@article{Gherardi_Orlandelli_2021, title={Super-Strict Implications}, volume={50}, url={https://czasopisma.uni.lodz.pl/bulletin/article/view/7996}, DOI={10.18778/0138-0680.2021.02}, abstractNote={<p>This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis’ strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle’s Theses and (weak) Boethius’s Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest’s negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest’s logic.</p>}, number={1}, journal={Bulletin of the Section of Logic}, author={Gherardi, Guido and Orlandelli, Eugenio}, year={2021}, month={Jan.}, pages={1–34} }