Super-Strict Implications

This paper introduces the logics of super-strict implications, where a implication is strengthening C.I. Lewis' strict that avoids not only paradoxes material but also those implication. The semantics implications obtained by (normal) relational for We consider all are based on frames modal in cube. it shown connexive they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation given means G3-style labelled calculi, proved structural rules inference admissible these calculi. It validity S5-based logic equivalent to G. Priest's negation-as-cancellation-based logic. Hence, we give cut-free calculus