Paraconsistent Logic and Weakening of Intuitionistic Negation

A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. In an earlier paper [Notre Dame J. Form. Log. 49 (2008), 401-424], we developed the systems of weakening of intuitionistic negation logic, called Z(n) and CZ(n), in the spirit of da Costa's approach by preserving, differently from da Costa, the fundamental properties of negation: antitonicity, inversion and additivity for distributive lattices. Taking into account these results, we make some observations on the modified systems of Zn and CZn, and their paraconsistent properties.