Towards Evaluation Games for Fuzzy Logics

  • Petr Cintula
  • Ondrej Majer

Abstract

The article provides two kinds of game-theoretical semantics for fuzzy logics with special attention to Łukasiewicz logic. The first one is a generalization of the evaluation games for classical logic. It is shown that it provides an interesting contribution to the model theory of fuzzy logics as, unlike the standard semantics, it can deal with the so-called non-safe models. The second kind of semantics makes explicit the intuition about fuzzy logics as logics of partial truth and provides a semantics in the form of a bargaining game. Finally, a basic kind of logic of informational independence of a Hintikka-Sandu style is introduced.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belluce, L. P. and Chang, C. C. (1963). A weak completeness theorem on infinite valued predicate logic. Journal of Symbolic Logic, 28(1):43–50.CrossRefGoogle Scholar
  2. Blass, A. (1992). A game semantics for linear logic. Annals of Pure and Applied Logic, 56(1– 3):183–220.CrossRefGoogle Scholar
  3. Fermöller, C. G. (2003). Parallel dialogue games and hypersequents for intermediate logics. In Mayer, M. C. and Pirri, F. editors, Proceedings of TABLEAUX Conference 2003, pages 48– 64, Rome.Google Scholar
  4. Hájek, P. (1998). Metamathematics of Fuzzy Logic, volume 4 of Trends in Logic. Kluwer, Dordrecht.Google Scholar
  5. Hájek, P. and Cintula, P. (2006). Triangular norm predicate fuzzy logics. To appear in Proceedings of Linz Seminar 2005.Google Scholar
  6. Hintikka, J. and Sandu, G. (1989). Informational independence as a semantical phenomenon. In Fenstad, J. E., Frolov, I. T., and Hilpinen, R., editors, Proceedings of LMPS, volume 8, pages 571–589. North-Holland, Amsterdam.Google Scholar
  7. Hintikka, J. and Sandu, G. (1997). Game-theoretical semantics. In van Benthem, J. and ter Meulen, A., editors, Handbook of Logic and Language, pages 361–410. Elsevier Science B.V., Oxford, Shannon, Tokyo, MIT Press, Cambridge, MA.CrossRefGoogle Scholar
  8. Łukasiewicz, J. (1920). O logice trojwartosciowej. Ruch filozoficzny, 5:170–171. (On Three-Valued Logic).Google Scholar
  9. Mundici, D. (1993). Ulam games, Łukasiewicz logic and AFC*-algebras. Fundamenta Infor-maticae, 18:151–161.Google Scholar
  10. Osborne, M. J. and Rubinstein, A. (1994). A Course in Game Theory. MIT Press, Cambridge, MA.Google Scholar
  11. Sandu, G. (1993). On the logic of informational independence and its applications. Journal of Philosophical Logic, 22:29–60.CrossRefGoogle Scholar
  12. Sandu, G. and Pietarinen, A.V. (2001). Partiality and games: propositional logic. Logic Journal of the Interest Group of Pure and Applied Logic, 9:107–127.Google Scholar
  13. von Neumann, J. and Morgenstern, O. (1994). Theory of Games and Economic Behavior. Wiley, New York.Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Petr Cintula
    • 1
  • Ondrej Majer
    • 2
  1. 1.Institute of Computer Science Academy of Sciences of the Czech RepublicPrague 8Czech Republic
  2. 2.Institute of Philosophy Academy of Sciences of the Czech RepublicPragueCzech Republic

Personalised recommendations