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Logica Universalis

, Volume 10, Issue 2–3, pp 339–357 | Cite as

Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic

  • Petra Murinová
  • Vilém Novák
Article

Abstract

In this paper, we provide an overview of some of the results obtained in the mathematical theory of intermediate quantifiers that is part of fuzzy natural logic (FNL). We briefly introduce the mathematical formal system used, the general definition of intermediate quantifiers and define three specific ones, namely, “Almost all”, “Most” and “Many”. Using tools developed in FNL, we present a list of valid intermediate syllogisms and analyze a generalized 5-square of opposition.

Keywords

Aristotle square of opposition fuzzy natural logic intermediate generalized quantifiers generalized Peterson’s square of opposition 

Mathematics Subject Classification

Primary 03-02 Secondary 03B15 03B50 03B52 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

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

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