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The Approximate Well-Founded Semantics for Logic Programs with Uncertainty

  • Yann Loyer
  • Umberto Straccia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)

Abstract

The management of uncertain information in logic programs becomes to be important whenever the real world information to be represented is of imperfect nature and the classical crisp true, false approximation is not adequate. A general framework, called Parametric Deductive Databases with Uncertainty (PDDU) framework [10], was proposed as a unifying umbrella for many existing approaches towards the manipulation of uncertainty in logic programs. We extend PDDU with (non-monotonic) negation, a well-known and important feature of logic programs. We show that, dealing with uncertain and incomplete knowledge, atoms should be assigned only approximations of uncertainty values, unless some assumption is used to complete the knowledge. We rely on the closed world assumption to infer as much default “false” knowledge as possible. Our approach leads also to a novel characterizations, both epistemic and operational, of the well-founded semantics in PDDU, and preserves the continuity of the immediate consequence operator, a major feature of the classical PDDU framework.

Keywords

Logic Program Logic Programming Ground Atom Combination Function Deductive Database 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Belnap, N.D.: How a computer should think. In: Ryle, G. (ed.) Contemporary aspects of philosophy, pp. 30–56. Oriel Press, Stocksfield (1977)Google Scholar
  2. 2.
    Dubois, D., Lang, J., Prade, H.: Towards possibilistic logic programming. In: Proc. of the 8th Int. Conf. on Logic Programming (ICLP 1991), pp. 581–595 (1991)Google Scholar
  3. 3.
    Fitting, M.: The family of stable models. J. of Logic Programming 17, 197–225 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Fitting, M.: A Kripke-Kleene-semantics for general logic programs. J. of Logic Programming 2, 295–312 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. Of the 5th Int. Conf. on Logic Programming, pp. 1070–1080 (1988)Google Scholar
  6. 6.
    Ginsberg, M.L.: Multi-valued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265–316 (1988)CrossRefGoogle Scholar
  7. 7.
    Kifer, M., Li, A.: On the semantics of rule-based expert systems with uncertainty. In: Gyssens, M., Van Gucht, D., Paredaens, J. (eds.) ICDT 1988. LNCS, vol. 326, pp. 102–117. Springer, Heidelberg (1988)Google Scholar
  8. 8.
    Kifer, M., Subrahmanian, V.S.: Theory of generalized annotaded logic programming and its applications. J. of Logic Programming 12, 335–367 (1992)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Lakshmanan, L.V.S., Shiri, N.: Probabilistic deductive databases. In: Int. Logic Programming Symposium, pp. 254–268 (1994)Google Scholar
  10. 10.
    Lakshmanan, L.V.S., Shiri, N.: A parametric approach to deductive databases with uncertainty. IEEE Transactions on Knowledge and Data Engineering 13(4), 554–570 (2001)CrossRefGoogle Scholar
  11. 11.
    Loyer, Y., Straccia, U.: The well-founded semantics in normal logic programs with uncertainty. In: Hu, Z., Rodríguez-Artalejo, M. (eds.) FLOPS 2002. LNCS, vol. 2441, pp. 152–166. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Loyer, Y., Straccia, U.: The well-founded semantics of logic programs over bilattices: an alternative characterisation. Technical Report ISTI-2003-TR-05, Istituto di Scienza e Tecnologie dell’Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy (2003) (submitted) Google Scholar
  13. 13.
    Lukasiewicz, T.: Fixpoint characterizations for many-valued disjunctive logic programs with probabilistic semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 336–350. Springer, Heidelberg (2001)Google Scholar
  14. 14.
    Ng, R., Subrahmanian, V.S.: Stable model semantics for probabilistic deductive databases. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1991. LNCS, vol. 542, pp. 163–171. Springer, Heidelberg (1991)Google Scholar
  15. 15.
    Ng, R., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1993)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Shapiro, E.Y.: Logic programs with uncertainties: A tool for implementing rule-based systems. In: Proc. of the 8th Int. Joint Conf. on Artificial Intelligence (IJCAI 1983), pp. 529–532 (1983)Google Scholar
  17. 17.
    van Emden, M.H.: Quantitative deduction and its fixpoint theory. J. of Logic Programming 4(1), 37–53 (1986)CrossRefGoogle Scholar
  18. 18.
    van Gelder, A., Ross, K.A., Schlimpf, J.S.: The well-founded semantics for general logic programs. J. of the ACM 38(3), 620–650 (1991)zbMATHGoogle Scholar
  19. 19.
    Wagner, G.: Negation in fuzzy and possibilistic logic programs. In: Martin, T., Arcelli, F. (eds.) Logic programming and Soft Computing. Research Studies Press, Hertfordshire (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Yann Loyer
    • 1
  • Umberto Straccia
    • 2
  1. 1.PRiSMUniversité de VersaillesVersaillesFrance
  2. 2.I.S.T.I. – C.N.R.PisaItaly

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