Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T05:12:51.420Z Has data issue: false hasContentIssue false
  • English
  • Français

Guarded resolution for Answer Set Programming

Published online by Cambridge University Press:  24 March 2010

V. W. MAREK  and
J. B. REMMEL
V. W. MAREK
Affiliation:
Department of Computer Science, University of Kentucky, Lexington, KY 40506, USA (e-mail: [email protected])
J. B. REMMEL
Affiliation:
Departments of Mathematics and Computer Science, University of California at San Diego, La Jolla, CA 92903, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate a proof system based on a guarded resolution rule and show its adequacy for the stable semantics of normal logic programs. As a consequence, we show that Gelfond–Lifschitz operator can be viewed as a proof-theoretic concept. As an application, we find a propositional theory EP whose models are precisely stable models of programs. We also find a class of propositional theories 𝓒P with the following properties. Propositional models of theories in 𝓒P are precisely stable models of P, and the theories in 𝓒T are of the size linear in the size of P.

Keywords

guarded resolutionproof-theory for Answer Set Programming
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 11 , Issue 1 , January 2011 , pp. 111 - 123
Copyright
Copyright © Cambridge University Press 2010

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

Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving, Cambridge University Press.CrossRefGoogle Scholar
Brass, J. and Dix, J. 1999. Semantics of (Disjunctive) logic programs based on partial evaluation. Journal of Logic Programming 40, 1–46.CrossRefGoogle Scholar
Davis, M., Logemann, G. and Loveland, D. W. 1962. A machine program for theorem-proving. Communications of the ACM 5 (7), 394–397.CrossRefGoogle Scholar
Dowling, W. F. and Gallier, J. H. 1984. Linear time algorithms for testing satisfiability of propositional Horn formulae. Journal of Logic Programming 1, 267–284.CrossRefGoogle Scholar
Dung, P. M. and Kanchansut, K. 1989. A fixpoint approach to declarative semantics of logic programs. In Proc. of North American Conference on Logic Programming, Lusk, E. L. and Overbeek, R. A., Eds. MIT Press, 604–625.Google Scholar
Erdem, E. and Lifschitz, V. 2003. Tight logic programs. Theory and Practice of Logic Programming 3, 499–518.CrossRefGoogle Scholar
Fages, F. 1994. Consistency of Clark's completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60.Google Scholar
Ferraris, P., Lee, J. and Lifschitz, V. 2006. A generalization of Lin–Zhao theorem. Annals of Mathematics and Artificial Intelligence 47, 79–101.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. of the Fifth International Conference and Symposium on Logic Programming. Kowalski, R. A. and Bowen, K. A., Eds. MIT Press, 1070–1080.Google Scholar
Karp, C. 1964. Languages with Expressions of Infinitary length. North-Holland, Amsterdam.Google Scholar
Lifschitz, V. 2008. Twelve definitions of a stable model. In 24th International Conference on Logic Programming, ICLP 2008, de la Banda, M. Garcia and Pontelli, E., Eds. Lecture Notes in Computer Science, vol. 5366. Springer, 37–51.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526–541.CrossRefGoogle Scholar
Lifschitz, V. and Razborov, A. 2006. Why are there so many loop formulas. Annals of Mathematics and Artificial Intelligence 7, 261–268.Google Scholar
Lin, F. and Zhao, Y. 2004. ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157 (1-2), 115–137.CrossRefGoogle Scholar
Marek, V. W. and Remmel, J. B. 2010. An application of proof-theory in answer set programming. Preliminary version at arXiv:0905.4076.Google Scholar
Marek, V. W. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm, Series Artificial Intelligence, Springer-Verlag, 375–398.CrossRefGoogle Scholar
Moskewicz, M. W., Madigan, C. F., Zhao, Y., Zhang, L. and Mali, S. 2001. Chaff: Engineering an efficient SAT solver. In Proc. of the 38th Design Automation Conference, DAC 2001, ACM Press, 530–535.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25 (3,4), 241–273.CrossRefGoogle Scholar
Truszczynski, M. 2006. Strong and uniform equivalence of nonmonotonic theories – an algebraic approach. Annals of Mathematics and Artificial Intelligence 48 (3-4), 245–265.CrossRefGoogle Scholar