasks or build applications, ranging from coding, mathematics, operations research, entertainment, online decision-making, question answering, etc.

Today's large language models (LLMs) routinely generate coherent, grammatical and seemingly meaningful paragraphs of text. This achievement has led to speculation that these networks are -- or will soon become -- "thinking machines", capable of performing tasks that require abstract knowledge and reasoning. Here, we review the capabilities of LLMs by considering their performance on two different aspects of language use: 'formal linguistic competence', which includes knowledge of rules and patterns of a given language, and 'functional linguistic competence', a host of cognitive abilities required for language understanding and use in the real world. Drawing on evidence from cognitive neuroscience, we show that formal competence in humans relies on specialized language processing mechanisms, whereas functional competence recruits multiple extralinguistic capacities that comprise human thought, such as formal reasoning, world knowledge, situation modeling, and social cognition. In line with this distinction, LLMs show impressive (although imperfect) performance on tasks requiring formal linguistic competence, but fail on many tests requiring functional competence. Based on this evidence, we argue that (1) contemporary LLMs should be taken seriously as models of formal linguistic skills; (2) models that master real-life language use would need to incorporate or develop not only a core language module, but also multiple non-language-specific cognitive capacities required for modeling thought. Overall, a distinction between formal and functional linguistic competence helps clarify the discourse surrounding LLMs' potential and provides a path toward building models that understand and use language in human-like ways.

Code provides a general syntactic structure to build complex programs and perform precise computations when paired with a code interpreter -- we hypothesize that language models (LMs) can leverage code-writing to improve Chain of Thought reasoning not only for logic and arithmetic tasks, but also for linguistic ones (and in particular, those that are a mix of both). For example, consider prompting an LM to write code that counts the number of times it detects sarcasm in an essay: the LM may struggle to write an implementation for "detect_sarcasm(string)" that can be executed by the interpreter (handling the edge cases would be insurmountable). However, LMs may still produce a valid solution if they are used not only to write the code, but also to selectively "emulate" the interpreter by generating the expected output of "detect_sarcasm(string)" and other lines of code (e.g., that the interpreter could not compile). In this work, we propose Chain of Code (CoT), a simple yet surprisingly effective extension that improves LM code-driven reasoning. The key idea is to encourage LMs to format linguistic sub-tasks in a program as flexible pseudocode that the compiler can explicitly catch undefined behaviors and hand off to simulate with an LM (as an "LMulator"). Experiments demonstrate that Chain of Code outperforms Chain of Thought and other baselines across a variety of benchmarks; on BIG-Bench Hard, Chain of Code achieves 84%, a gain of 12% over Chain of Thought. CoT scales well with large and small models alike, and broadens the scope of reasoning questions that LMs can correctly answer by "thinking in code". Project webpage: https://chain-of-code.github.io/.

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general artificial intelligence, there has been a surge of interest in investigating the reasoning ability of the LLMs. Whereas the textual and numerical reasoning benchmarks adopted by previous works are rather shallow and simple, it is hard to conclude that the LLMs possess strong reasoning ability by merely achieving positive results on these benchmarks. Recent efforts have demonstrated that the LLMs are poor at solving sequential decision-making problems that require common-sense planning by evaluating their performance on the reinforcement learning benchmarks. In this work, we conduct an in-depth assessment of several state-of-the-art LLMs' reasoning ability based on the inductive logic programming (ILP) benchmark, which is broadly recognized as a representative and challenging measurement for evaluating logic program induction/synthesis systems as it requires inducing strict cause-effect logic to achieve robust deduction on independent and identically distributed (IID) and out-of-distribution (OOD) test samples. Our evaluations illustrate that compared with the neural program induction systems which are much smaller in model size, the state-of-the-art LLMs are much poorer in terms of reasoning ability by achieving much lower performance and generalization using either natural language prompting or truth-value matrix prompting.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Logical rules are essential for uncovering the logical connections between relations, which could improve the reasoning performance and provide interpretable results on knowledge graphs (KGs). Although there have been many efforts to mine meaningful logical rules over KGs, existing methods suffer from the computationally intensive searches over the rule space and a lack of scalability for large-scale KGs. Besides, they often ignore the semantics of relations which is crucial for uncovering logical connections. Recently, large language models (LLMs) have shown impressive performance in the field of natural language processing and various applications, owing to their emergent ability and generalizability. In this paper, we propose a novel framework, ChatRule, unleashing the power of large language models for mining logical rules over knowledge graphs. Specifically, the framework is initiated with an LLM-based rule generator, leveraging both the semantic and structural information of KGs to prompt LLMs to generate logical rules. To refine the generated rules, a rule ranking module estimates the rule quality by incorporating facts from existing KGs. Last, a rule validator harnesses the reasoning ability of LLMs to validate the logical correctness of ranked rules through chain-of-thought reasoning. ChatRule is evaluated on four large-scale KGs, w.r.t. different rule quality metrics and downstream tasks, showing the effectiveness and scalability of our method.

