Arithmetical Complexity of First-order Predicate Fuzzy Logics Over Distinguished Semantics

First-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness properties

This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms (mainly continuous and weak nilpotent minimum t-norms). We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finit...

Monadic Fuzzy Predicate Logics

Two variants of monadic fuzzy predicate logic are analyzed and compared with the full fuzzy predicate logic with respect to nite model property (properties) and arithmetical complexity of sets of tautologies, satis-able formulas and of analogous notion restricted to nite models.

Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies

This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ∆-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate ...

Chapter XI: Arithmetical Complexity of First-Order Fuzzy Logics

A duality between LM-fuzzy possibility computations and their logical semantics

Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. T...