New Generation Computing

, Volume 9, Issue 3–4, pp 365–385 | Cite as

Classical negation in logic programs and disjunctive databases

  • Michael Gelfond
  • Vladimir Lifschitz
Special Issue

Abstract

An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter.

Keywords

Disjunctive Databases Incomplete Information Logic Programming Negation as Failure Nonmonotonic Reasoning Stable Models 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1).
    Bidoit, N. and Froidevaux, C., “Minimalism Subsumes Default Logic and Cricumscription,” inProc. of LICS-87, pp. 89–97, 1987.Google Scholar
  2. 2).
    Bidoit, N. and Froidevaux, C., “Negation by Default and Nonstratifiable Logic Programs,”Technical Report, 437, Université Paris XI, 1988.Google Scholar
  3. 3).
    Blair, H. and Subrahmanian, V. S., “Paraconsistent Logic Programming,”Theoretical Computer Science, 68, pp. 135–154, 1989.MATHCrossRefMathSciNetGoogle Scholar
  4. 4).
    Fitting, M., “A Kripke-Kleene Semantics for Logic Programs,”Journal of Logic Programming, 2, 4, pp. 295–312, 1985.MATHCrossRefMathSciNetGoogle Scholar
  5. 5).
    Gelfond, M. and Lifschitz, V., “The Stable Model Semantics for Logic Programming,” inLogic Programming (R. Kowalski and K. Bowen, eds.):Proc. of the Fifth Int’l Conf. and Symp., pp. 1070–1080, 1988.Google Scholar
  6. 6).
    Gelfond, M. and Lifschitz, V., “Compiling Circumscriptive Theories into Logic Programs,” inNon-Monotonic Reasoning (M. Reinfrank, J. de Kleer, M. Ginsberg and E. Sandewall, eds.):2nd International Workshop (Lecture Notes in Artificial Intelligence, 346), Springer-Verlag, pp. 74–99, 1989.Google Scholar
  7. 7).
    Gelfond, M. and Lifschitz, V., “Logic Programs with Classical Negation,” inLogic Programming (D. Warren and P. Szeredi, eds.):Proc. of the Seventh Int’l Conf., pp. 579–597, 1990.Google Scholar
  8. 8).
    Gelfond, M., “On Stratified Autoepistemic Theories,” inProc. AAAI-87, pp. 207–211, 1987.Google Scholar
  9. 9).
    Gelfond, M., “Autoepistemic Logic and Formalization of Commonsense Reasoning,” inNon-Monotonic Reasoning (M. Reinfrank, J. de Kleer, M. Ginsberg and E. Sandewall, eds.):2nd International Workshop (Lecture Notes in Artificial Intelligence, 346), Springer-Verlag, pp. 176–186, 1989.Google Scholar
  10. 10).
    Kowalski, R. and Sadri, F., “Logic Programs with Exceptions,” inLogic Programming (D. Warren and P. Szeredi, eds.):Proc. of the Seventh Int’l Conf., pp. 598–613, 1990.Google Scholar
  11. 11).
    Kowalski, R., “The Treatment of Negation in Logic Programs for Representing Legislation,” inProc. of the Second Int’l Conf. on Artificial Intelligence and Law, pp. 11–15, 1989.Google Scholar
  12. 12).
    Lifschitz, V., “Between Circumscription and Autoepistemic Logic,” inProc. of the First Int’l Conf. on Principles of Knowledge Representation and Reasoning (R. Brachman, H. Levesque and R. Reiter, eds.), pp. 235–244, 1989.Google Scholar
  13. 13).
    Lin, F. and Shoham, Y., “Argument Systems: A Uniform Basis for Nonmonotonic Reasoning,” inProc. of the First Int’l Conf. on Principles of Knowledge Representation and Reasoning (R. Brachman, H. Levesque and R. Reiter, eds.), pp. 245–255, 1989.Google Scholar
  14. 14).
    Lloyd, J.,Foundations of Logic Programming, Springer-Verlag, 1984.Google Scholar
  15. 15).
    Marek, W. and Truszczyński, M., “Autoepistemic Logic, Defaults and Truth Maintenance,”Manuscript, 1989.Google Scholar
  16. 16).
    Marek, W. and Truszczyński, M., “Relating Autoepistemic and Default Logic,” inProc. of the First Int’l Conf. on Principles of Knowledge Representation and Reasoning (R. Brachman, H. Levesque and R. Reiter, eds.), pp. 276–288, 1989.Google Scholar
  17. 17).
    McCarthy, J., “Applications of Circumscription to Formalizing Common Sense Knowledge,”Artificial Intelligence, 26, 3, pp. 89–116, 1986.CrossRefMathSciNetGoogle Scholar
  18. 18).
    Minker, J., “On Indefinite Data Bases and the Closed World Assumption,” inProc. of CADE-82, pp. 292–308, 1982.Google Scholar
  19. 19).
    Moore, R., “Semantical Considerations on Nonmonotonic Logic,”Artificial Intelligence, 25, 1, pp. 75–94, 1985.MATHCrossRefMathSciNetGoogle Scholar
  20. 20).
    Poole, D. and Goebel, R., “Gracefully Adding Negation and Disjunction to Prolog,” inProc. of the Third Int’l Conf. on Logic Programming (E. Shapiro, ed.), pp. 635–641, 1986.Google Scholar
  21. 21).
    Przymusinski, T., “On the Relationship between Logic Programming and Non-Monotonic Reasoning,” inProc. AAAI-88, pp. 444–448, 1988.Google Scholar
  22. 22).
    Przymusinski, T., “Three-Valued Formalizations of Non-Monotonic Reasoning and Logic Programming,” inProc. of the First Int’l Conf. on Principles of Knowledge Representation and Reasoning (R. Brachman, H. Levesque and R. Reiter, eds.), pp. 341–348, 1989.Google Scholar
  23. 23).
    Przymusinski, T., “Extended Stable Semantics for Normal and Disjunctive Programs,” inLogic Programming (D. Warren and P. Szeredi, eds.):Proc. of the Seventh Int’l Conf., pp. 459–477, 1990.Google Scholar
  24. 24).
    Reiter, R., “On Closed World Data Bases,” inLogic and Data Bases (H. Gallaire and J. Minker, eds.), Plenum Press, New York, pp. 119–140, 1978.Google Scholar
  25. 25).
    Reiter, R., “A Logic for Default Reasoning,”Artificial Intelligence, 13, 1, 2, pp. 81–132, 1980.MATHCrossRefMathSciNetGoogle Scholar
  26. 26).
    Van Gelder, A., Ross, K. and Schlipf, J., “The Well-Founded Semantics for General Logic Programs,”Journal of ACM, 1991, Vol. 38 No. 3 July 1991, pp. 620–650, 1991.MATHGoogle Scholar
  27. 27).
    Wagner, G., “The Two Sources of Nonmonotonicity in Vivid Logic: Weak Falsity and Inconsistency Handling,” inProc. of the Workshop on Nonmonotonic Reasoning (G. Brewka and H. Freitag, eds.), 1989.Google Scholar

Copyright information

© Ohmsha, Ltd. and Springer 1991

Authors and Affiliations

  • Michael Gelfond
    • 1
  • Vladimir Lifschitz
    • 2
  1. 1.University of Texas at El PasoEl Paso
  2. 2.University of Texas at AustinAustin

Personalised recommendations