CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.
@cite_25: We provide a direct and modular translation from the temporal logics CTL, ETL, FCTL (CTL extended with the ability to express fairness) and the Modal µ-calculus to Monadic inf-Datalog with built-in predicates. We call it inf-Datalog because the semantics we provide is a little different from the conventional Datalog least fixed point semantics, in that some recursive rules (corresponding to least fixed points) are allowed to unfold only finitely many times, whereas others (corresponding to greatest fixed points) are allowed to unfold infinitely many times.We characterize the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal µ-calculus and Modal µ-calculus). Our translation is interesting because it is direct and succinct. Moreover the fragments of Monadic inf-Datalog that we have exhibited have very simple syntactic characterizations as subsets of what we call Modal inf-Datalog programs.
@cite_3: We provide a translation from CTL to DatalogSucc. The translation has the following advantages: a) It is natural. b) It provides intuition to the expressive power of CTL and its various fragments. c) It uses a fragment of DatalogSucc which is close to the expressive power of CTL.
In previous work @cite_25 we showed that the model checking problem for CTL can be reduced to the query evaluation problem for fragments of Datalog. In more detail, @cite_25 presents a direct and modular translation from the temporal logics CTL, ETL, FCTL (CTL extended with the ability to express fairness) and the modal @math -calculus to Monadic inf-Datalog with built-in predicates. It is called inf-Datalog because the semantics differ from the conventional Datalog least fixed point semantics, in that some recursive rules (corresponding to least fixed points) are allowed to unfold only finitely many times, whereas others (corresponding to greatest fixed points) are allowed to unfold infinitely many times. The work in @cite_3 , which is a preliminary version of some of the results presented here, embeds CTL into a fragment of Datalog @math .