Modal logic
Topological Perspective on the Hybrid Proof Rules
Electronic Notes in Theoretical Computer Science (ENTCS)
Axiomatizing Hybrid Products of Monotone Neighborhood Frames
Electronic Notes in Theoretical Computer Science (ENTCS)
Sequent systems for lewis' conditional logics
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
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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.