ECSQARU 2005: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 687-700 | Cite as
Query Answering in Normal Logic Programs Under Uncertainty
Conference paper
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.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.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.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.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.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.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.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.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.Fitting, M.C.: Fixpoint semantics for logic programming - a survey. Theoretical Computer Science 21(3), 25–51 (2002)CrossRefMathSciNetGoogle Scholar
- 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.Ginsberg, M.L.: Multi-valued logics: a uniform approach to reasoning in artificial intelligence. Computational Intelligence 4, 265–316 (1988)CrossRefGoogle Scholar
- 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.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.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.Lukasiewicz, T.: Probabilistic logic programming. In: Proc. of the 13th European Conf. on Artificial Intelligence (ECAI 1998), pp. 388–392 (1998)Google Scholar
- 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.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.Ng, R., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1993)CrossRefMathSciNetGoogle Scholar
- 19.Straccia, U.: Top-down query answering for logic programs over bilattices. Technical Report, ISTI-CNR, Pisa, Italy (2004)Google Scholar
- 20.Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics (5), 285–309 (1955)Google Scholar
- 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.Vojtáš, P.: Fuzzy logic programming. Fuzzy Sets and Systems 124, 361–370 (2004)CrossRefGoogle Scholar
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