Non-transitive Correspondence Analysis

Abstract

The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic $${\mathbf{NC}}_{\mathbf{3}}$$ NC 3 . As a result, for each binary extension of $${\mathbf{NC}}_{\mathbf{3}}$$ NC 3 , we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining n-sequent proof systems for any n-valent logic with deterministic or non-deterministic matrices is not applicable to $${\mathbf{NC}}_{\mathbf{3}}$$ NC 3 and its binary extensions.