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Analysis of the Number of Valid Peterson’s Syllogisms

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Fuzzy Logic and Technology, and Aggregation Operators (EUSFLAT 2023, AGOP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14069))

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Abstract

This publication aims to continue the study of fuzzy Peterson’s logical syllogisms with fuzzy intermediate quantifiers. The main idea of this article is not to formally or semantically prove the validity of syllogisms, as was the case in previous publications. The main idea is to find a mathematical formula by which we are able to derive the number of valid Peterson syllogisms based on the number of intermediate quantifiers.

Supported by OP PIK CZ.01.1.02/0.0/0.0/17147/0020575 AI-Met4Laser: Consortium for industrial research and development of new applications of laser technologies using artificial intelligence methods (10/2020–6/2023), of the Ministry of Industry and Trade of the Czech Republic.

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Notes

  1. 1.

    In Peterson’s approach, we use the term valid syllogism. Our definition is based on strong conjunction then we use the term strongly valid syllogism.

  2. 2.

    Many authors speak about terms instead of formulas. We call S, P, M formulas as is common in logic.

  3. 3.

    We count affirmative and negative form of the same quantifier as one quantifier. The number of quantifiers on the page xx is \(k=5\).

  4. 4.

    The size of the quantifier “Q B’s are A” is determined by the proportion of B which has the property A.

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Author information

Authors and Affiliations

  1. University of Ostrava, 30. dubna 22, 701 03, Ostrava, Czech Republic

    Karel Fiala

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

    Petra Murinová

Authors
  1. Karel Fiala
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  2. Petra Murinová
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Corresponding author

Correspondence to Karel Fiala .

Editor information

Editors and Affiliations

  1. University of the Balearic Islands, Palma, Spain

    Sebastia Massanet

  2. University of Oviedo, Gijón, Spain

    Susana Montes

  3. University of the Balearic Islands, Palma, Spain

    Daniel Ruiz-Aguilera

  4. University of the Balearic Islands, Palma, Spain

    Manuel González-Hidalgo

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Fiala, K., Murinová, P. (2023). Analysis of the Number of Valid Peterson’s Syllogisms. In: Massanet, S., Montes, S., Ruiz-Aguilera, D., González-Hidalgo, M. (eds) Fuzzy Logic and Technology, and Aggregation Operators. EUSFLAT AGOP 2023 2023. Lecture Notes in Computer Science, vol 14069. Springer, Cham. https://doi.org/10.1007/978-3-031-39965-7_32

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  • DOI: https://doi.org/10.1007/978-3-031-39965-7_32

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