Throughout the course of my Ph.D., I have been designing the user experience (UX) of various machine learning (ML) systems. In this workshop, I share two projects as case studies in which people engage with ML in much more complicated and nuanced ways than the technical HCML work might assume. The first case study describes how cardiology teams in three hospitals used a clinical decision-support system that helps them decide whether and when to implant an artificial heart to a heart failure patient. I demonstrate that physicians cannot draw on their decision-making experience by seeing only patient data on paper. They are also confused by some fundamental premises upon which ML operates. For example, physicians asked: Are ML predictions made based on clinicians' best efforts? Is it ethical to make decisions based on previous patients' collective outcomes? In the second case study, my collaborators and I designed an intelligent text editor, with the goal of improving authors' writing experience with NLP (Natural Language Processing) technologies. We prototyped a number of generative functionalities where the system provides phrase-or-sentence-level writing suggestions upon user request. When writing with the prototype, however, authors shared that they need to "see where the sentence is going two paragraphs later" in order to decide whether the suggestion aligns with their writing; Some even considered adopting machine suggestions as plagiarism, therefore "is simply wrong". By sharing these unexpected and intriguing responses from these real-world ML users, I hope to start a discussion about such previously-unknown complexities and nuances of -- as the workshop proposal states -- "putting ML at the service of people in a way that is accessible, useful, and trustworthy to all".

Language Models (LMs) have shown impressive performance in various natural language tasks. However, when it comes to natural language reasoning, LMs still face challenges such as hallucination, generating incorrect intermediate reasoning steps, and making mathematical errors. Recent research has focused on enhancing LMs through self-improvement using feedback. Nevertheless, existing approaches relying on a single generic feedback source fail to address the diverse error types found in LM-generated reasoning chains. In this work, we propose Multi-Aspect Feedback, an iterative refinement framework that integrates multiple feedback modules, including frozen LMs and external tools, each focusing on a specific error category. Our experimental results demonstrate the efficacy of our approach to addressing several errors in the LM-generated reasoning chain and thus improving the overall performance of an LM in several reasoning tasks. We see a relative improvement of up to 20% in Mathematical Reasoning and up to 18% in Logical Entailment.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

The ISO 26262 standard from 2016 represents the state of the art for a safety-guided development of safety-critical electric/electronic vehicle systems. These vehicle systems include advanced driver assistance systems and vehicle guidance systems. The development process proposed in the ISO 26262 standard is based upon multiple V-models, and defines activities and work products for each process step. In many of these process steps, scenario based approaches can be applied to achieve the defined work products for the development of automated driving functions. To accomplish the work products of different process steps, scenarios have to focus on various aspects like a human understandable notation or a description via time-space variables. This leads to contradictory requirements regarding the level of detail and way of notation for the representation of scenarios. In this paper, the authors present requirements for the representation of scenarios in different process steps defined by the ISO 26262 standard, propose a consistent terminology based on prior publications for the identified levels of abstraction, and demonstrate how scenarios can be systematically evolved along the phases of the development process outlined in the ISO 26262 standard.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the truth-telling or lying behavior, which influences the logical implications of each statement. Solving these puzzles requires not only direct deductions from individual statements, but the ability to assess the truthfulness of statements by reasoning through various hypothetical scenarios. As such, knights and knaves puzzles serve as compelling examples of suppositional reasoning. In this paper, we introduce TruthQuest, a benchmark for suppositional reasoning based on the principles of knights and knaves puzzles. Our benchmark presents problems of varying complexity, considering both the number of characters and the types of logical statements involved. Evaluations on TruthQuest show that large language models like Llama 3 and Mixtral-8x7B exhibit significant difficulties solving these tasks. A detailed error analysis of the models' output reveals that lower-performing models exhibit a diverse range of reasoning errors, frequently failing to grasp the concept of truth and lies. In comparison, more proficient models primarily struggle with accurately inferring the logical implications of potentially false statements.

This article presents the Cogni-CISMeF project, which aims at improving medical information search in the CISMeF system (Catalog and Index of French-language health resources) by including a conversational agent to interact with the user in natural language. To study the cognitive processes involved during the information search, a bottom-up methodology was adopted. Experimentation has been set up to obtain human dialogs between a user (playing the role of patient) dealing with medical information search and a CISMeF expert refining the request. The analysis of these dialogs underlined the use of discursive evidence: vocabulary, reformulation, implicit or explicit expression of user intentions, conversational sequences, etc. A model of artificial agent is proposed. It leads the user in its information search by proposing to him examples, assistance and choices. This model was implemented and integrated in the CISMeF system. ---- Cet article d\'ecrit le projet Cogni-CISMeF qui propose un module de dialogue Homme-Machine \`a int\'egrer dans le syst\`eme d'indexation de connaissances m\'edicales CISMeF (Catalogue et Index des Sites M\'edicaux Francophones). Nous avons adopt\'e une d\'emarche de mod\'elisation cognitive en proc\'edant \`a un recueil de corpus de dialogues entre un utilisateur (jouant le r\^ole d'un patient) d\'esirant une information m\'edicale et un expert CISMeF af inant cette demande pour construire la requ\^ete. Nous avons analys\'e la structure des dialogues ainsi obtenus et avons \'etudi\'e un certain nombre d'indices discursifs : vocabulaire employ\'e, marques de reformulation, commentaires m\'eta et \'epilinguistiques, expression implicite ou explicite des intentions de l'utilisateur, encha\^inement conversationnel, etc. De cette analyse, nous avons construit un mod\`ele d'agent artificiel dot\'e de capacit\'es cognitives capables d'aider l'utilisateur dans sa t\^ache de recherche d'information. Ce mod\`ele a \'et\'e impl\'ement\'e et int\'egr\'e dans le syst\`eme CISMeF.

