New Generation Computing

, Volume 11, Issue 2, pp 107–124 | Cite as

On the autoepistemic reconstruction of logic programming

  • Y. J. Jiang
Regular Papers


Current semantics of logic programs normally ignore thesyntactical aspects of the programs. As a result, only the meanings ofsome well-behaved programs can be captured by these semantics. In this paper however, we propose a new semantics of logic programs that can reflectsome of the syntactical behaviours of the programs. The central notion of the semantics is the concept of aneutral clause p ← A which does not affect the behaviour of p in a program. The logic that underlies the semantics is based on anintensional extension of Levesque’s autoepistemicpredicate logic. It differs from existing autoepistemic logics in that it isquantificational andconstructive. We will also compare and contrast our semantics with some well-known semantics. In particular, we will show how to capture the undefined value of a logic program without resorting to a three-valued nonmonotonic formalism. This is achieved by translating an incoherent AE logic program to a program with multiple AE extensions whose intersection can then be used to characterize the undefined value of a logic program.


Negation as Failure Semantics of Logic Programs Nonmonotonic Reasoning Autoepistemic Predicate Logic Closed World Assumption Completion Semantics Stable Model Semantics Stratification Well-founded Semantics Three-valued Autoepistemic Semantics 


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  1. 1).
    Apt, K., et al “Towards a Theory of Declarative Knowledge” inFoundation of Deductive and Logic Programming (J. Minker, ed.), Morgan Kaufmann, pp. 89–142, 1988.Google Scholar
  2. 2).
    Bonanti, P., “Autoepistemic Logics as a Unifying Framework for the Semantics of Logic Programs,”ICLP 1992.Google Scholar
  3. 3).
    Clark, K., “Negation as Failure,” inLogic and Database (H. Galliare and J. Minker, eds.), Plenum Press, New York, pp. 293–322, 1978.Google Scholar
  4. 4).
    Dung, P. and Kanchanasutt, “A Fixpoint Semantics for Logic Programs with Negation,”9th TCS&ST, India, LNCS Notes, 1989.Google Scholar
  5. 5).
    van Emden, M. and Kowalski, R., “The Semantics of Predicate Logic as a Programming Language,”JACM, 23, 4, pp. 733–742, 1976.MATHCrossRefGoogle Scholar
  6. 6).
    Fitting, M., “A Kripke-Kleene Semantics for Logic Programs.”J. Logic Program 2, pp. 295–312, 1985.MATHCrossRefMathSciNetGoogle Scholar
  7. 7).
    Gabbay, D.,Modal Probability Foundations for Negation as Failure, Dept. of Computing, Imperial College, London, 1986.Google Scholar
  8. 8).
    Gelfond, M., “On Stratified Autoepistemic Theories,”AAAI 87, 1987.Google Scholar
  9. 9).
    Gelfond, M. and Lifschitz, V., “The Stable Model Semantics of Logic Programming,”Int. Conf. on Logic Programming, 1988.Google Scholar
  10. 10).
    Jiang, Y. J., “An Intensional Autoepistemic Predicate Logic,” to appear, 1991.Google Scholar
  11. 11).
    Jiang, Y. J., “An International Epistemic Logic,”Studia Logica Vol. 2, 1993.Google Scholar
  12. 12).
    Kunen, K., “Negation in Logic Programming,”J. of Logic Programming 4, pp. 289–308, 1987.MATHCrossRefMathSciNetGoogle Scholar
  13. 13).
    Konolige, K., “Resolution and Quantified Epistemic Logics,”8th Int. Conf. on Automated Deduction, LNCS Note 230, pp. 199–208, 1986.MathSciNetGoogle Scholar
  14. 14).
    Konolige, K. “On the Relationship between Circumscription and AE Logic,”IJCAI 85, 1989.Google Scholar
  15. 15).
    Levesque, H. J., “All I Know: Abridged Report,”AAAI 87, a full version, Dept. of Comp. Science, Toronto University, 1987.Google Scholar
  16. 16).
    Lifschitz, V., “Between Circumscription and Autoepistemic Logic,”1st Int. Conf. on Principles of Knowledge Representation (Reiter et al., eds.), 1989.Google Scholar
  17. 17).
    Marek, W. and Truszczynski, “Stable Semantics for Logic Programs and Default Theories,”NACLP 89, 1989.Google Scholar
  18. 18).
    Moore, R. C., “Semantic Considerations of Non-monotonic Logic,”Artificial Intelligence, 25, 1, 1985.CrossRefGoogle Scholar
  19. 19).
    Moore, R. C., “Autoepistemic Logic,”SRI 3068, 1986.Google Scholar
  20. 20).
    Niemela, I., “Autoepistemic Predicate Logic,”ECAI 88, pp. 595–599, 1988.Google Scholar
  21. 21).
    Prymusinski, T., “Perfect Model Semantics,”ICLP 1988, 1988.Google Scholar
  22. 22).
    Przymusinski, T., “Nonmonotonic Formalisms and Logic Programming,”ICLP 89, 1989.Google Scholar
  23. 23).
    Przymusinski, H. and Przymusinski, T., “Weakly Perfect Model Semantics for Logic Programs,”ICLP 1988, 1988.Google Scholar
  24. 24).
    Przymusinski, T., “Three-valued Nonmonotonic Formalisms and Sémantics of Logic Programs,”Artificial Intelligence 49, pp. 309–343, 1991.MATHCrossRefMathSciNetGoogle Scholar
  25. 25).
    Reiter, R., “A Logic for Default Reasoning,”Artificial Intelligence, 13, 1980.Google Scholar
  26. 26).
    Reiter, R., “Closed World Assumption,”Logic and Database (H. Galliare and J. Minker, eds.), Plenum Press, New York, pp. 293–322, 1988.Google Scholar
  27. 27).
    Van Gelder, A., et al., “The Well-founded Semantics for General Logic Programs,”JACM 38, pp. 620–650, 1991.MATHGoogle Scholar
  28. 28).
    Marek, W., and Subrahmanian, V., “The Relationship between Logic Program Semantics and Nonmonotonic Reasoning,”ICLP 89, pp. 600–617, 1989.MathSciNetGoogle Scholar

Copyright information

© Ohmsha, Ltd. and Springer 1993

Authors and Affiliations

  • Y. J. Jiang
    • 1
  1. 1.Department of ComputingImperial CollegeLondonUK

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