Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T06:00:30.299Z Has data issue: false hasContentIssue false
  • English
  • Français

On equivalence of infinitary formulas under the stable model semantics

Published online by Cambridge University Press:  16 May 2014

AMELIA HARRISON ,
VLADIMIR LIFSCHITZ  and
MIROSLAW TRUSZCZYNSKI
AMELIA HARRISON
Affiliation:
Department of Computer Science, University of Texas, Austin, TX, USA (e-mail: ameliaj@cs.utexas.edu)
VLADIMIR LIFSCHITZ
Affiliation:
Department of Computer Science, University of Texas, Austin, TX, USA (e-mail: ameliaj@cs.utexas.edu)
MIROSLAW TRUSZCZYNSKI
Affiliation:
Department of Computer Science, University of Kentucky, Lexington, Kentucky, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming.

Keywords

answer set programmingsemantics of aggregatesintuitionistic logicstrong equivalence
Type
Rapid Publications from the 12th International Conference on Logic Programming and Nonmonotonic Reasoning
Information
Theory and Practice of Logic Programming , Volume 15 , Issue 1 , January 2015 , pp. 18 - 34
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ferraris, P. 2005. Answer sets for propositional theories. In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), Springer, Berlin, Heidelberg, 119–131.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proceedings of International Logic Programming Conference and Symposium, Kowalski, R. and Bowen, K., Eds. MIT Press, Cambridge, MA, 1070–1080.Google Scholar
Harrison, A. 2013. On the semantics of Gringo and proving strong equivalence. In Theory and Practice of Logic Programming (Online Supplement). URL: http://journals.cambridge.org/downloadsup.php?file=/tlp2013035.pdf.Google Scholar
Harrison, A., Lifschitz, V. and Truszczynski, M. 2013. On equivalent transformations of infinitary formulas under the stable model semantics (preliminary report). In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), Springer, Berlin, Heidelberg, 387–394.Google Scholar
Hosoi, T. 1966. The axiomatization of the intermediate propositional systems Sn of Gödel. Journal of the Faculty of Science of the University of Tokyo 13, 183–187.Google Scholar
Kalmár, L. 1935. Über die Axiomatisierbarkeit des Aussagenkalküls. Acta Scientiarum Mathematicarum 7, 222–243.Google Scholar
Karp, C. R. 1964. Languages with Expressions of Infinite Length. North-Holland, Amsterdam, the Netherlands.Google Scholar
Lifschitz, V., Morgenstern, L. and Plaisted, D. 2008. Knowledge representation and classical logic. In Handbook of Knowledge Representation, van Harmelen, F., Lifschitz, V. and Porter, B., Eds. Elsevier, Philadelphia, PA, 3–88.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526–541.Google Scholar
Lifschitz, V. and Yang, F. 2012. Lloyd-Topor completion and general stable models. In Working Notes of the 5th Workshop of Answer Set Programming and Other Computing Paradigms (ASPOCP 2012).Google Scholar
Pearce, D. 1997. A new logical characterization of stable models and answer sets. In Non-Monotonic Extensions of Logic Programming (Lecture Notes in Artificial Intelligence, 1216), Dix, J., Pereira, L. and Przymusinski, T., Eds. Springer, Berlin, Germany, 57–70.Google Scholar
Scott, D. and Tarski, A. 1958. The sentential calculus with infinitely long expressions. Colloquium Mathematicae 6, 165–170.CrossRefGoogle Scholar
Truszczynski, M. 2012. Connecting first-order ASP and the logic FO(ID) through reducts. In Correct Reasoning: Essays on Logic-Based AI in Honor of Vladimir Lifschitz, Springer Berlin, Heidelberg, 543–559.CrossRefGoogle Scholar