Hybrid counterfactual logics David Lewis meets Arthur prior again

Journal of Logic, Language and Information 18 (4):515-539 (2009)
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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

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2009-05-18

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Katsuhiko Sano
Hokkaido University

Citations of this work

Proof analysis for Lewis counterfactuals.Sara Negri & Giorgio Sbardolini - 2016 - Review of Symbolic Logic 9 (1):44-75.
Axiomatizing hybrid products.Katsuhiko Sano - 2010 - Journal of Applied Logic 8 (4):459-474.

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References found in this work

Counterfactuals.David K. Lewis - 1973 - Malden, Mass.: Blackwell.
Conditional Logic.Donald Nute - 1989 - Journal of Symbolic Logic 54 (4):1477-1479.
Arthur Prior and Hybrid Logic.Patrick Blackburn - 2006 - Synthese 150 (3):329-372.

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