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.

Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln and a generalized BL-chain B are described in terms of weak ...

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 ...

We prove that every subvariety of BL-algebras which is not finitely generated is not σ-canonical. We also prove π-canonicity for an infinite family of subvarieties of BL-algebras that are not finitely generated. To do so ...

We give sufficient conditions for a BL-algebra to be isomorphic to a poset product of BL-chains which are poset product indecomposable.

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 ...

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 ...

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 ...

En esta tesis estudiamos una subvariedad MG contenida en la variedad de BL-álgebras generada por una BL-cadena dada por la suma ordinal de la MV-álgebra [0,1] y el hoop de Gödel [0,1]. Se da la descripción del álgebra libre ...

A representation theorem for a class of BL-algebras with finite spectrum is presented. Although the class comprised by our result is not the whole class of BL-algebras with finite spectrum, it applies to some important ...