Commutative basic algebras and non-associative fuzzy logics

Archive for Mathematical Logic 48 (3-4):243-255 (2009)
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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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Citations of this work

Simple Logics for Basic Algebras.Ja̅nis Cı̅rulis - 2015 - Bulletin of the Section of Logic 44 (3/4):95-110.
Axiomatization of non-associative generalisations of Hájek's BL and psBL.Yaroslav Petrukhin - 2020 - Journal of Applied Non-Classical Logics 30 (1):1-15.

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References found in this work

Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
Algebraic foundations of many-valued reasoning.Roberto Cignoli - 1999 - Boston: Kluwer Academic Publishers. Edited by Itala M. L. D'Ottaviano & Daniele Mundici.
Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Book Reviews. [REVIEW]P. Hájek - 2002 - Studia Logica 72 (3):433-443.

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