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.

This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the ...

The algebra of logic, as an explicit algebraic system showing the underlying mathematical structure of logic, was introduced by George Boole (1815-1864) in his book The Mathematical Analysis of Logic (1847). The methodology ...

In this paper we present an algebraic version of the annotated predicate logics Q tau [1] by using the concept of Curry Algebras [5]. The algebraic structure obtained is called Curry Algebras Q tau. We study some basic ...

This paper is a sequel to [5], [6]. We present the Curry monadic system N-1* which has as extensions the Curry monadic algebras C-1* and P-1*. All those systems are extensions of the classical monadic algebras introduced ...

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 ...

This paper deals with conceptions of formality underlying 19th Century symbolic logic, where notations and manipulation of signs played an important role. It is devoted specifically to the case of Ernst Schröder’s “formal ...