caa a22 4500 475800079 CHVBK 20180406123735.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1023/A:1008322226835 doi (NATIONALLICENCE)springer-10.1023/A:1008322226835 Montagna Franco Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100, Siena, Italy aut An Algebraic Approach to Propositional Fuzzy Logic [Elektronische Daten] [Franco Montagna] We investigate the variety corresponding to a logic (introduced in Esteva and Godo, 1998, and called ŁΠ there), which is the combination of Łukasiewicz 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 ŁΠ $$ \frac{1}{2} $$ algebras, corresponding to the logic obtained from ŁΠ by the adding of a constant and of a defining axiom for one half. We also connect ŁΠ $$ \frac{1}{2} $$ algebras with structures, called f-semifields, arising from the theory of lattice-ordered rings, and prove that every ŁΠ $$ \frac{1}{2} $$ algebra $$ \mathcal{A} $$ can be regarded as a structure whose domain is the interval [0, 1] of an f-semifield $$ \mathcal{F} $$ , and whose operations are the truncations of the operations of $$ \mathcal{F} $$ to [0, 1]. We prove that such a structure $$ \mathcal{F} $$ is uniquely determined by $$ \mathcal{A} $$ up to isomorphism, and we establish an equivalence between the category of ŁΠ $$ \frac{1}{2} $$ algebras and that of f-semifields. Kluwer Academic Publishers, 2000 fuzzy logic nationallicence MV algebras nationallicence product nationallicence Journal of Logic, Language and Information Kluwer Academic Publishers 9/1(2000-01-01), 91-124 0925-8531 9:1<91 2000 9 10849 https://doi.org/10.1023/A:1008322226835 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008322226835 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Montagna Franco Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100, Siena, Italy aut NATIONALLICENCE 773 0- Journal of Logic, Language and Information Kluwer Academic Publishers 9/1(2000-01-01), 91-124 0925-8531 9:1<91 2000 9 10849 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer