Constructive discursive logic: Paraconsistency in constructivism

Abstract

We propose a constructive discursive logic with strong negation CDLSN based on Nelson’s constructive logic N - as a constructive version of Jaśkowski’s discursive logic. In CDLSN, discursive negation is defined similar to intuitionistic negation and discursive implication is defined as material implication using discursive negation. We give an axiomatic system and Kripke semantics with a completeness proof. We also discuss some possible applications of CDLSN for common-sense reasoning.