A General Omitting Types Theorem in Mathematical Fuzzy Logic

Abstract

This article is a contribution to the theoretical study of weighted structures in fuzzy logic. We consider an important item from classical model theory: the construction of models that do not have any collection satisfying certain prescribed properties, that is, an omitting types theorem. We generalize the work done by Cintula and Diaconescu (Omitting Types Theorem for Fuzzy Logics, IEEE Transactions on Fuzzy Systems 27(2):273–277, 2019), who solved the problem for standard one-sided types. Instead, we introduce types for fuzzy structures as pairs of sets of formulas with free variables (expressing, respectively, properties to be satisfied and those to be avoided) and prove the corresponding omitting types theorem in the framework of uninorm-based logics.