In this chapter we give a detailed presentation of the most important aspects of Hajek´s basic Logic BL and their algebraic counterpart, BL-algebras.

Fuzzy possibilistic logic is an important formalism for approximate reasoning. It extends the well-known basic propositional logic BL, introduced by Hájek, by offering the ability to reason about possibility and necessity ...

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 ...

The aim of this paper is to survey the tools needed to prove the standard completeness of Hájek Basic Logic with respect to continuous t-norms. In particular, decompositions of   totally ordered BL-algebras into simpler ...

In the present paper we extend previous results by completely characterizing dual canonical subvarieties of BL-algebras. These are subvarieties of algebras that satisfy the equation x^k=x^{k+1} for some integer k>0. As a ...

Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0,1] and a basic hoop H. We present a geometrical characterization of elements in the finitely ...

Product Logic Π is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum ...