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Commutative basic algebras and non-associative fuzzy logics

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Abstract

Several investigations in probability theory and the theory of expert systems show that it is important to search for some reasonable generalizations of fuzzy logics (e.g. Łukasiewicz, Gödel or product logic) having a non-associative conjunction. In the present paper, we offer a non-associative fuzzy logic L CBA having as an equivalent algebraic semantics lattices with section antitone involutions satisfying the contraposition law, so-called commutative basic algebras. The class (variety) CBA of commutative basic algebras was intensively studied in several recent papers and includes the class of MV-algebras. We show that the logic L CBA is very close to the Łukasiewicz one, both having the same finite models, and can be understood as its non-associative generalization.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00, Olomouc, Czech Republic

    Michal Botur & Radomír Halaš

Authors
  1. Michal Botur
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  2. Radomír Halaš
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Correspondence to Radomír Halaš.

Additional information

This work is supported by the Research and Development Council of the Czech Government via the project MSM6198959214.

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Botur, M., Halaš, R. Commutative basic algebras and non-associative fuzzy logics. Arch. Math. Logic 48, 243–255 (2009). https://doi.org/10.1007/s00153-009-0125-7

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  • DOI: https://doi.org/10.1007/s00153-009-0125-7

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