Completeness for monadic fuzzy logics via functional algebras

摘要

We study S5-modal (monadic) expansions of extensions of Hajek's basic logic BL. Hajek proposed Hilbert-style systems axiomatizing these logics and we prove that completeness theorems for these logics follow from algebraic representation results, namely, functional representations of finitely subdirectly irreducible algebras. We prove a general theorem linking these concepts and give two major applications, namely, for the S5-modal expansions of Lukasiewicz and Godel logics. (C) 2020 Elsevier B.V. All rights reserved.