Arithmetical complexity of fuzzy predicate logics — A survey II

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

All promiment examples of first-order predicate fuzzy logics are undecidable. This leads to the problem of the arithmetical complexity of their sets of tautologies and satisfiable sentences. This paper is a contribution to the general study of this problem. We propose the classes of first-order core and ∆-core fuzzy logics as a good framework to address these arithmetical complexity issues. We ...

Chapter XI: Arithmetical Complexity of First-Order Fuzzy Logics

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.

On Reduced Semantics for Fuzzy Predicate Logics

Our work is a contribution to the model-theoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts being studied are the Leibniz congruence and the relative relation. On the one hand, the Leibniz congruence of a model identifies the elements that are indistinguishable...

Solution of some problems in the arithmetical complexity of first-order fuzzy logics

This short paper addresses the open problems left in the paper [5]. Besides giving solutions to these two problems, some clarification concerning the role of the full vocabulary (including functional symbols) in the proofs there given is also discussed.