We argue that enabling human-AI dialogue, purposed to support joint reasoning (i.e., 'inquiry'), is important for ensuring that AI decision making is aligned with human values and preferences. In particular, we point to logic-based models of argumentation and dialogue, and suggest that the traditional focus on persuasion dialogues be replaced by a focus on inquiry dialogues, and the distinct challenges that joint inquiry raises. Given recent dramatic advances in the performance of large language models (LLMs), and the anticipated increase in their use for decision making, we provide a roadmap for research into inquiry dialogues for supporting joint human-LLM reasoning tasks that are ethically salient, and that thereby require that decisions are value aligned.

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that often demands high-level abstract reasoning about program properties, which is challenging for verification tools. We propose a general methodology to combine the power of LLMs and automated reasoners for automated program verification. We formally describe this methodology as a set of derivation rules and prove its soundness. We instantiate the calculus as a sound automated verification procedure, which led to practical improvements on a set of synthetic and competition benchmarks.

We explore whether Large Language Models (LLMs) are capable of logical reasoning with distorted facts, which we call Deduction under Perturbed Evidence (DUPE). DUPE presents a unique challenge to LLMs since they typically rely on their parameters, which encode mostly accurate information, to reason and make inferences. However, in DUPE, LLMs must reason over manipulated or falsified evidence present in their prompts, which can result in false conclusions that are valid only under the manipulated evidence. Our goal with DUPE is to determine whether LLMs can arrive at these false conclusions and identify whether the dominant factor influencing the deduction process is the encoded data in the parameters or the manipulated evidence in the prompts. To evaluate the DUPE capabilities of LLMs, we create a DUPEd version of the StrategyQA dataset, where facts are manipulated to reverse the answer to the question. Our findings show that even the most advanced GPT models struggle to reason on manipulated facts - showcasing poor DUPE skills - with accuracy dropping by 45% compared to the original dataset. We also investigate prompt settings inspired from student simulation models, which mitigate the accuracy drop to some extent. Our findings have practical implications for understanding the performance of LLMs in real-world applications such as student simulation models that involve reasoning over inaccurate information.

Despite the significant strides made by generative AI in just a few short years, its future progress is constrained by the challenge of building modular and robust systems. This capability has been a cornerstone of past technological revolutions, which relied on combining components to create increasingly sophisticated and reliable systems. Cars, airplanes, computers, and software consist of components-such as engines, wheels, CPUs, and libraries-that can be assembled, debugged, and replaced. A key tool for building such reliable and modular systems is specification: the precise description of the expected behavior, inputs, and outputs of each component. However, the generality of LLMs and the inherent ambiguity of natural language make defining specifications for LLM-based components (e.g., agents) both a challenging and urgent problem. In this paper, we discuss the progress the field has made so far-through advances like structured outputs, process supervision, and test-time compute-and outline several future directions for research to enable the development of modular and reliable LLM-based systems through improved specifications.

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study investigating the detection of formally valid inferences in controlled fragments of natural language for which the satisfiability problem becomes increasingly complex. We find that, while transformer-based language models perform surprisingly well in these scenarios, a deeper analysis re-veals that they appear to overfit to superficial patterns in the data rather than acquiring the logical principles governing the reasoning in these fragments.

Recent powerful pre-trained language models have achieved remarkable performance on most of the popular datasets for reading comprehension. It is time to introduce more challenging datasets to push the development of this field towards more comprehensive reasoning of text. In this paper, we introduce a new Reading Comprehension dataset requiring logical reasoning (ReClor) extracted from standardized graduate admission examinations. As earlier studies suggest, human-annotated datasets usually contain biases, which are often exploited by models to achieve high accuracy without truly understanding the text. In order to comprehensively evaluate the logical reasoning ability of models on ReClor, we propose to identify biased data points and separate them into EASY set while the rest as HARD set. Empirical results show that state-of-the-art models have an outstanding ability to capture biases contained in the dataset with high accuracy on EASY set. However, they struggle on HARD set with poor performance near that of random guess, indicating more research is needed to essentially enhance the logical reasoning ability of current models.

