Proof analysis in modal logic

Journal of Philosophical Logic 34 (5/6):507 - 544 (2005)
Abstract
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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    Melvin Fitting (2012). Prefixed Tableaus and Nested Sequents. Annals of Pure and Applied Logic 163 (3):291 - 313.
    Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.

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