Connexive Gentzen

Abstract

Connexive logic contains propositional theses such as NCpNp and CCpqNCpNq that are false in two-valued logic. It derives from remarks made by Sextus Empiricus in the fourth century B.C. The logic of causal and subjunctive conditionals is also connexive, since ‘If X is dropped, it will hit the floor’ contradicts ‘If X is dropped, it will not hit the floor’. In the paper below, a Gentzen Sequenzenkalkul formulation of connexive logic is constructed, and a proof is given of the elimination theorem.