Large Language Models (LLMs) are revolutionizing several areas of Artificial Intelligence. One of the most remarkable applications is creative writing, e.g., poetry or storytelling: the generated outputs are often of astonishing quality. However, a natural question arises: can LLMs be really considered creative? In this article we firstly analyze the development of LLMs under the lens of creativity theories, investigating the key open questions and challenges. In particular, we focus our discussion around the dimensions of value, novelty and surprise as proposed by Margaret Boden in her work. Then, we consider different classic perspectives, namely product, process, press and person. We discuss a set of ``easy'' and ``hard'' problems in machine creativity, presenting them in relation to LLMs. Finally, we examine the societal impact of these technologies with a particular focus on the creative industries, analyzing the opportunities offered by them, the challenges arising by them and the potential associated risks, from both legal and ethical points of view.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Large language models can produce creative and diverse responses. However, to integrate them into current developer workflows, it is essential to constrain their outputs to follow specific formats or standards. In this work, we surveyed 51 experienced industry professionals to understand the range of scenarios and motivations driving the need for output constraints from a user-centered perspective. We identified 134 concrete use cases for constraints at two levels: low-level, which ensures the output adhere to a structured format and an appropriate length, and high-level, which requires the output to follow semantic and stylistic guidelines without hallucination. Critically, applying output constraints could not only streamline the currently repetitive process of developing, testing, and integrating LLM prompts for developers, but also enhance the user experience of LLM-powered features and applications. We conclude with a discussion on user preferences and needs towards articulating intended constraints for LLMs, alongside an initial design for a constraint prototyping tool.

Recent advances in the area of legal information systems have led to a variety of applications that promise support in processing and accessing legal documents. Unfortunately, these applications have various limitations, e.g., regarding scope or extensibility. Furthermore, we do not observe a trend towards open access in digital libraries in the legal domain as we observe in other domains, e.g., economics of computer science. To improve open access in the legal domain, we present our approach for an open source platform to transparently process and access Legal Open Data. This enables the sustainable development of legal applications by offering a single technology stack. Moreover, the approach facilitates the development and deployment of new technologies. As proof of concept, we implemented six technologies and generated metadata for more than 250,000 German laws and court decisions. Thus, we can provide users of our platform not only access to legal documents, but also the contained information.

Recent literature uses language to build foundation models for audio. These Audio-Language Models (ALMs) are trained on a vast number of audio-text pairs and show remarkable performance in tasks including Text-to-Audio Retrieval, Captioning, and Question Answering. However, their ability to engage in more complex open-ended tasks, like Interactive Question-Answering, requires proficiency in logical reasoning -- a skill not yet benchmarked. We introduce the novel task of Audio Entailment to evaluate an ALM's deductive reasoning ability. This task assesses whether a text description (hypothesis) of audio content can be deduced from an audio recording (premise), with potential conclusions being entailment, neutral, or contradiction, depending on the sufficiency of the evidence. We create two datasets for this task with audio recordings sourced from two audio captioning datasets -- AudioCaps and Clotho -- and hypotheses generated using Large Language Models (LLMs). We benchmark state-of-the-art ALMs and find deficiencies in logical reasoning with both zero-shot and linear probe evaluations. Finally, we propose "caption-before-reason", an intermediate step of captioning that improves the zero-shot and linear-probe performance of ALMs by an absolute 6% and 3%, respectively.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

We present KNOW--the Knowledge Navigator Ontology for the World--the first ontology designed to capture everyday knowledge to augment large language models (LLMs) in real-world generative AI use cases such as personal AI assistants. Our domain is human life, both its everyday concerns and its major milestones. We have limited the initial scope of the modeled concepts to only established human universals: spacetime (places, events) plus social (people, groups, organizations). The inclusion criteria for modeled concepts are pragmatic, beginning with universality and utility. We compare and contrast previous work such as Schema.org and Cyc--as well as attempts at a synthesis of knowledge graphs and language models--noting how LLMs already encode internally much of the commonsense tacit knowledge that took decades to capture in the Cyc project. We also make available code-generated software libraries for the 12 most popular programming languages, enabling the direct use of ontology concepts in software engineering. We emphasize simplicity and developer experience in promoting AI interoperability.

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and others parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

Recent availability of Large Language Models (LLMs) has led to the development of numerous LLM-based approaches aimed at providing natural language interfaces for various end-user tasks. These end-user tasks in turn can typically be accomplished by orchestrating a given set of APIs. In practice, natural language task requests (user queries) are often incomplete, i.e., they may not contain all the information required by the APIs. While LLMs excel at natural language processing (NLP) tasks, they frequently hallucinate on missing information or struggle with orchestrating the APIs. The key idea behind our proposed approach is to leverage logical reasoning and classical AI planning along with an LLM for accurately answering user queries including identification and gathering of any missing information in these queries. Our approach uses an LLM and ASP (Answer Set Programming) solver to translate a user query to a representation in Planning Domain Definition Language (PDDL) via an intermediate representation in ASP. We introduce a special API "get_info_api" for gathering missing information. We model all the APIs as PDDL actions in a way that supports dataflow between the APIs. Our approach then uses a classical AI planner to generate an orchestration of API calls (including calls to get_info_api) to answer the user query. Our evaluation results show that our approach significantly outperforms a pure LLM based approach by achieving over 95\% success rate in most cases on a dataset containing complete and incomplete single goal and multi-goal queries where the multi-goal queries may or may not require dataflow among the APIs.

Large language models LLMs like ChatGPT have reached the 100 Mio user barrier in record time and might increasingly enter all areas of our life leading to a diverse set of interactions between those Artificial Intelligence models and humans. While many studies have discussed governance and regulations deductively from first-order principles, few studies provide an inductive, data-driven lens based on observing dialogues between humans and LLMs especially when it comes to non-collaborative, competitive situations that have the potential to pose a serious threat to people. In this work, we conduct a user study engaging over 40 individuals across all age groups in price negotiations with an LLM. We explore how people interact with an LLM, investigating differences in negotiation outcomes and strategies. Furthermore, we highlight shortcomings of LLMs with respect to their reasoning capabilities and, in turn, susceptiveness to prompt hacking, which intends to manipulate the LLM to make agreements that are against its instructions or beyond any rationality. We also show that the negotiated prices humans manage to achieve span a broad range, which points to a literacy gap in effectively interacting with LLMs.

Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or probabilistic) representation has been a major obstacle to this research. This paper investigates a modern approach to this problem where the facts and rules are provided as natural language sentences, thus bypassing a formal representation. We train transformers to reason (or emulate reasoning) over these sentences using synthetically generated data. Our models, that we call RuleTakers, provide the first empirical demonstration that this kind of soft reasoning over language is learnable, can achieve high (99%) accuracy, and generalizes to test data requiring substantially deeper chaining than seen during training (95%+ scores). We also demonstrate that the models transfer well to two hand-authored rulebases, and to rulebases paraphrased into more natural language. These findings are significant as it suggests a new role for transformers, namely as limited "soft theorem provers" operating over explicit theories in language. This in turn suggests new possibilities for explainability, correctability, and counterfactual reasoning in question-answering.

In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : cdots . Such type systems are called cumulative if for any type A we have that A : Type_{i} implies A : Type_{i+1}. The predicative calculus of inductive constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present and establish the soundness of the predicative calculus of cumulative inductive constructions (pCuIC) which extends the cumulativity relation to inductive types.

The capabilities and limitations of Large Language Models have been sketched out in great detail in recent years, providing an intriguing yet conflicting picture. On the one hand, LLMs demonstrate a general ability to solve problems. On the other hand, they show surprising reasoning gaps when compared to humans, casting doubt on the robustness of their generalisation strategies. The sheer volume of data used in the design of LLMs has precluded us from applying the method traditionally used to measure generalisation: train-test set separation. To overcome this, we study what kind of generalisation strategies LLMs employ when performing reasoning tasks by investigating the pretraining data they rely on. For two models of different sizes (7B and 35B) and 2.5B of their pretraining tokens, we identify what documents influence the model outputs for three simple mathematical reasoning tasks and contrast this to the data that are influential for answering factual questions. We find that, while the models rely on mostly distinct sets of data for each factual question, a document often has a similar influence across different reasoning questions within the same task, indicating the presence of procedural knowledge. We further find that the answers to factual questions often show up in the most influential data. However, for reasoning questions the answers usually do not show up as highly influential, nor do the answers to the intermediate reasoning steps. When we characterise the top ranked documents for the reasoning questions qualitatively, we confirm that the influential documents often contain procedural knowledge, like demonstrating how to obtain a solution using formulae or code. Our findings indicate that the approach to reasoning the models use is unlike retrieval, and more like a generalisable strategy that synthesises procedural knowledge from documents doing a similar form of reasoning.

We present PutnamBench, a new multilingual benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1697 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the theorems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. Proving the theorems requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

This study evaluates the performance of OpenAI's o1-preview model in higher-order cognitive domains, including critical thinking, systematic thinking, computational thinking, data literacy, creative thinking, logical reasoning, and scientific reasoning. Using established benchmarks, we compared the o1-preview models's performance to human participants from diverse educational levels. o1-preview achieved a mean score of 24.33 on the Ennis-Weir Critical Thinking Essay Test (EWCTET), surpassing undergraduate (13.8) and postgraduate (18.39) participants (z = 1.60 and 0.90, respectively). In systematic thinking, it scored 46.1, SD = 4.12 on the Lake Urmia Vignette, significantly outperforming the human mean (20.08, SD = 8.13, z = 3.20). For data literacy, o1-preview scored 8.60, SD = 0.70 on Merk et al.'s "Use Data" dimension, compared to the human post-test mean of 4.17, SD = 2.02 (z = 2.19). On creative thinking tasks, the model achieved originality scores of 2.98, SD = 0.73, higher than the human mean of 1.74 (z = 0.71). In logical reasoning (LogiQA), it outperformed humans with average 90%, SD = 10% accuracy versus 86%, SD = 6.5% (z = 0.62). For scientific reasoning, it achieved near-perfect performance (mean = 0.99, SD = 0.12) on the TOSLS,, exceeding the highest human scores of 0.85, SD = 0.13 (z = 1.78). While o1-preview excelled in structured tasks, it showed limitations in problem-solving and adaptive reasoning. These results demonstrate the potential of AI to complement education in structured assessments but highlight the need for ethical oversight and refinement for broader applications.

Semantic code search is the task of retrieving a code snippet given a textual description of its functionality. Recent work has been focused on using similarity metrics between neural embeddings of text and code. However, current language models are known to struggle with longer, compositional text, and multi-step reasoning. To overcome this limitation, we propose supplementing the query sentence with a layout of its semantic structure. The semantic layout is used to break down the final reasoning decision into a series of lower-level decisions. We use a Neural Module Network architecture to implement this idea. We compare our model - NS3 (Neuro-Symbolic Semantic Search) - to a number of baselines, including state-of-the-art semantic code retrieval methods, and evaluate on two datasets - CodeSearchNet and Code Search and Question Answering. We demonstrate that our approach results in more precise code retrieval, and we study the effectiveness of our modular design when handling compositional queries.

