Eliminability of cut in hypersequent calculi for some modal logics of linear frames

Hypersequent calculus HC for three modal logics of linear frames (K4.3, KD4.3 and S4.3) is presented.Adequacy of HC for these logics is shown.Eliminability of Cut is demonstrated. Hypersequent calculi, introduced independently by Pottinger and Avron, provide a powerful generalization of ordinary sequent calculi. In the paper we present a proof of eliminability of cut in hypersequent calculi for three modal logics of linear frames: K4.3, KD4.3 and S4.3. Our cut-free calculus is based on Avron's HC formalization for Godel-Dummett's logic. The presented proof of eliminability of cut is purely syntactical and based on Ciabattoni, Metcalfe, Montagna's proof of eliminability of cut for hypersequent calculi for some fuzzy logics with modalities.

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