Monadic BL-algebras: The equivalent algebraic semantics of Hajek's monadic fuzzy logic

摘要

In this article we introduce the variety of monadic BL-algebras as BL-algebras endowed with two monadic operators. and.. After a study of the basic properties of this variety we show that this class is the equivalent algebraic semantics of the monadic fragment of Hajek's basic predicate logic. In addition, we start a systematic study of the main subvarieties of monadic BL-algebras, some of which constitute the algebraic semantics of well-known monadic logics: monadic Godel logic and monadic Lukasiewicz logic. In the last section we give a complete characterization of totally ordered monadic BL-algebras. (C) 2016 Elsevier B.V. All rights reserved.