Equivalence in Answer Set Programming

  • Mauricio Osorio
  • Juan A. Navarro
  • José Arrazola
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2372)

Abstract

We study the notion of strong equivalence between two Answer Set programs and we show how some particular cases of testing strong equivalence between programs can be reduced to verify if a formula is a theorem in intuitionistic or classical logic. We present some program transformations for disjunctive programs, which can be used to simplify the structure of programs and reduce their size. These transformations are shown to be of interest for both computational and theoretical reasons. Then we propose how to generalize such transformations to deal with free programs (which allow the use of default negation in the head of clauses). We also present a linear time transformation that can reduce an augmented logic program (which allows nested expressions in both the head and body of clauses) to a program consisting only of standard disjunctive clauses and constraints.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Arrazola, J. Dix and M. Osorio. Confluent term rewriting systems for nonmonotonic reasoning. Computación y Sistemas, II(2–-3):299–324, 1999.Google Scholar
  2. 2.
    Y. Babovich, E. Erdem, and V. Lifschitz. Fages’ theorem and answer set programming. In Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, 2000.Google Scholar
  3. 3.
    C. Baral and M. Gelfond. Reasoning agents in dynamic domain. In J. Minker, editor, Logic Based Artificial Intelligence, pages 257–279. Kluwer, 2000.Google Scholar
  4. 4.
    S. Brass and J. Dix. Characterizations of the Disjunctive Stable Semantics by Partial Evaluation. Journal of Logic Programming, 32(3):207–228, 1997.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    S. Brass and J. Dix. Characterizations of the Disjunctive Well-founded Semantics: Confluent Calculi and Iterated GCWA. Journal of Automated Reasoning, 20(1):143–165, 1998.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    S. Brass, J. Dix, B. Freitag and U. Zukowski. Transformation-based bottom-up computation of the well-founded model. Theory and Practice of Logic Programming, 1(5):497–538, 2001.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Y. Dimopoulos, B. Nebel and J. Koehler. Encoding planning problems in nonmonotonic logic programs. In Proceedings of the Fourth European Conference on Planning, pages 169–181. Springer-Verlag, 1997.Google Scholar
  8. 8.
    J. Dix. A Classification-Theory of Semantics of Normal Logic Programs: II. Weak Properties. Fundamenta Informaticae, XXII(3):257–288, 1995.MathSciNetGoogle Scholar
  9. 9.
    J. Dix, J. Arrazola and M. Osorio. Confluent rewriting systems in non-monotonic reasoning. Computación y Sistemas, Volume II, No. 2–3:104–123, 1999.Google Scholar
  10. 10.
    J. Dix, M. Osorio and C. Zepeda. A General Theory of Confluent Rewriting Systems for Logic Programming and its Applications. Annals of Pure and Applied Logic, Volume 108, pages 153–188, 2001.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    M. Gelfond, M. Balduccini and J. Galloway. Diagnosing Physical Systems in A-Prolog. In T. Eiter, W. Faber and M. Truszczynski, editors, Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning, pages 213–226, Vienna, Austria, 2001.Google Scholar
  12. 12.
    M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In R. Kowalski and K. Bowen, editors, 5th Conference on Logic Programming, pages 1070–1080. MIT Press, 1988.Google Scholar
  13. 13.
    D. Jongh and A. Hendriks. Characterization of strongly equivalent logic programs in intermediate logics. http://turing.wins.uva.nl/lhendrik/, 2001.
  14. 14.
    V. Lifschitz. Foundations of logic programming. In Principles of Knowledge Representation, pages 69–127. CSLI Publications, 1996.Google Scholar
  15. 15.
    V. Lifschitz, D. Pearce and A. Valverde. Strongly equivalent logic programs. ACM Transactions on Computational Logic, 2:526–541, 2001.CrossRefMathSciNetGoogle Scholar
  16. 16.
    J. Lloyd. Foundations of Logic Programming. Springer, Berlin, 1987. 2nd edition.Google Scholar
  17. 17.
    M. Osorio, J. Nieves and C. Giannella. Useful transformation in answer set programming. In A. Provetti and T. Son, editors, Answer Set Programming: Towards Efficient and Scalable Knowledge Representation and Reasoning, pages 146–152. AAAI Press, Stanford, USA, 2001.Google Scholar
  18. 18.
    M. Osorio and F. Zacarias. High-level logic programming. In B. Thalheim and K.-D. Schewe, editors, FolKS, LNCS 1762, pages 226–240. Springer Verlag, Berlin, 2000.Google Scholar
  19. 19.
    A. Pettorossi and M. Proietti. Transformation of Logic Programs. In D. Gabbay, C. Hogger and J. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 5, pages 697–787. Oxford University Press, 1998.Google Scholar
  20. 20.
    C. Sakama and K. Inoue. Negation as Failure in the Head. Journal of Logic Programming, 35(1):39–78, 1998.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    P. Simons. Towards constraint satisfaction through logic programs and the stable model semantics. Technical Report 47, Helsinki University of Technology, Digital Systems Laboratory, August 1997.Google Scholar
  22. 22.
    L. Tang, V. Lifschitz and H. Turner. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence, 25:369–389, 1999.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    P. Taylor, J. Girard and Y. Lafont. Proofs and types. Cambridge University Press, 1989.Google Scholar
  24. 24.
    H. Zhang. Sato: A decision procedure for propositional logic. Association for Automated Reasoning Newsletter, 22:1–3, March 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Mauricio Osorio
    • 1
  • Juan A. Navarro
    • 1
  • José Arrazola
    • 1
  1. 1.CENTIAUniversidad de las AméricasCholula, PueblaMéxico

Personalised recommendations