Fuzzy propositional logic. Algebraic approach

Studia Logica 36 (3):189 - 194 (1977)
Abstract
The present paper contains some technical results on a many-valued logic with truth values from the interval of real numbers [0; 1]. This logic, discussed originally in [1], latter in [2] and [3], was called the logic of fuzzy concepts. Our aim is to give an algebraic axiomatics for fuzzy propositional logic. For this purpose the variety of L-algebras with signature en- riched with a unary operation { involution is stud- ied. A one-to-one correspondence between congruences on an LI-algebra and lters of a special kind is used to prove the representation theorem for LI-algebras. By this theorem every LI-algebra is isomorphic to a subdirect product of chains. The full characteristic of the subdirectly irreducible LI-algebras is given . It turns out that the variety of all L-algebras, as well as any of its subvarieties, is generated by its nite algebras
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