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On Modeling of Generalized Syllogisms with Intermediate Quantifiers

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Fuzzy Techniques: Theory and Applications (IFSA/NAFIPS 2019 2019)

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Abstract

In our previous papers, we introduced a general principle in fuzzy natural logic in which the class of intermediate quantifiers can be introduced, and proved all of 105 generalized syllogisms. We also proposed generalized Peterson’s square of opposition with generalized definitions of contrary, contradictory, sub-contrary and subalterns. This approach is devoted to designing generalized Peterson’s rules which will be used for verification of the validity of generalized syllogisms with intermediate quantifiers based on its position inside in generalized Peterson’s square of opposition.

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Notes

  1. 1.

    It follows the concept of natural logic which was proposed by Lakoff in [5].

  2. 2.

    This fuzzy logic is called fuzzy type theory and was proposed in [11].

  3. 3.

    Recall that the quantifiers defined below are quantifiers of type \(\langle 1,1\rangle \).

  4. 4.

    The precise mathematical formula which represents commented pro perty is defined in [10] by formula (13).

  5. 5.

    We refer to our detailed papers where \(\mathbf {5}\)-square could be found.

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Acknowledgements

The paper has been supported by the project “LQ1602 IT4Innovations excellence in science”.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, NSC IT4Innovations, University of Ostrava, Ostrava, Czech Republic

    Petra Murinová

Authors
  1. Petra Murinová
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Correspondence to Petra Murinová .

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Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Ralph Baker Kearfott

  2. Center for Computing Research (CIC), Instituto Politecnico Nacional, Ciudad de Mexico, Mexico

    Ildar Batyrshin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Marek Reformat

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  5. Department of Computer Science, University of Texas at El Paso , El Paso, TX, USA

    Vladik Kreinovich

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Murinová, P. (2019). On Modeling of Generalized Syllogisms with Intermediate Quantifiers. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_36

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