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International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making

IUKM 2015: Integrated Uncertainty in Knowledge Modelling and Decision Making pp 19–31Cite as

Combining Fuzziness and Context Sensitivity in Game Based Models of Vague Quantification

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

Abstract

We introduce a game semantic approach to fuzzy models of vague quantification that addresses a number of problems with previous frameworks. The main tool is the introduction of a new logical operator that supports context based evaluations of suitably quantified formulas.

C.G. Fermüller—Supported by Austrian Science Fund (FWF) I1827-N25.

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References

  1. Barker, C.: The dynamics of vagueness. Linguistics & Philosophy 25(1), 1–36 (2002)

    Article  Google Scholar 

  2. Cintula, P., Hájek, P., Noguera, C. (eds.): Handbook of Mathematical Fuzzy Logic. College Publications (2011)

    Google Scholar 

  3. Delgado, M., Ruiz, M.D., Sánchez, D., Vila, M.A.: Fuzzy quantification: a state of the art. Fuzzy Sets and Systems 242, 1–30 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fermüller, C.G.: Hintikka-style semantic games for fuzzy logics. In: Beierle, C., Meghini, C. (eds.) FoIKS 2014. LNCS, vol. 8367, pp. 193–210. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  5. Fermüller, C.G., Kosik, R.: Combining supervaluation and degree based reasoning under vagueness. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 212–226. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Fermüller, C.G., Metcalfe, G.: Giles’s game and the proof theory of Łukasiewicz logic. Studia Logica 92(1), 27–61 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fermüller, C.G., Roschger, C.: Randomized game semantics for semi-fuzzy quantifiers. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part IV. CCIS, vol. 300, pp. 632–641. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Fermüller, C.G., Roschger, C.: Bridges between contextual linguistic models of vagueness and t-norm based fuzzy logic. In: Montagna, F. (ed.) Petr Hájek on Mathematical Fuzzy Logic, vol. 6, pp. 91–114. Springer (2014)

    Google Scholar 

  9. Fermüller, C.G., Roschger, C.: Randomized game semantics for semi-fuzzy quantifiers. Logic Journal of the IGPL 223(3), 413–439 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fernando, T., Kamp, H.: Expecting many. In: Proceedings of SALT, vol. 6, pp. 53–68 (2011)

    Google Scholar 

  11. Giles, R.: A non-classical logic for physics. Studia Logica 33(4), 397–415 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  12. Giles, R.: A non-classical logic for physics. In: Wojcicki, R., Malinkowski, G. (eds.) Selected Papers on Łukasiewicz Sentential Calculi, pp. 13–51. Polish Academy of Sciences (1977)

    Google Scholar 

  13. Glöckner, I.: Fuzzy Quantifiers. STUDFUZZ, vol. 193. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  14. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers (2001)

    Google Scholar 

  15. Kamp, H., Van Genabith, J., Reyle, U.: Discourse representation theory. In: Handbook of Philosophical Logic, vol. 15, pp. 125–394. Springer (2011)

    Google Scholar 

  16. Kennedy, C.: Vagueness and grammar: The semantics of relative and absolute gradable adjectives. Linguistics & Philosophy 30(1), 1–45 (2007)

    Article  Google Scholar 

  17. Lappin, S.: An intensional parametric semantics for vague quantifiers. Linguistics & Philosophy 23(6), 599–620 (2000)

    Article  Google Scholar 

  18. Liu, Y., Kerre, E.E.: An overview of fuzzy quantifiers (I) interpretations. Fuzzy Sets and Systems 95(1), 1–21 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. Metcalfe, G., Olivetti, N., Gabbay, D.: Proof Theory for Fuzzy Logics. Applied Logic, vol. 36. Springer (2008)

    Google Scholar 

  20. Sauerland, U.: Vagueness in language: The case against fuzzy logic revisited. In: Cintula, P., Fermüller, C., Godo, L., Hájek, P. (eds.) Understanding Vagueness - Logical, Philosophical and Linguistic Perspectives. College Publications (2011)

    Google Scholar 

  21. Shapiro, S.: Vagueness in Context. Oxford University Press, USA (2006)

    Book  Google Scholar 

  22. Solt, S.: Vagueness in quantity: Two case studies from a linguistic perspective. In: Cintula, P., Fermüller, C., Godo, L., Hájek, P. (eds.) Understanding Vagueness - Logical, Philosophical and Linguistic Perspectives. College Publications (2011)

    Google Scholar 

  23. Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers & Mathematics with Applications 9(1), 149–184 (1983)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Vienna University of Technology, Vienna, Austria

    Christian G. Fermüller

Authors
  1. Christian G. Fermüller
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Correspondence to Christian G. Fermüller .

Editor information

Editors and Affiliations

  1. Science and Technology, Japan Advanced Institute of, Nomi, Japan

    Van-Nam Huynh

  2. Science, Dept of Systems Innovation, Osaka University,Graduate School of, Osaka, Japan

    Masahiro Inuiguchi

  3. Université de Technologie de Compiègne, Compiègne, France

    Thierry Demoeux

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Fermüller, C.G. (2015). Combining Fuzziness and Context Sensitivity in Game Based Models of Vague Quantification. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_4

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  • DOI: https://doi.org/10.1007/978-3-319-25135-6_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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