Large language models (LLMs) have demonstrated impressive performance in various natural language processing tasks, yet their ability to perform multi-step logical reasoning remains an open challenge. Although Chain-of-Thought prompting has improved logical reasoning by enabling models to generate intermediate steps, it lacks mechanisms to assess the coherence of these logical transitions. In this paper, we propose a novel, lightweight evaluation strategy for logical reasoning that uses query-key alignments inside transformer attention heads. By computing a single forward pass and extracting a "QK-score" from carefully chosen heads, our method reveals latent representations that reliably separate valid from invalid inferences, offering a scalable alternative to traditional ablation-based techniques. We also provide an empirical validation on multiple logical reasoning benchmarks, demonstrating improved robustness of our evaluation method against distractors and increased reasoning depth. The experiments were conducted on a diverse set of models, ranging from 1.5B to 70B parameters.

Statutory reasoning is the task of determining whether a legal statute, stated in natural language, applies to the text description of a case. Prior work introduced a resource that approached statutory reasoning as a monolithic textual entailment problem, with neural baselines performing nearly at-chance. To address this challenge, we decompose statutory reasoning into four types of language-understanding challenge problems, through the introduction of concepts and structure found in Prolog programs. Augmenting an existing benchmark, we provide annotations for the four tasks, and baselines for three of them. Models for statutory reasoning are shown to benefit from the additional structure, improving on prior baselines. Further, the decomposition into subtasks facilitates finer-grained model diagnostics and clearer incremental progress.

Introduction: Recently, the effectiveness of Large Language Models (LLMs) has increased rapidly, allowing them to be used in a great number of applications. However, the risks posed by the generation of false information through LLMs significantly limit their applications in sensitive areas such as healthcare, highlighting the necessity for rigorous validations to determine their utility and reliability. To date, no study has extensively compared the performance of LLMs on Polish medical examinations across a broad spectrum of specialties on a very large dataset. Objectives: This study evaluated the performance of three Generative Pretrained Transformer (GPT) models on the Polish Board Certification Exam (Pa\'nstwowy Egzamin Specjalizacyjny, PES) dataset, which consists of 297 tests. Methods: We developed a software program to download and process PES exams and tested the performance of GPT models using OpenAI Application Programming Interface. Results: Our findings reveal that GPT-3.5 did not pass any of the analyzed exams. In contrast, the GPT-4 models demonstrated the capability to pass the majority of the exams evaluated, with the most recent model, gpt-4-0125, successfully passing 222 (75%) of them. The performance of the GPT models varied significantly, displaying excellence in exams related to certain specialties while completely failing others. Conclusions: The significant progress and impressive performance of LLM models hold great promise for the increased application of AI in the field of medicine in Poland. For instance, this advancement could lead to the development of AI-based medical assistants for healthcare professionals, enhancing the efficiency and accuracy of medical services.

Large Language Models (LLMs) have shown superior capability to solve reasoning problems with programs. While being a promising direction, most of such frameworks are trained and evaluated in settings with a prior knowledge of task requirements. However, as LLMs become more capable, it is necessary to assess their reasoning abilities in more realistic scenarios where many real-world problems are open-ended with ambiguous scope, and often require multiple formalisms to solve. To investigate this, we introduce the task of reasoning in the wild, where an LLM is tasked to solve a reasoning problem of unknown type by identifying the subproblems and their corresponding formalisms, and writing a program to solve each subproblem, guided by a tactic. We create a large tactic-guided trajectory dataset containing detailed solutions to a diverse set of reasoning problems, ranging from well-defined single-form reasoning (e.g., math, logic), to ambiguous and hybrid ones (e.g., commonsense, combined math and logic). This allows us to test various aspects of LLMs reasoning at the fine-grained level such as the selection and execution of tactics, and the tendency to take undesired shortcuts. In experiments, we highlight that existing LLMs fail significantly on problems with ambiguous and mixed scope, revealing critical limitations and overfitting issues (e.g. accuracy on GSM8K drops by at least 50\%). We further show the potential of finetuning a local LLM on the tactic-guided trajectories in achieving better performance. Project repo is available at github.com/gblackout/Reason-in-the-Wild

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

Rationality is the quality of being guided by reason, characterized by decision-making that aligns with evidence and logical principles. It plays a crucial role in reliable problem-solving by ensuring well-grounded and consistent solutions. While large language models (LLMs) have made significant progress in generating human-like text, they still exhibit limitations such as bounded knowledge space and inconsistent outputs. In response, recent efforts have shifted toward developing multimodal and multi-agent systems, as well as integrating modules like external tools, programming codes, symbolic reasoners, utility function, and conformal risk controls rather than relying solely on a single LLM for decision-making. This paper surveys the state-of-the-art advancements in language and multimodal agents, evaluates how they contribute to make intelligent agents more rational, and identifies open challenges and future research directions. We maintain an open repository at https://github.com/bowen-upenn/Agent_Rationality.

