Hybrid counterfactual logics

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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DOI 10.1007/s10849-009-9090-0
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References found in this work BETA
Counterfactuals.David K. Lewis - 1973 - Blackwell.
A Theory of Conditionals.Robert C. Stalnaker - 1968 - Americal Philosophical Quarterly:98-112.
Nominal Tense Logic.Patrick Blackburn - 1992 - Notre Dame Journal of Formal Logic 34 (1):56-83.
Tense, Temporal Reference, and Tense Logic.Patrick Blackburn - 1994 - Journal of Semantics 11 (1-2):83-101.

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Citations of this work BETA
Proof Analysis for Lewis Counterfactuals.Sara Negri & Giorgio Sbardolini - forthcoming - Review of Symbolic Logic:1-32.
Axiomatizing Hybrid Products.Katsuhiko Sano - 2010 - Journal of Applied Logic 8 (4):459-474.

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