Strong Boethius' thesis and consequential implication
Journal of Philosophical Logic 26 (5):569-588 (1997)
| 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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