Article

Journal of Logic, Language and Information

, Volume 18, Issue 4, pp 515-539

First online:

Hybrid Counterfactual Logics

David Lewis Meets Arthur Prior Again
  • Katsuhiko SanoAffiliated withDepartment of Humanistic Informatics, Graduate School of Letters, Kyoto University Email author 

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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.

Keywords

Counterfactual logic David Lewis Contextually definite description Hybrid logic Arthur Prior The limit assumption Strong completeness Decidability Bisimulation Pure completeness