Fuzzy Autoepistemic Logic: Reflecting about Knowledge of Truth Degrees

  • Marjon Blondeel
  • Steven Schockaert
  • Martine De Cock
  • Dirk Vermeir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6717)

Abstract

Autoepistemic logic is one of the principal formalisms for nonmonotonic reasoning. It extends propositional logic by offering the ability to reason about an agent’s (lack of) knowledge or beliefs. Moreover, it is well known to generalize the stable model semantics of answer set programming. Fuzzy logics on the other hand are multi-valued logics, which allow to model the intensity with which a property is satisfied. We combine these ideas to a fuzzy autoepistemic logic which can be used to reason about one’s knowledge about the degrees to which proporties are satisfied. In this paper we show that many properties from classical autoepistemic logic remain valid under this generalization and that the important relation between autoepistemic logic and answer set programming is preserved in the sense that fuzzy autoepistemic logic generalizes fuzzy answer set programming.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Banerjee, M., Dubois, D.: A simple modal logic for reasoning about revealed beliefs. In: Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 805–816 (2009)Google Scholar
  2. 2.
    Bauters, K., Schockaert, S., De Cock, M., Vermeir, D.: Possibilistic answer set programming revisited. In: Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (2010)Google Scholar
  3. 3.
    Damásio, C.V., Medina, J., Ojeda-Aciego, M.: Sorted multi-adjoint logic programs: termination results and applications. In: Proceedings of the 9th European Conference on Logics in Artificial Intelligence, pp. 260–273 (2004)Google Scholar
  4. 4.
    Dubois, D., Prade, H., Schockaert, S.: Règles et méta-règles dans le cadre de la théorie des possibilités et de la logique possibiliste. In: Rencontres Francophones sur la Logique Floue et ses Applications, pp. 115–122 (2010)Google Scholar
  5. 5.
    Egly, U., Eiter, T., Tompits, H., Woltran, S.: Solving advanced reasoning tasks using quantified boolean formulas. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence, pp. 417–422 (2000)Google Scholar
  6. 6.
    Gelfond, M.: On stratified autoepistemic theories. In: Proceedings of the Sixth National Conference on Artificial Intelligence, pp. 207–211 (1987)Google Scholar
  7. 7.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the Fifth International Conference and Symposiom on Logic Programming, pp. 1070–1080 (1988)Google Scholar
  8. 8.
    Hajek, P.: Metamathematics of Fuzzy Logic. Springer, Heidelberg (2001)MATHGoogle Scholar
  9. 9.
    Hajek, P.: On fuzzy modal logics. Fuzzy Sets and Systems 161, 18 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Janssen, J., Schockaert, S., Vermeir, D., De Cock, M.: General fuzzy answer set programs. In: Proceedings of the International Workshop on Fuzzy Logic and Applications, pp. 353–359 (2009)Google Scholar
  11. 11.
    Koutras, C.D., Koletsos, G., Zachos, S.: Many-valued modal non-monotonic reasoning: Sequential stable sets and logics with linear truth spaces. Fundamenta Informaticae 38(3), 281–324 (1999)MathSciNetMATHGoogle Scholar
  12. 12.
    Koutras, C.D., Zachos, S.: Many-valued reflexive autoepistemic logic. Logic Journal of the IGPL 8(1), 403–418 (2000)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Lifschitz, V., Schwarz, G.: Extended logic programs as autoepistemic theories. In: Proceedings of the Second International Workshop on Logic Programming and Nonmonotonic Reasoning, pp. 101–114 (1993)Google Scholar
  14. 14.
    Marek, W.: Stable theories in autoepistemic logic. Unpublished note, Department of Computer Science, University of Kentucky (1986)Google Scholar
  15. 15.
    Marek, W., Truszczynski, M.: Autoepistemic logic. Journal of the Association for Computing Machinery 38(3), 587–618 (1991)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Moore, R.C.: Semantical considerations on nonmonotonic logic. In: Proceedings of the Eighth International Joint Conference on Artificial Intelligence, pp. 272–279 (1983)Google Scholar
  17. 17.
    Moore, R.C.: Possible-world semantics in autoepistemic logic. In: Proceedings of the Non-Monotonic Reasoning Workshop, pp. 344–354 (1984)Google Scholar
  18. 18.
    Schockaert, S., Janssen, J., Vermeir, D., De Cock, M.: Answer sets in a fuzzy equilibrium logic. In: Proceedings of the 3rd International Conference on Web Reasoning and Rule Systems, pp. 135–149 (2009)Google Scholar
  19. 19.
    Sim, K.M.: Epistemic logic and logical omniscience: A survey. International Journal of Intelligent Systems 12, 57–81 (1997)CrossRefMATHGoogle Scholar
  20. 20.
    Stalnaker, R.: A note on non-monotonic modal logic. Artificial Intelligence 64(2), 183–196 (1993)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Straccia, U.: Annotated answer set programming. In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (2006)Google Scholar
  22. 22.
    von Wright, G.: An Essay in Modal Logic. In: Studies in Logic and the Foundations of Mathematics. North-Holland Pub. Co., Amsterdam (1951)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Marjon Blondeel
    • 1
  • Steven Schockaert
    • 2
  • Martine De Cock
    • 2
  • Dirk Vermeir
    • 1
  1. 1.Dept. of Computer ScienceVrije Universiteit BrusselBelgium
  2. 2.Dept. of Applied Mathematics and Computer ScienceGhent UniversityBelgium

Personalised recommendations