Query Answering in Normal Logic Programs Under Uncertainty

  • Umberto Straccia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3571)

Abstract

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively.

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References

  1. 1.
    Belnap, N.D.: A useful four-valued logic. In: Epstein, G., Dunn, J.M. (eds.) Modern uses of multiple-valued logic, pp. 5–37. Reidel, Dordrecht (1977)Google Scholar
  2. 2.
    Böhler, E., Gla§er, C., Schwarz, B., Wagner, K.: Generation problems. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 392–403. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Chen, W., Warren, D.S.: Tabled evaluation with delaying for general logic programs. Journal of the ACM 43(1), 20–74 (1996)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Damásio, C.V., Medina, J., Aciego, M.O.: Sorted multi-adjoint logic programs: Termination results and applications. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 252–265. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Damásio, C.V., Medina, J., Aciego, M.O.: A tabulation proof procedure for residuated logic programming. In: Proc. of the 6th Europ. Conf. on Art. Intelligence, ECAI 2004 (2004)Google Scholar
  6. 6.
    Damásio, C.V., Pereira, L.M.: A survey of paraconsistent semantics for logic programs. In: Gabbay, D., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 241–320. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  7. 7.
    Viegas Damásio, C., Pereira, L.M.: Antitonic logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, p. 379. Springer, Heidelberg (2001)Google Scholar
  8. 8.
    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. The MIT Press, Cambridge (1991)Google Scholar
  9. 9.
    Fitting, M.C.: Fixpoint semantics for logic programming - a survey. Theoretical Computer Science 21(3), 25–51 (2002)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proc. of the 5th Int. Conf. on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  11. 11.
    Ginsberg, M.L.: Multi-valued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265–316 (1988)CrossRefGoogle Scholar
  12. 12.
    Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. Journal of Logic Programming 12, 335–367 (1992)CrossRefMathSciNetGoogle Scholar
  13. 13.
    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
  14. 14.
    Loyer, Y., Straccia, U.: The approximate well-founded semantics for logic programs with uncertainty. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 541–550. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Lukasiewicz, T.: Probabilistic logic programming. In: Proc. of the 13th European Conf. on Artificial Intelligence (ECAI 1998), pp. 388–392 (1998)Google Scholar
  16. 16.
    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
  17. 17.
    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
  18. 18.
    Ng, R., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1993)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Straccia, U.: Top-down query answering for logic programs over bilattices. Technical Report, ISTI-CNR, Pisa, Italy (2004)Google Scholar
  20. 20.
    Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics (5), 285–309 (1955)Google Scholar
  21. 21.
    van Gelder, A., Ross, K.A., Schlimpf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)MATHGoogle Scholar
  22. 22.
    Vojtáš, P.: Fuzzy logic programming. Fuzzy Sets and Systems 124, 361–370 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Umberto Straccia
    • 1
  1. 1.ISTI – CNRPisa (PI)Italy

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