Fuzzy Reasoning Based on Propositional Modal Logic

  • Zaiyue Zhang
  • Yuefei Sui
  • Cungen Cao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)


In order to deal with some vague assertions more efficiently, fuzzy modal logics have been discussed by many researchers. This paper introduces the notation of fuzzy assertion based on propositional modal logic. As an extension of the traditional semantics about the modal logics, the fuzzy Kripke semantics are considered and the formal system of the fuzzy reasoning based on propositional modal logic is established and the properties about the satisfiability of the reasoning system are discussed.


propositional modal logic fuzzy assertion fuzzy reasoning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)zbMATHGoogle Scholar
  2. 2.
    Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.): Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 1-4. Clarendon Press, Oxford (1994)Google Scholar
  3. 3.
    Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.): Handbook of Logic in Computer Science, vol. 1-3. Clarendon Press, Oxford (1992)Google Scholar
  4. 4.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Fagin, R.F., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1996)Google Scholar
  6. 6.
    Hájek, P., Harmancová, D.: A many-valued modal logics. In: Proceedings of IPMU 1996, pp. 1021–1024 (1996)Google Scholar
  7. 7.
    Straccia, U.: A fuzzy description logic. In: Proceedings of AAAI 1998, 15th National Conference on Artificial Intelligence, Madison, Wisconsin (1998)Google Scholar
  8. 8.
    Beihai, Z.: An introduction to modal logic, pp. 141–165. Beijing University Press, Beijing (1991) (in Chinese)Google Scholar
  9. 9.
    Buchheit, M., Donini, F.M., Scharerf, A.: Decidable reasoning in terminological knowledge representation systems. In: Proc. of the 13th Int. Joint Conf. on Artificial Intelligence (IJCAI 1993), pp. 704–709 (1993)Google Scholar
  10. 10.
    Kripke, S.A.: Semantical analysis of modal logic II. In: Addsion, J.W., et al. (eds.) The Theory of Models, pp. 206–220. North-Holland, Amsterdam (1965)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Zaiyue Zhang
    • 1
  • Yuefei Sui
    • 2
  • Cungen Cao
    • 2
  1. 1.Joint Laboratory of Intelligent Computing, Department of Computer ScienceEast China Shipbuilding InstituteZhenjiangP.R. China
  2. 2.Key Laboratory of Intelligent Information Processing, Institute of Computing TechnologyChinese Academy of SciencesBeijingP.R. China

Personalised recommendations