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The Method of Tree-hypersequents for Modal Propositional Logic

Abstract : In this paper we present a method, that we call the tree-hypersequent method, for generating contraction-free and cut-free sequent calculi for modal propositional logics. We show how this method works for the systems K, KD, K4 and KD4, by giving a sequent calculus for these systems which are normally presented in the Hilbert style, and by proving all the main results in a purely syntactical way.
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Francesca Poggiolesi. The Method of Tree-hypersequents for Modal Propositional Logic. David Makinson, Jacek Malinowski, Heinrich Wansing. Towards Mathematical Philosophy, 28, Springer, pp.31-51, 2009, Trends in logic, 978-1-4020-9083-7. ⟨10.1007/978-1-4020-9084-4_3⟩. ⟨halshs-00775815⟩

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