A Dialectic Contra-Classical Logic

The paper presents a contra-classical dialectic logic, inspired and motivated by Hegel s dialectics. Its axiom schemes are (H-1) :proves Phi ->-Phi (H-2) :proves-Phi ->Phi (H-3) :proves (Phi ->psi)->(Phi ->psi) (H-4) :proves(Phi ->-psi)-> (Phi ->psi) (0.1) Thus, in a sense, this dialectic logic is a kind of "mirror image" of connexive logic. The informal interpretation of `->' 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:Phi ->psi is read as Phi determines psi, namely, necessarily, if Phi 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.