Abstract
We extend a theorem by François Fages about the relationship between the completion semantics and the answer set semantics of logic programs to a class of programs with nested expressions permitted in the bodies of rules. Fages’ theorem is important from the perspective of answer set programming:whenever the two semantics are equivalent, answer sets can be computed by propositional solvers,such as sato, instead of answer set solvers, such as smodels. The need to extend Fages theorem to programs with nested expressions is related to the use of choice rules in the input language of SMODELS.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Krzysztof Apt, Howard Blair,and Adrian Walker.Towards a theory of declarative knowledge. In Jack Minker,editor,Foundations of Deductive Databases and Logic Programming,pages 89–148.Morgan Kaufmann, San Mateo,CA,1988.
Yuliya Babovich, Esra Erdem,and Vladimir Lifschitz. Fages’ theorem and answer set programming. In Proc. NMR-2000, 2000.
Roberto Bayardo and Robert Schrag.Using CSP look-back techniques to solve realworld SAT instances. In Proc. IJCAI-97,pages 203–208,1997.
Keith Clark.Negation as failure. In Herve Gallaire and Jack Minker,editors,Logic and Data Bases,pages 293–322.Plenum Press, New York,1978.
Marc Denecker and Bert Van Nuffelen.Experiments for integration CLP and abduction.10 In Krysztof R. Apt, Antonios C. Kakas, Eric Monfroy,and Francesca Rossi, editors,Proceedings of the 1999 ERCIM/COMPULOG workshop on Constraints, pages 1–15,1999.
Thomas Eiter, Nicola Leone, Christinel Mateis, Gerald Pfeifer,and Francesco Scarcello.A deductive system for non-monotonic reasoning. In Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning,pages 363–374. Springer-Verlag, 1997
François Fages.Consistency of Clark’s completion and existence of stable models. Journal of Methods of Logic in Computer Science,1:51–60,1994.
Paolo Ferraris and Vladimir Lifschitz.Weight constraints as nested expressions.11 Unpublished draft,2001.
Michael Gelfond and Vladimir Lifschitz.The stable model semantics for logic programming. In Robert Kowalski and Kenneth Bowen,editors,Logic Programming: Proc. Fifth Int’l Conf. and Symp.,pages 1070–1080,1988.
Vladimir Lifschitz, Lappoon R. Tang,and Hudson Turner.Nested expressions in logic programs.Annals of Mathematics and Artificial Intelligence,25:369–389,1999.
Vladimir Lifschitz.Answer set planning. In Proc. ICLP-99,pages 23–27,1999.
John Lloyd and Rodney Topor.Making Prolog more expressive.Journal of Logic Programming,3:225–240,1984.
Ilkka Niemelä and Patrik Simons.Efficient implementation of the well-founded and stable model semantics. In Proc. Joint Int’l Conf. and Symp. on Logic Programming, pages 289–303,1996.
Nikolay Pelov, Emmanuel De Mot,and Marc Denecker.Logic programming approaches for representing and solving constraint satisfaction problems:a comparison.12 In Parigot M. and Voronkov A.,editors,Proceedings of the 7th International Conference on Logic for Programming and Automated Reasoning,volume 1955 of Lecture Notes in Artificial Intelligence,pages 225–239. Springer,2000.
Pascal van Hentenryck.Constraint Satisfaction in Logic Programming. MIT Press, 1989.
Hantao Zhang.SATO:An efficient propositional prover. In Proc. CADE-97,1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Erdem, E., Lifschitz, V. (2001). Fages’ Theorem for Programs with Nested Expressions. In: Codognet, P. (eds) Logic Programming. ICLP 2001. Lecture Notes in Computer Science, vol 2237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45635-X_24
Download citation
DOI: https://doi.org/10.1007/3-540-45635-X_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42935-7
Online ISBN: 978-3-540-45635-3
eBook Packages: Springer Book Archive