A modal sequent calculus for a fragment of arithmetic

Studia Logica 39 (2-3):245 - 256 (1980)
Abstract
Global properties of canonical derivability predicates (the standard example is Pr() in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, interpolation and the fixed point theorem.
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Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.
Wolfgang Rautenberg (1983). Modal Tableau Calculi and Interpolation. Journal of Philosophical Logic 12 (4):403 - 423.

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