Journal of Symbolic Logic

Implication with Possible Exceptions

Herman Jurjus and Harrie de Swart

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We introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not determine the meaning of deducibility and inference as implication-without-exceptions.

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J. Symbolic Logic, Volume 66, Issue 2 (2001), 517-535.

First available in Project Euclid: 6 July 2007

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Jurjus, Herman; de Swart, Harrie. Implication with Possible Exceptions. J. Symbolic Logic 66 (2001), no. 2, 517--535.

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