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An infinitary encoding of temporal equilibrium logic*

Published online by Cambridge University Press:  03 September 2015

PEDRO CABALAR
Affiliation:
Department of Computer Science, University of Corunna, Spain (e-mail: cabalar@udc.es, concepcion.vidalm@udc.es)
MARTÍN DIÉGUEZ
Affiliation:
IRIT, University of Toulouse, France (e-mail: martin.dieguez@irit.fr)
CONCEPCIÓN VIDAL
Affiliation:
Department of Computer Science, University of Corunna, Spain (e-mail: cabalar@udc.es, concepcion.vidalm@udc.es)

Abstract

This paper studies the relation between two recent extensions of propositional Equilibrium Logic, a well-known logical characterisation of Answer Set Programming. In particular, we show how Temporal Equilibrium Logic, which introduces modal operators as those typically handled in Linear-Time Temporal Logic (LTL), can be encoded into Infinitary Equilibrium Logic, a recent formalisation that allows the use of infinite conjunctions and disjunctions. We prove the correctness of this encoding and, as an application, we further use it to show that the semantics of the temporal logic programming formalism called TEMPLOG is subsumed by Temporal Equilibrium Logic.

Type
Regular Papers
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

*

This research was partially supported by Spanish MEC project TIN2013-42149-P, Xunta de Galicia GPC2013/070, the French Spanish Laboratory for Advanced Studies in Information, Representation and Processing (LEA-IREP) and the Centre International de Mathématiques et Informatique de Toulouse (CIMI).

