Author:
Norihiro Kamide
Affiliation:
Teikyo University, Japan
Keyword(s):
Connexive Logic, Nelson’s Paraconsistent Logic, Duality, Sequent Calculus, Cut-elimination Theorem, Embedding Theorem.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Knowledge Representation and Reasoning
;
Symbolic Systems
Abstract:
Duality in constructive (or intuitionistic) logics is an important basic property since the dual counterpart of
a given constructive logic can obtain a refutation or falsification of the information or knowledge which is
described by the given logic. In this paper, duality in some intuitinistic paraconsistent logics is investigated.
A constructive connexive logic (connexive logic for short) and Nelson’s paraconsistent four-valued logic are
addressed as an example of such intuitionistic paraconsistent logics. A new logic called dual connexive logic
(dCN), which is the dual counterpart of the connexive logic (CN), is introduced as a Gentzen-type sequent
calculus. Some theorems for embedding dCN into CN and vice versa, which represent the duality between
them, are shown. Similar embedding results cannot be shown for Nelson’s paraconsistent four-valued logic.
But, similar embedding results can be shown for an extended Nelson logic with co-implication.