An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained in a given answer set by defining two justification methods, both of which make use of the correspondence between answer sets of a logic program and stable extensions of the assumption-based argumentation (ABA) framework constructed from the same logic program. Attack Trees justify a literal in argumentation-theoretic terms, i.e. using arguments and attacks between them, whereas ABA-Based Answer Set Justifications express the same justification structure in logic programming terms, that is using literals and their relationships. Interestingly, an ABA-Based Answer Set Justification corresponds to an admissible fragment of the answer set in question, and an Attack Tree corresponds to an admissible fragment of the stable extension corresponding to this answer set.
@cite_33: An abstract framework for structured arguments is presented, which instantiates Dung's (‘On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n-Person Games’, Artificial Intelligence, 77, 321–357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it...
@cite_12: We suggest a method for justifying why a literal is or is not contained in the answer set of a logic program. This method makes use of argumentation theory, more precisely of stable ASPIC+ extensions. We describe a way to translate a logic program into an ASPIC+ argumentation theory and investigate the relation between answer sets of the logic program and stable extensions of the translated ASPIC+ argumentation theory. The structure of ASPIC+ arguments with respect to a stable extension is then used for the justification of literals with respect to an answer set. We also present an implementation of our justification method which displays justifications
Argumentation-Based Answer Set Justification @cite_12 is the first work that applies argumentation theory to answer set programming, and in particular for the justification of answer sets. There, the ASPIC+ argumentation framework @cite_33 is used instead of ABA.