Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T12:00:42.338Z Has data issue: false hasContentIssue false
  • English
  • Français

A Logical Characterization of the Preferred Models of Logic Programs with Ordered Disjunction

Published online by Cambridge University Press:  23 September 2021

ANGELOS CHARALAMBIDIS Open the ORCID record for ANGELOS CHARALAMBIDIS [Opens in a new window] ,
PANOS RONDOGIANNIS  and
ANTONIS TROUMPOUKIS
ANGELOS CHARALAMBIDIS
Affiliation:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece (e-mails: a.charalambidis@di.uoa.gr, prondo@di.uoa.gr, antru@di.uoa.gr)
PANOS RONDOGIANNIS
Affiliation:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece (e-mails: a.charalambidis@di.uoa.gr, prondo@di.uoa.gr, antru@di.uoa.gr)
ANTONIS TROUMPOUKIS
Affiliation:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Athens, Greece (e-mails: a.charalambidis@di.uoa.gr, prondo@di.uoa.gr, antru@di.uoa.gr)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.

Keywords

ordered disjunctionanswer setslogic of here-and-therepreferences
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 629 - 645
Check for updates
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
© The Author(s), 2021. Published by Cambridge University Press

References

Aguado, F., Cabalar, P., Fandinno, J., Pearce, D., Pérez, G. and Vidal, C. 2019. Revisiting explicit negation in answer set programming. Theory and Practice of Logic Programming 19, 5–6, 908–924.CrossRefGoogle Scholar
Balduccini, M. and Mellarkod, V. S. 2003. Cr-prolog with ordered disjunction. In Answer Set Programming, Advances in Theory and Implementation, Proceedings of the 2nd Intl. ASP 2003 Workshop, Messina, Italy, September 26–28, 2003. CEUR Workshop Proceedings, vol. 78. CEUR-WS.org.Google Scholar
Brewka, G. 2002. Logic programming with ordered disjunction. In Proceedings of the Eighteenth National Conference on Artificial Intelligence and Fourteenth Conference on Innovative Applications of Artificial Intelligence, July 28 – August 1, 2002, Edmonton, Alberta, Canada. AAAI Press/The MIT Press, 100–105.Google Scholar
Brewka, G., Benferhat, S. and Berre, D. L. 2004. Qualitative choice logic. Artificial Intelligence 157, 1–2, 203–237.CrossRefGoogle Scholar
Brewka, G., Niemelä, I. and Syrjänen, T. 2004. Logic programs with ordered disjunction. Computational Intelligence 20, 2, 335–357.CrossRefGoogle Scholar
Cabalar, P. 2011. A logical characterisation of ordered disjunction. AI Communication 24, 2, 165–175.CrossRefGoogle Scholar
Faber, W., Tompits, H. and Woltran, S. 2008. Notions of strong equivalence for logic programs with ordered disjunction. In Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, September 16-19, 2008, Brewka, G. and Lang, J., Eds. AAAI Press, 433–443.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3/4, 365–386.Google Scholar
Heyting, A. 1930. Die formalen regeln der intuitionistischen logik. Sitzungsbericht PreuBische Akademie der Wissenschaften Berlin, physikalisch-mathematische Klasse II, 42–56.Google Scholar
Kärger, P., Lopes, N., Olmedilla, D. and Polleres, A. 2008. Towards logic programs with ordered and unordered disjunction. In Proceedings of Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP2008), 24th International Conference on Logic Programming (ICLP 2008). 46–60.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 4, 526–541.CrossRefGoogle Scholar
Nelson, D. 1949. Constructible falsity. The Journal of Symbolic Logic 14, 1, 16–26.CrossRefGoogle Scholar
Pearce, D. 1996. A new logical characterisation of stable models and answer sets. In Non-Monotonic Extensions of Logic Programming, NMELP 1996, Bad Honnef, Germany, September 5–6, 1996, Selected Papers. Lecture Notes in Computer Science, vol. 1216. Springer, 57–70.Google Scholar
van Emden, M. H. and Kowalski, R. A. 1976. The semantics of predicate logic as a programming language. Journal of ACM 23, 4, 733–742.CrossRefGoogle Scholar
Supplementary material: PDF

Charalambidis et al. Supplementary Materials

Charalambidis et al. Supplementary Materials

Download Charalambidis et al. Supplementary Materials(PDF)
PDF 276.1 KB