Strongly Equivalent Temporal Logic Programs

Aguado, Felicidad; Cabalar, Pedro; Pérez, Gilberto; Vidal, Concepción

doi:10.1007/978-3-540-87803-2_3

Cited by 15 publications

(14 citation statements)

References 13 publications

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“…Formally, this means that we cannot have rules where a head atom without depends on a body atom with . In our example, (5)- (8) are also splitable TLP rules whereas, for instance, the following TLP rules are not in splitable form:…”

Section: Introductionmentioning

confidence: 99%

“…In [8] it was shown how to use equivalence in the logic of THT as a sufficient condition for strong equivalence of two arbitrary TEL theories. The THTequivalence test was performed by translating THT into LTL and using a model checker afterwards.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent work [9], it was shown that TEL could be reduced to a normal form closer to logic programs where, roughly speaking, in place of an atom p we can also use p, and any rule can be embraced by . This normal form received the name of Temporal Logic Programs (TLPs) -for instance, (5)- (8) are TLP rules.…”

Section: Introductionmentioning

confidence: 99%

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Loop Formulas for Splitable Temporal Logic Programs

Aguado

Cabalar

Pérez

et al. 2011

Logic Programming and Nonmonotonic Reasoning

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Abstract. In this paper, we study a method for computing temporal equilibrium models, a generalisation of stable models for logic programs with temporal operators, as in Linear Temporal Logic (LTL). To this aim, we focus on a syntactic subclass of these temporal logic programs called splitable and whose main property is satisfying a kind of "future projected" dependence present in most dynamic scenarios in Answer Set Programming (ASP). Informally speaking, this property can be expressed as "past does not depend on the future." We show that for this syntactic class, temporal equilibrium models can be captured by an LTL formula, that results from the combination of two well-known techniques in ASP: splitting and loop formulas. As a result, an LTL model checker can be used to obtain the temporal equilibrium models of the program.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Loop Formulas for Splitable Temporal Logic Programs

Aguado

Cabalar

Pérez

et al. 2011

Logic Programming and Nonmonotonic Reasoning

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“…To overcome these difficulties, in [11] a temporal extension of ASP, called Temporal Equilibrium Logic (TEL), was considered. This extension is an orthogonal combination of linear-time temporal logic (LTL) (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…The definition of TEL has allowed studying problems like the aforementioned strong equivalence [11] of two temporal theories, but it had mostly remained as a theoretical tool, since there was no method for computing the temporal stable models of a temporal theory, at least until quite recently. In a first step in this direction, the paper [14] started from the normal form for TEL called temporal logic programs (TLPs) from [15] and showed that, when a syntactic subclass is considered (the so-called splitable TLPs), its temporal stable models can be obtained by a translation into LTL.…”

Section: Introductionmentioning

confidence: 99%

Automata-Based Computation of Temporal Equilibrium Models

Cabalar

Demri

2012

Logic-Based Program Synthesis and Transformation

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Abstract. Temporal Equilibrium Logic (TEL) is a formalism for temporal logic programming that generalizes the paradigm of Answer Set Programming (ASP) introducing modal temporal operators from standard Linear-time Temporal Logic (LTL). In this paper we solve some open problems that remained open for TEL like decidability, complexity assessment and computation of temporal equilibrium models for arbitrary theories. We propose a method for the latter that consists in building a Büchi automaton that accepts exactly the temporal equilibrium models of a given theory, providing an automata-based decision procedure and illustrating the ω-regularity of such sets. We are able to show that TEL satisfiability can be solved in exponential space and it is hard for polynomial space. Finally, given two theories, we provide a decision procedure to check whether they have the same temporal equilibrium models.

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References

2011

An Introduction to Practical Formal Methods Using Temporal Logic

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Strongly Equivalent Temporal Logic Programs

Cited by 15 publications

References 13 publications

Loop Formulas for Splitable Temporal Logic Programs

Loop Formulas for Splitable Temporal Logic Programs

Automata-Based Computation of Temporal Equilibrium Models

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