Implication with possible exceptions
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AbstractWe 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.
2014 ◽
pp. 149-158
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2011 ◽
Vol 2
(2)
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pp. 56-66
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2009 ◽
Vol 19
(1)
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pp. 17-26
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2012 ◽
Vol 5
(4)
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pp. 666-678
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2006 ◽
Vol 71
(3)
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pp. 903-957
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2018 ◽
Vol 11
(2)
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pp. 279-294
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