Preferred Answer Sets for Ordered Logic Programs

  • Davy Van Nieuwenborgh
  • Dirk Vermeir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2424)

Abstract

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a “best” answer set.Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones.We showthat such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure as well as disjunction.We illustrate an application of the approach by considering database repairs, where minimal repairs are shown to correspond to preferred answer sets.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Marcelo Arenas, Leopoldo Bertossi, and Jan Chomicki. Specifying and querying database repairs using logic programs with exceptions. In Proceedings of the 4th International Conference on Flexible Query Answering Systems, pages 27–41, Warsaw, Octobre 2000. Springer-Verlag.Google Scholar
  2. 2.
    Thomas Eiter, Georg Gottlob, and Nicola Leone. Abduction from logic programs: Semantics and complexity. Theoretical Computer Science, 189(1–2):129–177, 1997.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    T. Eiter and G. Gottlob. Complexity results for disjunctive logic programming and application to nonmonotnic logics. In Proceedings of the 1983 International Logic Programming Symposium, pages 266–279, Vancouver, October 1993. MIT Press.Google Scholar
  4. 4.
    Michael Gelfond and Vladimir Lifschitz. The stable model semantics for logic programming. In Robert A. Kowalski and Kenneth A. Bowen, editors, Logic Programming, Proceedings of the Fifth International Conference and Symposium, pages 1070–1080, Seattle, Washington, August 1988. The MIT Press.Google Scholar
  5. 5.
    Robert A. Kowalski and Fariba Sadri. Logic programs with exceptions. In David H. D. Warren and Peter Szeredi, editors, Proceedings of the Seventh International Conference on Logic Programming, pages 598–613, Jerusalem, 1990. The MIT Press.Google Scholar
  6. 6.
    Els Laenens and Dirk Vermeir. Assumption-free semantics for ordered logic programs: On the relationship between well-founded and stable partial models. Journal of Logic and Computation, 2(2):133–172, 1992.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Vladimir Lifschitz. Answer set programming and plan generation. Journal of Artificial Intelligence, to appear.Google Scholar
  8. 8.
    Raymond Reiter. A theory of diagnosis from first principles. Artificial Intelligence, 32(1):57–95, 1987.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chiaki Sakama and Katsumi Inoue. An alternative approach to the semantics of disjunctive logic programs and deductive databases. Journal of Automated Reasoning, 13(1):145–172, 1994.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    M.H. van Emden and R. Kowalski. The semantics of predicate logic as a programming language. Journal of the Association for Computing Machinery, 23(4):733–742, 1976.MATHMathSciNetGoogle Scholar
  11. 11.
    M. De Vos and D. Vermeir. Semantic forcing in disjunctive logic programs. Computational Intelligence, 17(4):651–684, 2001.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Davy Van Nieuwenborgh
    • 1
  • Dirk Vermeir
    • 1
  1. 1.Dept. of Computer ScienceVrije Universiteit Brussel, VUBBrussel

Personalised recommendations