Constructive discursive logic with strong negation

Seiki Akama, Jair Minoro Abe, Kazumi Nakamatsu


Jaskowski’s discursive logic (or discussive logic) is the first formal paraconsistent logic which is classified as a non-adjunctive system. It is now recognized that discursive logic is not generally appropriate for paraconsistent reasoning. To improve it in a constructive setting, we propose a constructive discursive logic with strong negation CDLSN based on Nelson’s constructive logic N-. 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 advantages of the proposed system over other paraconsistent systems.

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