Possibilistic Minimal Models for Possibilistic Normal Programs

  • Rubén Octavio Vélez Salazar
  • José Arrazola Ramírez
  • Ivan Martínez Ruiz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8265)

Abstract

In this paper we present possibilistic minimal models for possibilistic normal programs, we relate them to the possibilistic C ω logic, PC ω L, and to minimal models of normal logic programs. Possibilistic stable models for possibilistic normal programs have been presented previously, but we present a more general type. We also characterize the provability of possibilistic atoms from possibilistic normal programs in terms of PC ω L.

Keywords

Logic Program Minimal Model Inference Rule Semantic Operator Possibilistic Logic 
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.
    Baral, C.: Knowledge representation, reasoning and declarative problem solving. Cambridge University Press (2003)Google Scholar
  2. 2.
    da Costa, N.C.A.: On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic 15(4), 497–510 (1974)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Inc., New York (1994)Google Scholar
  4. 4.
    Erdogan, S.T., Lifschitz, V.: Definitions in answer set programming. In: Lifschitz, V., Niemelä, I. (eds.) Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), pp. 114–126 (2004)Google Scholar
  5. 5.
    Estrada-Estrada, O.H., Arrazola-Ramírez, J.R.E., Osorio-Galindo, M.J.: Possibilistic intermediate logic. Int. J. Adv. Intell. Paradigms 4(2), 149–167 (2012)CrossRefGoogle Scholar
  6. 6.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming, pp. 1070–1080. MIT Press (1988)Google Scholar
  7. 7.
    Halpern, J.: Reasoning about uncertainty. Massachusetts Institue of Technology (2003)Google Scholar
  8. 8.
    Arrazola, J., Borja, V., Osorio, M., Navarro, J.: Ground non-monotonic modal logic s5: new results. Journal of Logic and Computation 15, 787–813 (2005)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Arrazola, J., Borja, V., Osorio, M., Navarro, J.: Logics with common weak completions. Journal of Logic and Computation 16, 867–890 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Marek, V.W.: Stable models and an alternative logic programming paradigm. In: In The Logic Programming Paradigm: a 25-Year Perspective, pp. 375–398. Springer (1999)Google Scholar
  11. 11.
    Nicolas, P., Garcia, L., Stéphan, I., Lefèvre, C.: Possibilistic uncertainty handling for answer set programming. Annals of Mathematics and Artificial Intelligence 47(1-2), 139–181 (2006)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Niemela, I.: Logic programs with stable model semantics as a constraint programming paradigm (1998)Google Scholar
  13. 13.
    Osorio, M., Pérez, J.A.N., Arrazola, J.: Applications of intuitionistic logic in answer set programming. CoRR, cs.LO/0305046 (2003)Google Scholar
  14. 14.
    Pearce, D.: Stable inference as intuitionistic validity. The Journal of Logic Programming 38, 79–91 (1999)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Pelletier, F., Elio, R.: Scope of Logic, Methodology and Philosophy of Science. Kluwer Academic Press (2002)Google Scholar
  16. 16.
    Zepeda, C., Dávila, R., Osorio, M. (eds.): Programas Logicos Disyuntivos y la demostrabilidad en C ω. Workshop in Logic, Language and Computation 2006. CEUR Workshop Proceedings (November 2006)Google Scholar
  17. 17.
    Shannon, C.: A mathematical theory of communication. The Bell System Technical Journal 27, 379–423 (1948)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Tversky, A., Kahneman, D.: Judgment under uncertainty: Heuristics and biases. Science 185(4157), 1124–1131 (1974)Google Scholar
  19. 19.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Rubén Octavio Vélez Salazar
    • 1
  • José Arrazola Ramírez
    • 1
  • Ivan Martínez Ruiz
    • 1
  1. 1.Benémerita Universidad Autónoma de PueblaMexico

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