Abstract

A strong negation in da Costa’s systems can be naturally extended from the strong negation (¬) of . 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 ${\rightarrow, \land, \lor, \neg}$ in $C_1$ satisfy all schemas and inference rules of classical logic. In the following paper we present a proof that all logics in the $C_n$ hierarchy also behave classically as $C_1$. This result tell us the existance of a common property among the paraconsistent family of logics created by da Costa.