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Classical modal display logic in the calculus of structures and minimal cut-free deep inference calculi for S5

Gore, Rajeev; Tiu, Alwen


We begin by showing how to faithfully encode the Classical Modal Display Logic (CMDL) of Wansing into the Calculus of Structures (CoS) of Guglielmi. Since every CMDL calculus enjoys cut-elimination, we obtain a cut-elimination theorem for all corresponding CoS calculi. We then show how our result leads to a minimal cut-free CoS calculus for modal logic S5. No other existing CoS calculi for S5 enjoy both these properties simultaneously.

CollectionsANU Research Publications
Date published: 2007
Type: Journal article
Source: Journal of Logic and Computation
DOI: 10.1093/logcom/exm026


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