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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.

Classical Modal Display Logic in the Calculus of Structures and Minimal Cut-free Deep Inference Calculi for S5