References

Aguado, F., Cabalar, P., Diéguez, M., Pérez, G., and Vidal, C. 2013. Temporal equilibrium logic: a survey. Journal of Applied Non-Classical Logics 23, 1–2, 224.CrossRefGoogle Scholar
Balbiani, P. and Diéguez, M. 2015. An axiomatisation of the logic of temporal here-and-there. (unpublished draft).Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Elsevier.CrossRefGoogle Scholar
Baudinet, M. 1992. A simple proof of the completeness of temporal logic programming. In Intensional Logics for Programming, del Cerro, L. F. and Penttonen, M., Eds. Clarendon Press, 5183.Google Scholar
Bieber, P., Fariñas del Cerro, L., and Herzig, A. 1988. MOLOG: a modal PROLOG. In 9th International Conference on Automated Deduction, Argonne, Illinois, USA, May 23-26, 1988, Proceedings. 762763.Google Scholar
Bozzelli, L. and Pearce, D. 2015. On the complexity of temporal equilibrium logic. In Proceedings of the 30th Annual ACM/IEEE Symposium of Logic in Computer Science (LICS'15) (July 6-10). Kyoto, Japan. (to appear).Google Scholar
Brewka, G., Eiter, T., and Truszczynski, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92103.CrossRefGoogle Scholar
Büchi, J. R. 1962. On a Decision Method in Restricted Second Order Arithmetic. In International Congress on Logic, Methodology, and Philosophy of Science. 111.Google Scholar
Cabalar, P. and Demri, S. 2011. Automata-based computation of temporal equilibrium models. In 21st International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR'11).Google Scholar
Cabalar, P. and Diéguez, M. 2011. STeLP - A Tool for Temporal Answer Set Programming. In Proceedings of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'11). 370375.Google Scholar
Cabalar, P. and Diéguez, M. 2014. Strong equivalence of non-monotonic temporal theories. In Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR'14).Google Scholar
Cabalar, P. and Vega, G. P. 2007. Temporal equilibrium logic: a first approach. In Proc. of the 11th International Conference on Computer Aided Systems Theory, (EUROCAST'07). LNCS (4739). 241248.Google Scholar
De Giacomo, G. and Vardi, M. Y. 2013. Linear temporal logic and linear dynamic logic on finite traces. In Proc. of the Twenty-Third Intl. Joint Conference on Artificial Intelligence (IJCAI'13). AAAI Press, 854860.Google Scholar
Fariñas del Cerro, L. 1986. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing 4, 1, 3550.CrossRefGoogle Scholar
Ferraris, P. 2005. Answer sets for propositional theories. In Proc. of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05). LNCS (vol. 3662). 119131.Google Scholar
Fujita, M., Kono, S., Tanaka, T., and Moto-oka, T. 1986. Tokio: Logic programming language based on temporal logic and its compilation into prolog. In Proc. of the 3rd Intl. Conf. on Logic Programming (LNAI 225). Springer-Verlag.Google Scholar
Gabbay, D. 1987. Modal and temporal logic programming. In Temporal Logics and their Applications, Galton, A., Ed. Academic Press, Chapter 6, 197237.Google Scholar
Gabbay, D., Pnueli, A., Shelah, S., and Stavi, J. 1980. On the temporal analysis of fairness. In Proceedings of the 7th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL'80). ACM, New York, NY, USA, 163173.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1993. Representing action and change by logic programs. Journal of Logic Programming 17, 2/3&4, 301321.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1998. Action languages. Linköping Electronic Articles in Computer and Information Science 3, 16 (October).Google Scholar
Harrison, A., Lifschitz, V., Pearce, D., and Valverde, A. 2014. Infinitary equilibrium logic. In Working Notes of Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP'14).Google Scholar
Harrison, A. J., Lifschitz, V., and Yang, F. 2014. The semantics of gringo and infinitary propositional formulas. In Proc. of the 14th Intl. Conf. on Principles of Knowledge Representation and Reasoning (KR'14), Vienna, Austria (July 20-24), Baral, C., Giacomo, G. D., and Eiter, T., Eds. AAAI Press.Google Scholar
Kamp, J. A. 1968. Tense logic and the theory of linear order. Ph.D. thesis, University of California at Los Angeles.Google Scholar
Karp, C. R. 1964. Languages with expressions of infinite length. Studies in logic and the foundations of mathematics. North-Holland Publication Company.Google Scholar
Lichtenstein, O., Pnueli, A., and Zuck, L. D. 1985. The glory of the past. In Proceedings of the Conference on Logic of Programs. Springer-Verlag, London, UK, UK, 196218.CrossRefGoogle Scholar
Manna, Z. and Pnueli, A. 1991. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag.Google Scholar
Marek, V. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: a 25-Year Perspective. Springer-Verlag, 169181.Google Scholar
Moszkowski, B. 1986. Executing Temporal Logic Programs. Cambridge University Press.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241273.CrossRefGoogle Scholar
Orgun, M. A. and Wadge, W. W. 1992. Theory and practice of temporal logic programming. In Intensional Logics for Programming, del Cerro, L. F. and Penttonen, M., Eds. Clarendon Press, Oxford, 2150.Google Scholar
Pearce, D. 1996. A new logical characterisation of stable models and answer sets. In Non monotonic extensions of logic programming. Proc. NMELP'96. (LNAI 1216). Springer-Verlag.Google Scholar
Pearce, D. 2006. Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47, 1–2, 341.CrossRefGoogle Scholar
Pearce, D. and Valverde, A. 2008. Quantified equilibrium logic and foundations for answer set programs. In Proc. of the 24th Intl. Conf. on Logic Programming, ICLP 2008, (Udine, Italy, December 9-13). Lecture Notes in Computer Science, vol. 5366. Springer, 546560.Google Scholar
Scott, D. and Tarski, A. 1958. The Sentential Calculus With Infinitely Long Expressions. Colloquium Mathematicae 6, 1, 165170.Google Scholar
Truszczyński, M. 2012. Connecting First-Order ASP and the Logic FO(ID) through Reducts. In Correct Reasoning - Essays on Logic-Based AI in Honour of Vladimir Lifschitz. Lecture Notes in Computer Science, vol. 7265. Springer, 543559.Google Scholar
van Emden, M. H. and Kowalski, R. A. 1976. The semantics of predicate logic as a programming language. Journal of the ACM 23, 733742.CrossRefGoogle Scholar
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