A Single Proof of Classical Behaviour in da Costa's Cn Systems

A strong negation in da Costa's Cn systems can be naturally extended from the strong negation (¬) of C1. In [Newton C. A. da Costa. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4):497–510, 10 1974] Newton da Costa proved the connectives {→,∧,∨,¬} in C1 satisfy all schemas and inference rules of classical logic. In the following paper we present a proof that all logics in the Cn herarchy also behave classically as C1. This result tell us the existance of a common property among the paraconsistent family of logics created by da Costa.