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From Graded Aristotle’s Hexagon to Graded Peterson’s Hexagon of Opposition in Fuzzy Natural Logic

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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

In this publication we will first focus on the construction of the graded Aristotle’s hexagon in fuzzy natural logic (see [8]). The main goal will be to mathematically formulate a new definition of the contradictory property. In past publications, this definition was based on delta operation, which gave very unnatural results. We will show that the contradictory property can behave more naturally. In the end, we will present another extension possibility in the form of a graded Peterson hexagon with fuzzy intermediate quantifiers.

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.

    The diagonal lines represent contradictories, the formulas \(\textbf{A}\) and \(\textbf{E}\) are contraries, \(\textbf{A}\) and \(\textbf{E}\) entail \(\textbf{U}\), while \(\textbf{Y}\) entails both formulas \(\textbf{I}\) as well as \(\textbf{O}\). It is interesting to see that the logical hexagon obtains three Aristotle’s squares of opposition, namely, \(\textbf{AEIO}, \textbf{AYOU}\) and \(\textbf{EYUI}\).

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Author information

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

  2. Universitá degli Studi di Milano-Bicocca, DISCo, Viale Sarca 336, 20126, Milan, Italy

    Stefania Boffa

Authors
  1. Petra Murinová
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  2. Stefania Boffa
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Correspondence to Petra Murinová .

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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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Murinová, P., Boffa, S. (2023). From Graded Aristotle’s Hexagon to Graded Peterson’s Hexagon of Opposition in Fuzzy Natural Logic. 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_31

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  • DOI: https://doi.org/10.1007/978-3-031-39965-7_31

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