Legal practice has witnessed a sharp rise in products incorporating artificial intelligence (AI). Such tools are designed to assist with a wide range of core legal tasks, from search and summarization of caselaw to document drafting. But the large language models used in these tools are prone to "hallucinate," or make up false information, making their use risky in high-stakes domains. Recently, certain legal research providers have touted methods such as retrieval-augmented generation (RAG) as "eliminating" (Casetext, 2023) or "avoid[ing]" hallucinations (Thomson Reuters, 2023), or guaranteeing "hallucination-free" legal citations (LexisNexis, 2023). Because of the closed nature of these systems, systematically assessing these claims is challenging. In this article, we design and report on the first preregistered empirical evaluation of AI-driven legal research tools. We demonstrate that the providers' claims are overstated. While hallucinations are reduced relative to general-purpose chatbots (GPT-4), we find that the AI research tools made by LexisNexis (Lexis+ AI) and Thomson Reuters (Westlaw AI-Assisted Research and Ask Practical Law AI) each hallucinate between 17% and 33% of the time. We also document substantial differences between systems in responsiveness and accuracy. Our article makes four key contributions. It is the first to assess and report the performance of RAG-based proprietary legal AI tools. Second, it introduces a comprehensive, preregistered dataset for identifying and understanding vulnerabilities in these systems. Third, it proposes a clear typology for differentiating between hallucinations and accurate legal responses. Last, it provides evidence to inform the responsibilities of legal professionals in supervising and verifying AI outputs, which remains a central open question for the responsible integration of AI into law.

When large language models (LMs) are applied in zero- or few-shot settings to discriminative tasks such as multiple-choice questions, their attentiveness (i.e., probability mass) is spread across many vocabulary tokens that are not valid choices. Such a spread across multiple surface forms with identical meaning is thought to cause an underestimation of a model's true performance, referred to as the "surface form competition" (SFC) hypothesis. This has motivated the introduction of various probability normalization methods. However, many core questions remain unanswered. How do we measure SFC or attentiveness? Are there direct ways of increasing attentiveness on valid choices? Does increasing attentiveness always improve task accuracy? We propose a mathematical formalism for studying this phenomenon, provide a metric for quantifying attentiveness, and identify a simple method for increasing it -- namely, in-context learning with even just one example containing answer choices. The formalism allows us to quantify SFC and bound its impact. Our experiments on three diverse datasets and six LMs reveal several surprising findings. For example, encouraging models to generate a valid answer choice can, in fact, be detrimental to task performance for some LMs, and prior probability normalization methods are less effective (sometimes even detrimental) to instruction-tuned LMs. We conclude with practical insights for effectively using prompted LMs for multiple-choice tasks.

Harnessing logical reasoning ability is a comprehensive natural language understanding endeavor. With the release of Generative Pretrained Transformer 4 (GPT-4), highlighted as "advanced" at reasoning tasks, we are eager to learn the GPT-4 performance on various logical reasoning tasks. This report analyses multiple logical reasoning datasets, with popular benchmarks like LogiQA and ReClor, and newly-released datasets like AR-LSAT. We test the multi-choice reading comprehension and natural language inference tasks with benchmarks requiring logical reasoning. We further construct a logical reasoning out-of-distribution dataset to investigate the robustness of ChatGPT and GPT-4. We also make a performance comparison between ChatGPT and GPT-4. Experiment results show that ChatGPT performs significantly better than the RoBERTa fine-tuning method on most logical reasoning benchmarks. With early access to the GPT-4 API we are able to conduct intense experiments on the GPT-4 model. The results show GPT-4 yields even higher performance on most logical reasoning datasets. Among benchmarks, ChatGPT and GPT-4 do relatively well on well-known datasets like LogiQA and ReClor. However, the performance drops significantly when handling newly released and out-of-distribution datasets. Logical reasoning remains challenging for ChatGPT and GPT-4, especially on out-of-distribution and natural language inference datasets. We release the prompt-style logical reasoning datasets as a benchmark suite and name it LogiEval.

Chain-of-Thought (CoT) reasoning has enabled Large Language Model (LLM) to achieve remarkable performance in various NLP tasks, including arithmetic problem-solving. However, this success does not generalize to small language model (sLM) like T5, due to their limited capacity and absence of emergent abilities associated with larger models. Recent works to enhance sLM through knowledge distillation have yielded some improvements but still face significant limitations, particularly high ambiguity from the variability in natural language expressions and substantial computational costs. In this paper, we investigate why sLM perform poorly on arithmetic reasoning tasks and hypothesize that natural language format variability introduces high ambiguity for these smaller models. Based on this hypothesis, we conduct experiments with equation-only format, which is a reasoning format that unifies arithmetic reasoning previously expressed in natural language formats into mathematical equations. Experiment results demonstrate that equation-only format effectively boosts the arithmetic reasoning abilities of sLM, especially in very small models like T5-Tiny.

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study large-scale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NaturalProver, a language model that generates proofs by conditioning on background references (e.g. theorems and definitions that are either retrieved or human-provided), and optionally enforces their presence with constrained decoding. On theorems from the NaturalProofs benchmark, NaturalProver improves the quality of next-step suggestions and generated proofs over fine-tuned GPT-3, according to human evaluations from university-level mathematics students. NaturalProver is capable of proving some theorems that require short (2-6 step) proofs, and providing next-step suggestions that are rated as correct and useful over 40% of the time, which is to our knowledge the first demonstration of these capabilities using neural language models.

