Abstract

The paper presents a contra-classical dialectic logic, inspired and motivated by Hegel s dialectics. Its axiom schemes are 0.1 Thus, in a sense, this dialectic logic is a kind of “mirror image“ of connexive logic. The informal interpretation of ‘ $$\rightarrow $$ ’ emerging from the above four axiom schemes is not of a conditional (or implication); rather, it is the relation of determination in the presence of truth-value gaps: $$\varphi \rightarrow \psi $$ is read as $$\varphi $$ determines $$\psi $$, namely, necessarily, if $$\varphi $$ is true, then $$\psi $$ is either true or false, not gappy. As far as I know, such a connective has not been considered before in the literature.