On the computation of disjunctive stable models

  • N. Leone
  • P. Rullo
  • F. Scarcello
Theoretical Aspects 2
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1134)

Abstract

An efficient algorithm for the computation of the stable model semantics of disjunctive logic programs is designed. Both soundness and completeness of the proposed method is formally proven. The computational complexity of the algorithm is also analyzed. In general, the algorithm runs in single exponential time and polynomial space (in the worst case); moreover, on some known tractable classes of programs it runs in polynomial time.

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References

  1. 1.
    Bell, C., Nerode, A., Ng, R., Subrahmanian, V. S., Implementing Stable Semantics by Linear Programming, Proceedings of LPNMR '93, MIT Press, Lisbon, Portugal, July, 1993, pp. 23–42.Google Scholar
  2. 2.
    Bell, C., Nerode, A., Ng, R., Subrahmanian, V. S., Mixed Integer Programming Methods for Computing Nonmonotonic Deductive Databases, Journal ACM, Vol.41, N.6, Nov. 1994, pp.1178–1215.CrossRefGoogle Scholar
  3. 3.
    Buccafurri, F., Leone, N., Rullo, P., Stable Models and their Computation for Logic Programming with Inheritance and True Negation, Journal of Logic Programming, Vol 27(1), April 96, pp. 5–43.Google Scholar
  4. 4.
    Cho Le Winski, P., Marek, W., Mikitiuk, A., Truszczyński, M., Experimenting with Nonmonotonic Reasoning, Proc. 12th International Conference on Logic Programming, MIT Press, 1995.Google Scholar
  5. 5.
    Cuadrado, J., Pimentel, S., A Truth Maintenance System Based on Stable Models, Proc. 1989 North American Conf. on Logic Programming, pp. 274–290, 1989.Google Scholar
  6. 6.
    Dix, J. and Müller, M., Implementing Semantics of Disjunctive Logic Program s Using Fringes and Abstract Properties, Proceedings of LPNMR'93, MIT Press, Lisbon, Portugal, July, 1993, pp. 43–59.Google Scholar
  7. 7.
    Fernández, J.A., and Minker, J., Semantics of Disjunctive Deductive Databases, Proc. 4th Intl. Conference on Database Theory (ICDT-92), pp. 21–50, Berlin, October, 1992.Google Scholar
  8. 8.
    Fuentes, L.O., Applying Uncertainty Formalisms to Well-Defined Problems, manuscript, 1991.Google Scholar
  9. 9.
    Gelfond, M., Lifschitz, V., Classical Negation in Logic Programs and Disjunctive Databases, New Generation Computing, 9:365–385, 1991.Google Scholar
  10. 10.
    Inoue, K, Koshimura, M., Hasegawa, R., Embedding Negation as Failure into a Model Generation Theorem Prover, Proc. of CADE'92, June 1992, pp. 400–415.Google Scholar
  11. 11.
    Leone, N., Rullo, P., Safe Computation of the Well-Founded Semantics of DATA-LOG Queries, Information Systems, Vol. 17, N. 1, Pergamon Press, Gennaio 1992, pp. 17–31.Google Scholar
  12. 12.
    Leone, N., Rullo, P., Scarcello, F., Declarative and Fixpoint Characterizations of Disjunctive Stable Models, Proc. of ILPS'95, Portland, Oregon, December 4–7, 1995, pp. 399–413.Google Scholar
  13. 13.
    Leone, N., Rullo, P., Scarcello, F., Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics and Computation, Technical Report TR 96-14 ISI-CNR, 1996.Google Scholar
  14. 14.
    Minker, J., On Indefinite Data Bases and the Closed World Assumption, Proceedings of the 6th Conference on Automated Deduction (CADE-82), pp. 292–308, 1982.Google Scholar
  15. 15.
    Przymusinski, T. C., On the Declarative Semantics of Stratified Deductive Databases and Logic Programs, in Found. of deductive databases and logic programming, Morgan Kaufman, 1987, pp. 193–216Google Scholar
  16. 16.
    Przymusinska, H., Przymusinski, T. C., Weakly Perfect Model Semantics for Logic Programs, Proc. Fifth Int. Conf. and Symp. on Logic Programming, 1988.Google Scholar
  17. 17.
    Przymusinski, T., Stable Semantics for Disjunctive Programs, New Gen. Comp., 9:401–424, 1991.Google Scholar
  18. 18.
    Ross, K.A., Modular Stratification and Magic Sets for Datalog Programs with Negation, Proc. ACM Symposium on Principles of Database Systems 1990., 1990.Google Scholar
  19. 19.
    Ruiz, C., Minker, J., Computing Stable and Partial Stable Models of Extended Disjunctive Logic Programs, in Nonmonotonic Extensions of Logic Programming, LNCS, Springer, pp.205–229, 1995.Google Scholar
  20. 20.
    Saccá, D., Zaniolo, C., Stable Models and Nondeterminism in Logic Programs with Negation, Proc. ACM PODS, 1990.Google Scholar
  21. 21.
    Seipel, D., Minker, J., Ruiz., C., Model Generation and State Generation for Disjunctive Logic Programs, Tech. Rep. CS-TR-3546 UMIACS-TR-95-99, Dept. of Computer Science and Institute for Advanced Computer Studies, University of Maryland, U.S.A., 1995.Google Scholar
  22. 22.
    Stuber, J., Computing Stable Models by Program Transformation, Proc. ICLP'94, pp. 58–73.Google Scholar
  23. 23.
    Subrahmanian, V.S., Nau, D., Vago, C., WFS + Branch and Bound=Stable Models, IEEE Transactions on Knowledge and Data Engineering, 1995.Google Scholar
  24. 24.
    Van Gelder, A., Ross, K. A., Schlipf, J. S., The Well-Founded Semantics for General Logic Programs, Journal of ACM, 38(3):620–650, 1991.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • N. Leone
    • 1
  • P. Rullo
    • 2
  • F. Scarcello
    • 3
  1. 1.Institut für InformationssystemeTU WienWienAustria
  2. 2.DIMET - Università di Reggio CalabriaReggio CalabriaItaly
  3. 3.DEIS - Università della CalabriaRendeItaly

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