A Semantic Model for Vague Quantifiers Combining Fuzzy Theory and Supervaluation Theory

  • Ka Fat Chow
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6953)


This paper introduces a semantic model for vague quantifiers (VQs) combining Fuzzy Theory (FT) and Supervaluation Theory (ST), which are the two main theories on vagueness, a common source of uncertainty in natural language. After comparing FT and ST, I will develop the desired model and a numerical method for evaluating truth values of vague quantified statements, called the Modified Glöckner’s Method, that combines the merits and overcomes the demerits of the two theories. I will also show how the model can be applied to evaluate truth values of complex quantified statements with iterated VQs.


vague quantifiers Generalized Quantifier Theory Fuzzy Theory Supervaluation Theory Modified Glöckner’s Method 


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  1. 1.
    Díaz-Hermida, F., Bugarín, A., Barro, S.: Definition and classification of semi-fuzzy quantifiers for the evaluation of fuzzy quantified sentences. International Journal of Approximate Reasoning 34, 49–88 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Fine, K.: Vagueness, Truth and Logic. Synthese 30, 265–300 (1975)CrossRefzbMATHGoogle Scholar
  4. 4.
    Glöckner, I.: DFS – An Axiomatic Approach to Fuzzy Quantification. Report TR97-06, Technical Faculty, University Bielefeld (1997)Google Scholar
  5. 5.
    Glöckner, I.: Fuzzy Quantifiers: A Computational Theory. Springer, Berlin (2006)zbMATHGoogle Scholar
  6. 6.
    Kamp, H.: Two Theories about Adjectives. In: Keenan, E.L. (ed.) Formal Semantics of Natural Language, pp. 123–155. Cambridge University Press, Cambridge (1975)CrossRefGoogle Scholar
  7. 7.
    Keefe, R.: Theories of Vagueness. Cambridge University Press, Cambridge (2000)Google Scholar
  8. 8.
    Keenan, E.L.: Some Properties of Natural Language Quantifiers: Generalized Quantifier Theory. Linguistics and Philosophy 25, 627–654 (2002)CrossRefGoogle Scholar
  9. 9.
    Keenan, E.L., Westerståhl, D.: Generalized Quantifiers in Linguistics and Logic. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 837–893. Elsevier Science, Amsterdam (1997)CrossRefGoogle Scholar
  10. 10.
    Losada, D.E., Díaz-Hermida, F., Bugarin, A.: Semi-fuzzy quantifiers for information retrieval. In: Herrera-Viedma, E., Pasi, G., Crestani, F. (eds.) Soft Computing in Web Information Retrieval: Models and Applications. Springer, Heidelberg (2006)Google Scholar
  11. 11.
    Westerståhl, D.: Quantifiers in Formal and Natural Language. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. IV, pp. 1–131. Reidel Publishing Company, Dordrecht (1989)CrossRefGoogle Scholar
  12. 12.
    Yager, R.R.: Reasoning with Fuzzy Quantified Statements: Part I. Kybernetes 14, 233–240 (1985a)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Yager, R.R.: Reasoning with Fuzzy Quantified Statements: Part II. Kybernetes 15, 111–120 (1985b)CrossRefzbMATHGoogle Scholar
  14. 14.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Zadeh, L.A.: A Computational Approach to Fuzzy Quantifiers in Natural Languages. Computers and Mathematics with Applications 9(1), 149–184 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ka Fat Chow
    • 1
  1. 1.The Hong Kong Polytechnic UniversityHong Kong

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