Conference Paper

Strongly Equivalent Temporal Logic Programs.

DOI: 10.1007/978-3-540-87803-2_3 Conference: Logics in Artificial Intelligence, 11th European Conference, JELIA 2008, Dresden, Germany, September 28 - October 1, 2008. Proceedings
Source: DBLP

ABSTRACT This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set
Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical
characterisation of ASP) and its monotonic basis, the intermediate logic of Here-and-There (HT). Trivially, equivalence in
this temporal extension of HT provides a sufficient condition for temporal strong equivalence and, as we show in the paper,
it can be transformed into a provability test into the standard Linear Temporal Logic (LTL), something that can be automatically
checked using any of the LTL available provers. The paper shows an example of the potential utility of this method by detecting
some redundant rules in a simple actions reasoning scenario.

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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 problems that remained open for TEL like decidability, bounds for computational complexity as well as 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 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 if they have the same temporal equilibrium models.
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    ABSTRACT: Equilibrium logic provides a logical foundation for the stable model semantics of logic programs. Recently, parametrized logic programming was introduced with the aim of presenting the syntax and natural semantics for parametrized logic programs, which are very expressive logic programs, in the sense that complex formulas are allowed to appear in the body and head of rules. Stable model semantics was defined for such parametrized logic programs. The aim of this paper is to introduce a parametrized version of equilibrium logic that extends parametrized logic programs to general theories, and to show how these can be used to characterize and to study strong equivalence of temporal logic programs.
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    ABSTRACT: In this paper, we present a declarative propositional temporal logic programming language called TeDiLog that is a combination of the temporal and disjunctive paradigms in Logic Programming. TeDiLog is, syntactically, a sublanguage of the well-known Propositional Linear-time Temporal Logic (PLTL). TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. The operational semantics of TeDiLog relies on a restriction of the invariant-free temporal resolution procedure for PLTL that was introduced by Gaintzarain et al. in 2013. We define a fixpoint semantics that captures the reverse (bottom-up) operational mechanism and prove its equivalence with the logical semantics. We also provide illustrative examples and comparison with other proposals.
    ACM Transactions on Computational Logic 11/2013; Volume 14(Issue 4):Article No. 28 -- 41 pages -- ACM (Association for Computing Machinery) New York, NY, USA. · 0.79 Impact Factor

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