Paving the Way for Temporal Grounding

In this paper we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. We provide several fundamental contributions that pave the way for the implementation of a grounding process, that is, a method that allows replacing variables by ground instances in all the possible (or better, relevant) ways

Revisiting Explicit Negation in Answer Set Programming

[Abstract] A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.Ministerio de Economía y Competitividad; TIC2017-84453-PXunta de Galicia; GPC ED431B 2019/03Xunta de Galicia; 2016-2019 ED431G/01, CITICCentre International de Math´ematiques et d’Informatique de Toulouse; ANR-11-LABEX-004

A Polynomial Reduction of Forks Into Logic Programs

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] In this research note we present additional results for an earlier published paper [1]. There, we studied the problem of projective strong equivalence (PSE) of logic programs, that is, checking whether two logic programs (or propositional formulas) have the same behaviour (under the stable model semantics) regardless of a common context and ignoring the effect of local auxiliary atoms. PSE is related to another problem called strongly persistent forgetting that consists in keeping a program’s behaviour after removing its auxiliary atoms, something that is known to be not always possible in Answer Set Programming. In [1], we introduced a new connective ‘|’ called fork and proved that, in this extended language, it is always possible to forget auxiliary atoms, but at the price of obtaining a result containing forks. We also proved that forks can be translated back to logic programs introducing new hidden auxiliary atoms, but this translation was exponential in the worst case. In this note we provide a new polynomial translation of arbitrary forks into regular programs that allows us to prove that brave and cautious reasoning with forks has the same complexity as that of ordinary (disjunctive) logic programs and paves the way for an efficient implementation of forks. To this aim, we rely on a pair of new PSE invariance properties.We wish to thank the anonymous reviewers for their useful suggestions that have helped to improve the paper. This work was partially supported by MICINN, Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain, grant GPC ED431B 2019/03, Universidade da Coruña/CISUG, Spain, (funding for open access charge) and National Science Foundation, USA, grant NSF Nebraska EPSCoR 95-3101-0060-402Xunta de Galicia; ED431B 2019/03USA. National Science Foundation; EPSCoR 95-3101-0060-40

Forgetting Auxiliary Atoms in Forks

©2019 Elsevier B.V. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/bync-nd/4.0/. This version of the article has been accepted for publication in Artificial Intelligence. The Version of Record is available online at https://doi.org/10.1016/j.artint.2019.07.005Versión final aceptada de: F. Aguado, P. Cabalar, J. Fandinno, D. Pearce, G. Pérez, and, C. Vidal, "Forgetting Auxiliary Atoms in Forks", Artificial Intelligence, Vol. 275, pp. 575-601, Oct. 2019, doi: 10.1016/j.artint.2019.07.005[Abstract]: In this work we tackle the problem of checking strong equivalence of logic programs that may contain local auxiliary atoms, to be removed from their stable models and to be forbidden in any external context. We call this property projective strong equivalence (PSE). It has been recently proved that not any logic program containing auxiliary atoms can be reformulated, under PSE, as another logic program or formula without them – this is known as strongly persistent forgetting. In this paper, we introduce a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There, in which we deal with a new connective ‘|’ we call fork. We provide a semantic characterisation of PSE for forks and use it to show that, in this extension, it is always possible to forget auxiliary atoms under strong persistence. We further define when the obtained fork is representable as a regular formula.We are grateful to the anonymous reviewers of the Artificial Intelligence Journal, and previously, to the reviewers of the workshop ASPOCP'17, for their comments and suggestions that have helped improve the paper substantially. This work has been partially supported by MINECO (grant TIN2017-84453-P) and Xunta de Galicia (grants GPC ED431B 2019/03 and 2016-2019 ED431G/01 for CITIC center), Spain; by the Salvador de Madariaga programme, Spain; by the European Regional Development Fund (ERDF); and by the Centre International de Mathématiques et d'Informatique de Toulouse (CIMI) through contract ANR-11-LABEX-0040-CIMI within the programme ANR-11-IDEX-0002-02.Xunta de Galicia; ED431B 2019/03Xunta de Galicia; 2016-2019 ED431G/0

Linear-Time Temporal Answer Set Programming

[Abstract]: 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.Xunta de Galicia; ED431B 2019/03We are thankful to the anonymous reviewers for their thorough work and their useful suggestions that have helped to improve the paper. A special thanks goes to Mirosaw Truszczy´nski for his support in improving the quality of our paper. We are especially grateful to David Pearce, whose help and collaboration on Equilibrium Logic was the seed for a great part of the current paper. This work was partially supported by MICINN, Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain (GPC ED431B 2019/03), R´egion Pays de la Loire, France, (projects EL4HC and etoiles montantes CTASP), European Union COST action CA-17124, and DFG grants SCHA 550/11 and 15, Germany

Temporal logic programs with variables

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