Archive for Mathematical Logic 48 (3-4):243-255 (2009)

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
Keywords Basic algebra  Lattice with section antitone involutions  MV-algebra  Residuated groupoid  Fuzzy logic
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DOI 10.1007/s00153-009-0125-7
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References found in this work BETA

Effect Algebras and Unsharp Quantum Logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.

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Citations of this work BETA

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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