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Linear-Time Temporal Answer Set Programming

Published online by Cambridge University Press:  27 December 2021

FELICIDAD AGUADO ,
PEDRO CABALAR Open the ORCID record for PEDRO CABALAR [Opens in a new window] ,
MARTÍN DIÉGUEZ Open the ORCID record for MARTÍN DIÉGUEZ [Opens in a new window] ,
GILBERTO PÉREZ ,
TORSTEN SCHAUB Open the ORCID record for TORSTEN SCHAUB [Opens in a new window] ,
ANNA SCHUHMANN  and
CONCEPCIÓN VIDAL
FELICIDAD AGUADO
Affiliation:
University of Corunna, Spain (e-mails: [email protected], [email protected])
PEDRO CABALAR
Affiliation:
University of Corunna, Spain (e-mails: [email protected], [email protected])
MARTÍN DIÉGUEZ
Affiliation:
Université d’Angers, France (e-mail: [email protected])
GILBERTO PÉREZ
Affiliation:
University of Corunna, Spain (e-mail: [email protected])
TORSTEN SCHAUB
Affiliation:
University of Potsdam, Germany (e-mails: [email protected], [email protected])
ANNA SCHUHMANN
Affiliation:
University of Potsdam, Germany (e-mails: [email protected], [email protected])
CONCEPCIÓN VIDAL
Affiliation:
University of Corunna, Spain (e-mail: [email protected])
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Abstract

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In 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.

Keywords

answer set programminglinear-time temporal logicequilibrium logicnon-monotonic reasoning
Type
Survey Article
Information
Theory and Practice of Logic Programming , Volume 23 , Issue 1 , January 2023 , pp. 2 - 56
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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