On n-contractive fuzzy logics: first results

In order to reach a deeper understanding of the structure of fuzzy logics, some very general new logics are defined. Namely, we consider the extensions of MTL by adding the generalized contraction and excluded middle laws introduced in Ref. 4 and we enrich this family by means of the axiom of weak cancellation and the Ω operator defined in Ref. 19. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embedding property, finite model property, decidability and standard completeness.