An Algebraic Approach to Propositional Fuzzy Logic |
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Authors: | Franco Montagna |
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Affiliation: | (1) Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100 Siena, Italy |
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Abstract: | We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called ![Lstrok](/content/p2511233n64323x1/xxlarge321.gif) there), which is the combination of ukasiewicz Logic and Product Logic, and in which Gödel Logic is interpretable. We present an alternative (and slightly simpler) axiomatization of such variety. We also investigate the variety, called the variety of ![Lstrok](/content/p2511233n64323x1/xxlarge321.gif)
algebras, corresponding to the logic obtained from ![Lstrok](/content/p2511233n64323x1/xxlarge321.gif) by the adding of a constant and of a defining axiom for one half. We also connect ![Lstrok](/content/p2511233n64323x1/xxlarge321.gif)
algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every ![Lstrok](/content/p2511233n64323x1/xxlarge321.gif)
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 ![Lstrok](/content/p2511233n64323x1/xxlarge321.gif)
algebras and that of f-semifields. |
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Keywords: | fuzzy logic MV algebras product |
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