On the relationship between well-founded and stable partial models

  • E. Laenens
  • D. Vermeir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 495)


The central issue of this paper is the definition of a new unifying semantics for ordered logic programs, called assumption-free semantics, capable of capturing different interesting semantics such as the well-founded and stable (partial model) semantics. It turns out that every ordered program possesses exactly one minimal assumption-free partial model which we call the well-founded partial model and one or more maximal assumption-free partial models called stable partial models. Moreover, this stable model semantics can be viewed as taking the best of the previous approaches for ordered programs while keeping their (common) underlying intuition. It is shown that the new concepts for ordered programs are proper generalizations of the corresponding concepts for classical logic programs, thus giving a new unifying definition for the traditional notions of well-founded and stable (partial) models. Furthermore, we discuss the relationship between stable and well-founded partial models, the main result being that the intersection of all stable partial models is exactly the well-founded partial model in all cases but a very special type of ordered programs, and map the results to the more restricted class of traditional logic programs.


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  1. Ben00a.
    M. Ben-Jacob and M. Fitting, “Stratified and three-valued logic programming semantics,” Proc. 5th Int. Conf. and Symp. on Logic Programming, pp. 1054–1068, 1988.Google Scholar
  2. Gel88a.
    A. Van Gelder, K. Ross, and J. S. Schlipf, “Unfounded Sets and Well-Founded Semantics for General Logic Programs,” in Proc. of the Symposium on Principles of Database Systems, pp. 221–230, 1988.Google Scholar
  3. Gel88b.
    M. Gelfond and V. Lifschitz, “The Stable Model Semantics for Logic Programming,” in Proc. of the Intl. Conf. on Logic Programming, pp. 1071–1079, 1988.Google Scholar
  4. Lae89a.
    E. Laenens and D. Vermeir, A Fixpoint Semantics of Ordered Logic, 1989. University of Antwerp, UIA Tech. Report 89-27Google Scholar
  5. Lae90a.
    E. Laenens and D. Vermeir, “A Fixpoint Semantics of Ordered Logic,” Journal of Logic and Computation, vol. 1, no. 2, pp. 159–185, 1990.Google Scholar
  6. Lae90b.
    E. Laenens, D. Sacca, and D. Vermeir, “Extending logic programming,” in Proceedings of the SIGMOD conference, pp. 184–193, 1990.Google Scholar
  7. Lae90c.
    E. Laenens and D. Vermeir, Assumption-free semantics for ordered logic programs: on the relationship between well-founded and stable partial models, 1990. University of Antwerp, Tech. Report 90-19Google Scholar
  8. Lae90d.
    E. Laenens, Foundations of Ordered Logic, 1990. PhD Thesis, University of Antwerp UIAGoogle Scholar
  9. Llo87a.
    J.W. Lloyd, in Foundations of Logic Programming, Springer Verlag, 1987.Google Scholar
  10. Nut88a.
    D. Nute, “Defeasible reasoning and decision support systems,” Decision support systems, vol. 4, pp. 97–110, 1988.CrossRefGoogle Scholar
  11. Prz89a.
    T. Przymusinski, “Three-Valued Formalizations of Non-Monotonic Reasoning and Logic Programming,” Proc. 1st Int. Conference on Principles of Knowledge Representation and Reasoning, pp. 341–349, 1989.Google Scholar
  12. Prz88a.
    T. C. Przymusinski, “Perfect Model Semantics,” in Proc. of the Intl. Conf. on Logic Programming, 1988.Google Scholar
  13. Prz89b.
    T. C. Przymusinski, “Every logic program has a natural stratification and an iterated fixed point model,” in Proc. of the Symposium on Principles Of Database Systems, pp. 11–21, 1989.Google Scholar
  14. Rei78a.
    R. Reiter, “On closed world databases,” Logic and Databases, pp. 55–76, Plenum, New York, 1978. Also in ‘Readings in nonmonotonic reasoning', M.L. GinsbergGoogle Scholar
  15. Sac90a.
    D. Sacca and C. Zaniolo, “Stable models and Non-determinism for logic programs with negation,” Proc. ACM Symp. on Principles of Database Systems, 1990.Google Scholar
  16. Ver89a.
    D. Vermeir, D. Nute, and P. Geerts, “A logic for defeasible perspectives,” in Proc. of the 1988 Tubingen Workshop on Semantic Networks and Nonmonotonic Reasoning, Vol. 1, pp. 1–27, SNS-Bericht 89-48, 1989.Google Scholar
  17. Ver90a.
    D. Vermeir, D. Nute, and P. Geerts, “Modeling Defeasible Reasoning with Multiple Agents,” in Proc. of the HICSS, Vol. III, pp. 534–543, 1990.Google Scholar
  18. You90a.
    Jia-Huai You and Li Yan Yuan, “Three-Valued Formalization of Logic Programming: Is It Needed?,” in Proc. of the PODS'90 conference, pp. 172–182, 1990.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • E. Laenens
    • 1
  • D. Vermeir
    • 1
  1. 1.Dept. of Math. and Computer ScienceUniversity of Antwerp, UIAWilrijkBelgium

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