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

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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.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Petra Murinová & Vilém Novák

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  1. Petra Murinová
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  2. Vilém Novák
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Correspondence to Petra Murinová.

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Murinová, P., Novák, V. Syllogisms and 5-Square of Opposition with Intermediate Quantifiers in Fuzzy Natural Logic. Log. Univers. 10, 339–357 (2016). https://doi.org/10.1007/s11787-016-0146-z

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  • DOI: https://doi.org/10.1007/s11787-016-0146-z

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