Implication-with-possible-exceptions

Abstract. We introduce an implication-with-possible-exceptions and define validity of rules-withpossible-exceptions by means of the topological notion of a full subset. Our implication-with-possibleexceptions 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: Conference
• Year: 2000
• Where: RELMICS
• Authors: Nerman Jurrjus, Harrie C. M. de Swart
• Keywords: Classical Propositional Logic, Define Validity, Preferential Consequence Relation, RELMICS 2000, Theoretical Computer Science