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Hybrid Counterfactual Logics: David Lewis Meets Arthur Prior Again

Katsuhiko Sano
Journal of Logic, Language, and Information
Vol. 18, No. 4, Hybrid Logic: Dedicated to the Memory of Volker Weber (Autumn, 2009), pp. 515-539
Published by: Springer
Stable URL: http://www.jstor.org/stable/40345508
Page Count: 25
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Hybrid Counterfactual Logics: David Lewis Meets Arthur Prior Again
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Abstract

The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis's counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference "The pig is Mary; Mary is pregnant; therefore the pig is pregnant" as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following technical advantages: (i) it preserves the completeness and decidability of Lewis's logic; (ii) it allows us to characterize the Limit Assumption as a proof-rule with some side-conditions; and (iii) it enables us to establish a general Kripke completeness result by using the proof-rule corresponding to the Limit Assumption.

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