Sistemes deductius algebritzables

Abstract

[en] Logics allow the study of reasoning’s validity. Essentially, there are two ways of representing logics, syntactically and semantically. The syntactic presentation builds on the notion of proof, which is defined by a set of inference rules or calculus, stating that a reasoning is correct if a proof of the conclusion can be constructed from the premises. The semantic representation is based on the notions of truth and interpretation, and the idea is that, if the premises are true, so is the conclusion. Semantic representation has also been studied using the logical matrices’ method. The existence of completeness theorems makes it possible to relate syntactic to semantics. Presently work studies the article [Blo89], by Blok and Pigozzi, where it is formally defined to be an algebraizable deductive system. Next, some characterization theorems of these will be proved. It will also be seen that, when a deductive system is algebraizable, it is easier to find a completeness theorem between syntactic calculus and a matrix semantic representation. This paper will conclude by considering some applications, such as the so-called bridge theorems, which relate the branches of logic and algebra.