Strong Boethius' thesis and consequential implication

Journal of Philosophical Logic 26 (5):569-588 (1997)
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Abstract

The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying "Aristotle's Thesis" (p does not imply not p) and "Weak Boethius' Thesis" (if p implies q, then p does not imply not q). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of "Strong Boethius' Thesis" (that p implies q implies that p does not imply not q) is identified

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The Development of Logic.William Kneale & Martha Kneale - 1962 - Philosophy 40 (151):79-83.
Mathematics of Modality.Robert Goldblatt - 1993 - Center for the Study of Language and Information Publications.

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