Abstract
AbstractIn this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.
Highlights
The term Temporal Logic Programming1 was introduced in the late 1980s to refer to an extension of logic programs that incorporates modal temporal operators, usually from Linear-time Temporal Logic or LTL (Kamp 1968; Pnueli 1977)
We have provided a wide overview of the main definitions and recent results for the formalism of Temporal Equilibrium Logic (TEL), a combination of Equilibrium Logic
An important breakthrough for the latter has been the introduction of a finite trace variant, TELf, more aligned with the usual problem solving orientation followed in Answer Set Programming (ASP)
Summary
The term Temporal Logic Programming was introduced in the late 1980s to refer to an extension of logic programs that incorporates modal temporal operators, usually from Linear-time Temporal Logic or LTL (Kamp 1968; Pnueli 1977). In the paper at hand, we give a revised definition of TEL that incorporates the new advances, present the most general version of the logic (which neither imposes nor forbids finiteness of traces) and specify the two variants: TELω for infinite traces, as first defined by Cabalar and Vega (2007), and TELf for finite ones, as recently introduced by Cabalar et al . We study a normal form for temporal theories under TEL semantics: what we call (modal) temporal logic programs This normal form is used as the basis for a pair of translations from temporal logic programs (for finite traces) into standard ASP programs.
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