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  1. The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1977 - In Wilfrid Hodges (ed.), Logic. New York: Penguin Books. pp. 1-32.
    Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers (...)
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  • Method of Tree-Hypersequents for Modal Propositional Logic.Francesca Poggiolesi - 2009 - In Jacek Malinowski David Makinson & Wansing Heinrich (eds.), Towards Mathematical Philosophy. Springer. pp. 31–51.
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  • Cut-free sequent calculi for some tense logics.Ryo Kashima - 1994 - Studia Logica 53 (1):119 - 135.
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  • On the proof theory of the modal logic for arithmetic provability.Daniel Leivant - 1981 - Journal of Symbolic Logic 46 (3):531-538.
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  • Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
    A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.
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  • A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic.Brian Hill & Francesca Poggiolesi - 2010 - Studia Logica 94 (1):47-72.
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  • The modal logic of provability: Cut-elimination. [REVIEW]Silvio Valentini - 1983 - Journal of Philosophical Logic 12 (4):471 - 476.
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  • Reflecting the semantic features of S5 at the syntactic level.Francesca Poggiolesi - 2010 - In Marcello D'Agostino, Federico Laudisa, Giulio Giorello, Telmo Pievani & Corrado Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. College Publications. pp. 13--25.
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