Temporal Answer Set Programming

TL;DR

This paper reviews Temporal Logic Programming, focusing on Temporal Equilibrium Logic (TEL), its semantics, translations, and practical solver implementations, advancing declarative temporal reasoning in knowledge representation.

Contribution

It introduces TEL, extends stable model semantics to temporal formulas, and develops a practical solver TELINGO for temporal logic programs.

Findings

TEL provides a proper extension of stable models for temporal formulas.

Translation techniques connect TEL with other logics like Quantified Equilibrium Logic.

TELINGO enables practical computation of temporal stable models.

Abstract

We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). We focus on recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL, but performs a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). We obtain a proper extension of the stable models semantics for the general case of arbitrary temporal formulas. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between infinite and finite traces. We also provide other useful results, such as the translation into other formalisms like Quantified Equilibrium Logic or Second-order LTL, and some techniques for computing temporal stable models based on automata. In a second part, we focus on practical aspects, defining a syntactic fragment called temporal logic programs closer to ASP, and explain how this has been exploited in the construction of the solver TELINGO.