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Revisiting Explicit Negation in Answer Set Programming

Published online by Cambridge University Press:  20 September 2019

FELICIDAD AGUADO ,
PEDRO CABALAR ,
JORGE FANDINNO Open the ORCID record for JORGE FANDINNO [Opens in a new window] ,
DAVID PEARCE ,
GILBERTO PÉREZ  and
CONCEPCIÓN VIDAL
FELICIDAD AGUADO
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: aguado@udc.es, cabalar@udc.es)
PEDRO CABALAR
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: aguado@udc.es, cabalar@udc.es)
JORGE FANDINNO
Affiliation:
IRIT, University of Toulouse, CNRS, France (e-mail: jorge.fandinno@irit.fr) Universität Potsdam, Germany (e-mail: fandinno@uni-potsdam.de)
DAVID PEARCE
Affiliation:
Universidad Politécnica de Madrid, Spain (e-mail: david.pearce@upm.es)
GILBERTO PÉREZ
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: gperez@udc.es, eicovima@udc.es)
CONCEPCIÓN VIDAL
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: gperez@udc.es, eicovima@udc.es)
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Abstract

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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.

Keywords

Answer set programmingNon-monotonic reasoningEquilibrium logicExplicit negation
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 19 , Special Issue 5-6: 35th International Conference on Logic Programming , September 2019 , pp. 908 - 924
Creative Commons
Creative Common License - CCCreative Common License - BY
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 in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2019

Footnotes

*

This work was partially supported by MINECO, Spain, grant TIC2017-84453-P, Xunta de Galicia, Spain (GPC ED431B 2019/03 and 2016-2019 ED431G/01, CITIC). The third author is funded 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 and the Alexander von Humboldt Foundation.

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, 2–24.CrossRefGoogle Scholar
Cabalar, P. 2011. Functional answer set programming. Theory and Practice of Logic Programming 11, 2-3, 203–233.Google Scholar
Cabalar, P., Fandinno, J., and Fariñas del Cerro, L. 2019. Founded world views with autoepistemic equilibrium logic. In Proc. of the 15th International Conference on Logic Programming and Non-monotonic Reasoning (LPNMR’19) (June 3-7).Google Scholar
Cabalar, P., Fariñas del Cerro, L., Pearce, D., and Valverde, A. 2014. A free logic for stable models with partial intensional functions. In Proc. of the 14th European Conf. on Logics in Artificial Intelligence, JELIA 2014, Funchal, Madeira, Portugal, September 24-26, Fermé, E. and Leite, J., Eds. Lecture Notes in Computer Science, vol. 8761. Springer, 340–354.Google Scholar
Cabalar, P., Odintsov, S., and Pearce, D. 2006. Strong negation in well-founded and partial stable semantics for logic programs. In Proc. of the 10th Ibero-American Artificial Intelligence Conf. (IBERAMIA’06), Ribeiro Preto, Brazil. Lecture Notes in Artificial Intelligence, vol. 4140. 592–601.Google Scholar
Fariñas del Cerro, L. and Herzig, A. 1996. Combining classical and intuitionistic logic, or: Intuitionistic implication as a conditional. In Proc. of the 1st Intl. Workshop on Frontiers of Combining Systems, Munich, Germany, March 26-29, Baader, F. and Schulz, K. U., Eds. Applied Logic Series, vol. 3. Kluwer Academic Publishers, 93–102.Google Scholar
Fariñas del Cerro, L., Herzig, A., and Su, E. I. 2015. Epistemic equilibrium logic. In Proc. of the Intl. Joint Conference on Artificial Intelligence (IJCAI’15). AAAI Press, 2964–2970.Google Scholar
Ferraris, P. 2005. Answer sets for propositional theories. In Proc. of the 8th Intl. Conf. on Logic Programming and Nonmonotonic Reasoning (LPNMR’05), Baral, C., Greco, G., Leone, N., and Terracina, G., Eds. Lecture Notes in Computer Science, vol. 3662. Springer, 119–131.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of the 5th Intl. Conference on Logic Programming (ICLP’88). 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Comput. 9, 3/4, 365–386.Google Scholar
Gelfond, M. and Lifschitz, V. 1993. Representing action and change by logic programs. Journal of Logic Programming 17, 2/3&4, 301–321.Google Scholar
Heyting, A. 1930. Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 42–56.Google Scholar
Lifschitz, V., Pearce, D., and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 4, 526–541.Google Scholar
Lifschitz, V., Tang, L. R., and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 3–4, 369–389.CrossRefGoogle Scholar
Marek, V. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. Springer-Verlag, 169–181.Google Scholar
Nelson, D. 1949. Constructible falsity. Journal of Symbolic Logic 14, 1626.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. AMAI 25, 241–273.Google Scholar
Odintsov, S. P. and Pearce, D. 2005. Routley semantics for answer sets. In Proc. of the 8th Logic Programming and Nonmonotonic Reasoning, LPNMR 2005, Diamante, Italy, Baral, C., Greco, G., Leone, N., and Terracina, G., Eds. Lecture Notes in Computer Science, vol. 3662. Springer, 343–355.Google Scholar
Ortiz, M. and Osorio, M. 2007. Strong negation and equivalence in the safe belief semantics. Journal of Logic and Computation 17, 499–515.Google Scholar
Pearce, D. 1997. A new logical characterisation of stable models and answer sets. In NMELP. Lecture Notes in Computer Science, vol. 1216. Springer, 57–70.Google Scholar
Pereira, L. M. and Alferes, J. J. 1992. Well founded semantics for logic programs with explicit negation. In Proceedings of the European Conference on Artificial Intelligence (ECAI’92). John Wiley & Sons, Montreal, Canada, 102–106.Google Scholar
Vakarelov, D. 1977. Notes on N-lattices and constructive logic with strong negation. Studia logica 36, 1-2, 109–125.Google Scholar
Vorob’ev, N. 1952a. A constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR 85, 465–468.Google Scholar
Vorob’ev, N. 1952b. The problem of deducibility in constructive propositional calculus with strong negation (in russian). Doklady Akademii Nauk SSR 85, 689–692.Google Scholar