A family of three-valued autoepistemic logics

  • Piero A. Bonatti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 549)


A unifying semantic framework for 2 and 3-valued autoepistemic logics is introduced. For instance, the logics introduced in [8] and [2] belong to this framework. All the logics that derive from the framework enjoy the usual stability properties of autoepistemic logics.

A new logic (called κ2-logic) is derived from the schema. It is shown that κ2-logic solves a number of problems affecting existing logics. Finally, it will be shown that a very large class of theories has a least stable expansion in κ2-logic. We show how the least stable expansion can be obtained through a fixpoint construction.


Nonmonotonic Reasoning Autoepistemic Logics Logic Programming 


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  1. [1]
    P. Bonatti. Monotonicity in AE theories: preliminary report In Proc. GULP'90, V Convegno Nationale sulla Programmazione Logica.Google Scholar
  2. [2]
    P. Bonatti. A more general solution to the multiple expansion problem. In Proc. Workshop on Non-Monotonic Reasoning and Logic Programming, NACLP'90.Google Scholar
  3. [3]
    M. Gelfond. On Stratified Autoepistemic Theories. In Proceedings AAAI-87, 207–211, 1987.Google Scholar
  4. [4]
    M. Gelfond, V. Lifschitz. Logic programs with classical negation. In Proc. of the Int. Joint Conference on Logic Programming, Israel, 1990.Google Scholar
  5. [5]
    H. G. Herzberger. Notes on Naive Semantics. In the Journal of Phil. Logic 11 (1982), 61–102.Google Scholar
  6. [6]
    J. Jaffar, J. Lassez. Constraint Logic Programming. In Proc. of 14th POPL, p. 111–119. ACM 1987.Google Scholar
  7. [7]
    J. Lobo, J. Minker, A. Rajasekar. Extending the Semantics of Logic Programs to Disjunctive Logic Programs. In Proc. of 6th International Conference on Logic Programming, 1989.Google Scholar
  8. [8]
    R. Moore. Semantical considerations on nonmonotonic logics. In Artificial Intelligence 25, pp. 75–94, 1985.Google Scholar
  9. [9]
    T. Przymusinski. Three-valued formalisations of non-monotonic reasoning. In Proc. of KR'89 — First Int. Conf. on Principles of Knowledge Representation and Reasoning (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Piero A. Bonatti
    • 1
  1. 1.Dipartimento di InformaticaUniversita' di PisaPisaItaly

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