Paraconsistent Logic and Weakening of Intuitionistic Negation

摘要

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 Z_n and CZ_n, and their paraconsistent properties.