Compatibility in algebra, in logic and in computer science

by Josep Maria Font (University of Barcelona)

Butlletí de la Societat Catalana de Matemàtiques 22 (2007) 75–11

This paper introduces the current view on the algebraic studies in Logic, especially in the domain of non-classical logics. The paper is organized around some pure algebraic concepts such as compatibility, Leibniz congruence, and the Leibniz operator. It is shown how these concepts allow to define a hierachy of logics and to classify them according to their behaviour as far as their algebraization is concerned, that is, by the kind of relation they have with their algebraic models, and by the properties of these models. The paper ends with a brief survey of some of the most recent research lines in the context of the emerging field now called Abstract Algebraic Logic.

[Paper written in Catalan]