Interchangeable formulas and categories of logics

CASTIGLIONI, JOSÉ LUIS; VIBRENTIS, FRANCISCO ANTONIO

Vichy

Congreso; 6th World Congress on Universal Logic; 2018

Vichy University - Campus France

The study of categories of logics is motivated, among other reasons, by questions such as how to combine logics and when they are equivalent. Categories of logics do not always have good categorical properties such as the existence of finite limits and colimits. The existence of these provides natural mechanisms for the factorization and combination of logics. One natural way to obtain from these categories new ones with better properties is to consider the quotient category induced by the interdemonstrability relation. In this case the existence of finite limits and colimits is only guaranteed when the objects involved are congruential logics.Here, we consider the category whose objects are Tarskian logics and whose morphisms are flexible translations that preserve the interchangeability relation between metaformulas. This relation induces a congruence on the class of morphisms of this category.In this communication, we study the quotient category induced by interchangeability and some of its categorical properties. For example, theexistence of finite products and coproducts, without needing to be restrictedto congruential logics. This is of interest since there are relevant examples,such as some logics of formal inconsistency that are not congruential.