This paper presents teaching materials, particularly assignments and ideas for classroom activities, from a new course on large language models (LLMs) taught at Charles University. The assignments include experiments with LLM inference for weather report generation and machine translation. The classroom activities include class quizzes, focused research on downstream tasks and datasets, and an interactive "best paper" session aimed at reading and comprehension of research papers.

Structured generation, the process of producing content in standardized formats like JSON and XML, is widely utilized in real-world applications to extract key output information from large language models (LLMs). This study investigates whether such constraints on generation space impact LLMs' abilities, including reasoning and domain knowledge comprehension. Specifically, we evaluate LLMs' performance when restricted to adhere to structured formats versus generating free-form responses across various common tasks. Surprisingly, we observe a significant decline in LLMs' reasoning abilities under format restrictions. Furthermore, we find that stricter format constraints generally lead to greater performance degradation in reasoning tasks.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

While question answering over knowledge bases (KBQA) has shown progress in addressing factoid questions, KBQA with numerical reasoning remains relatively unexplored. In this paper, we focus on the complex numerical reasoning in KBQA and propose a new task, NR-KBQA, which necessitates the ability to perform both multi-hop reasoning and numerical reasoning. We design a logic form in Python format called PyQL to represent the reasoning process of numerical reasoning questions. To facilitate the development of NR-KBQA, we present a large dataset called MarkQA, which is automatically constructed from a small set of seeds. Each question in MarkQA is equipped with its corresponding SPARQL query, alongside the step-by-step reasoning process in the QDMR format and PyQL program. Experimental results of some state-of-the-art QA methods on the MarkQA show that complex numerical reasoning in KBQA faces great challenges.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

Charts are very popular for analyzing data. When exploring charts, people often ask a variety of complex reasoning questions that involve several logical and arithmetic operations. They also commonly refer to visual features of a chart in their questions. However, most existing datasets do not focus on such complex reasoning questions as their questions are template-based and answers come from a fixed-vocabulary. In this work, we present a large-scale benchmark covering 9.6K human-written questions as well as 23.1K questions generated from human-written chart summaries. To address the unique challenges in our benchmark involving visual and logical reasoning over charts, we present two transformer-based models that combine visual features and the data table of the chart in a unified way to answer questions. While our models achieve the state-of-the-art results on the previous datasets as well as on our benchmark, the evaluation also reveals several challenges in answering complex reasoning questions.

This paper proposes a research direction to advance AI which draws inspiration from cognitive theories of human decision making. The premise is that if we gain insights about the causes of some human capabilities that are still lacking in AI (for instance, adaptability, generalizability, common sense, and causal reasoning), we may obtain similar capabilities in an AI system by embedding these causal components. We hope that the high-level description of our vision included in this paper, as well as the several research questions that we propose to consider, can stimulate the AI research community to define, try and evaluate new methodologies, frameworks, and evaluation metrics, in the spirit of achieving a better understanding of both human and machine intelligence.

Purpose: Bangladesh's legal system struggles with major challenges like delays, complexity, high costs, and millions of unresolved cases, which deter many from pursuing legal action due to lack of knowledge or financial constraints. This research seeks to develop a specialized Large Language Model (LLM) to assist in the Bangladeshi legal system. Methods: We created UKIL-DB-EN, an English corpus of Bangladeshi legal documents, by collecting and scraping data on various legal acts. We fine-tuned the GPT-2 model on this dataset to develop GPT2-UKIL-EN, an LLM focused on providing legal assistance in English. Results: The model was rigorously evaluated using semantic assessments, including case studies supported by expert opinions. The evaluation provided promising results, demonstrating the potential for the model to assist in legal matters within Bangladesh. Conclusion: Our work represents the first structured effort toward building an AI-based legal assistant for Bangladesh. While the results are encouraging, further refinements are necessary to improve the model's accuracy, credibility, and safety. This is a significant step toward creating a legal AI capable of serving the needs of a population of 180 million.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

Autonomous driving technology, a catalyst for revolutionizing transportation and urban mobility, has the tend to transition from rule-based systems to data-driven strategies. Traditional module-based systems are constrained by cumulative errors among cascaded modules and inflexible pre-set rules. In contrast, end-to-end autonomous driving systems have the potential to avoid error accumulation due to their fully data-driven training process, although they often lack transparency due to their "black box" nature, complicating the validation and traceability of decisions. Recently, large language models (LLMs) have demonstrated abilities including understanding context, logical reasoning, and generating answers. A natural thought is to utilize these abilities to empower autonomous driving. By combining LLM with foundation vision models, it could open the door to open-world understanding, reasoning, and few-shot learning, which current autonomous driving systems are lacking. In this paper, we systematically review a research line about Large Language Models for Autonomous Driving (LLM4AD). This study evaluates the current state of technological advancements, distinctly outlining the principal challenges and prospective directions for the field. For the convenience of researchers in academia and industry, we provide real-time updates on the latest advances in the field as well as relevant open-source resources via the designated link: https://github.com/Thinklab-SJTU/Awesome-LLM4AD.

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text.