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Implication with possible exceptions

Published online by Cambridge University Press:  12 March 2014

Herman Jurjus  and
Harrie de Swart
Herman Jurjus
Affiliation:
Department of Philosophy, Tilburg University, P.O. Box 90153, Nl 5000 Le Tilburg, The, Netherlands, E-mail: hhjurjus@hetnet.nl
Harrie de Swart
Affiliation:
Department of Philosophy, Tilburg University, P.O. Box 90153, Nl 5000 Le Tilburg, The, Netherlands, E-mail: H.C.M.deSwart@kub.nl
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 517 - 535
Copyright
Copyright © Association for Symbolic Logic 2001

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