Advertisement

A Formal Model of the Intermediate Quantifiers “A Few”, “Several” and “A Little”

  • Vilém Novák
  • Petra MurinováEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)

Abstract

In this paper, we extend the model of intermediate quantifiers by three new ones, namely “a few, a little” and “several”. We proved some of the fundamental properties of these quantifiers and relations to the other ones. We also demonstrate that they naturally fall in the generalized square of opposition.

Notes

Acknowledgements

The work was supported from ERDF/ESF by the project “Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region” No. CZ.02.1.01/0.0/0.0/17-049/0008414.

References

  1. 1.
    Andrews, P.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer, Dordrecht (2002)CrossRefGoogle Scholar
  2. 2.
    Cignoli, R.L.O., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  3. 3.
    Murinová, P., Novák, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets Syst. 186, 47–80 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Murinová, P., Novák, V.: Analysis of generalized square of opposition with intermediate quantifiers. Fuzzy Sets Syst. 242, 89–113 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Murinová, P., Novák, V.: The theory of intermediate quantifiers in fuzzy natural logic revisited and the model of “Many”. Fuzzy Sets Syst. (Submitted)Google Scholar
  6. 6.
    Novák, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst. 159(22), 2939–2969 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Novák, V.: A formal theory of intermediate quantifiers. Fuzzy Sets Syst. 159(10), 1229–1246 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Novák, V., Perfilieva, I., Dvořák, A.: Insight into Fuzzy Modeling. Wile, Hoboken (2016)CrossRefGoogle Scholar
  9. 9.
    Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston (1999)CrossRefGoogle Scholar
  10. 10.
    Peterson, P.L.: On the logic of “few”, “many” and “most”. Notre Dame J. Form. Log. 20, 155–179 (1979)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Thompson, B.E.: Syllogisms using “few”, “many” and “most”. Notre Dame J. Form. Log. 23, 75–84 (1982)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy Modeling, NSC IT4InnovationsUniversity of OstravaOstrava 1Czech Republic

Personalised recommendations