An algebraic approach to propositional fuzzy logic

Journal of Logic, Language and Information 9 (1):91-124 (2000)
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Abstract

We investigate the variety corresponding to a logic, which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative axiomatization of such variety. We also investigate the variety, called the variety of algebras, corresponding to the logic obtained from by the adding of a constant and of a defining axiom for one half. We also connect algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every algebra can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield, and whose operations are the truncations of the operations of to [0, 1]. We prove that such a structure is uniquely determined by up to isomorphism, and we establish an equivalence between the category of algebras and that of f-semifields

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Citations of this work

Product Ł ukasiewicz Logic.Rostislav Horčík & Petr Cintula - 2004 - Archive for Mathematical Logic 43 (4):477-503.
MVW-rigs and product MV-algebras.Alejandro Estrada & Yuri A. Poveda - 2018 - Journal of Applied Non-Classical Logics 29 (1):78-96.

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References found in this work

Zum intuitionistischen aussagenkalkül.K. Gödel - 1932 - Anzeiger der Akademie der Wissenschaften in Wien 69:65--66.
A complete many-valued logic with product-conjunction.Petr Hájek, Lluis Godo & Francesc Esteva - 1996 - Archive for Mathematical Logic 35 (3):191-208.
Fuzzy logic and fuzzy set theory.Gaisi Takeuti & Satoko Titani - 1992 - Archive for Mathematical Logic 32 (1):1-32.

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