Contracting Logics

In this paper, inspired in the field of belief revision, it is presented a novel operation for defining a new logic given a known logic. The operation consists in removing some (maybe undesirable) derived rule from a logic. Besides removing the ‘undesirable’ rule, this operation (called contraction) should change the logic in a minimal way. This paper presents formal definitions for contraction operations over logics, both as sets of rationality postulates and by means of concrete constructions. This allowed us to generalize several notions of maximality of logics presented in the literature. Furthermore, the proposed constructions are applied to the study of some paraconsistent and intermediate logics.