C1-Compatible Transitive Extensions of System CT

Abstract

Da Costa's main logics can be built up as extensions of a system of common logic, which is classical positive logic plus a classicality symbol and a weak negation satisfying converse double negation and excluded middle. Common logic can alternatively be strengthened into transitive (gradualistic) logic. The choice between those two strengthenings depends on philosophical options. Both approaches are close relatives which constitute a natural sub-family of the larger paraconsistent kind.