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Modular Focused Proof Systems for Intuitionistic Modal Logics

Kaustuv Chaudhuri 1 Sonia Marin 1 Lutz Straßburger 1
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : Focusing is a general technique for syntactically compartmentalizing the non-deterministic choices in a proof system, which not only improves proof search but also has the representational benefit of distilling sequent proofs into synthetic normal forms. However, since focusing is usually specified as a restriction of the sequent calculus, the technique has not been transferred to logics that lack a (shallow) sequent presentation, as is the case for some of the logics of the modal cube. We have recently extended the focusing technique to classical nested sequents, a generalization of ordinary sequents. In this work we further extend focusing to intuitionistic nested sequents, which can capture all the logics of the intuitionistic S5 cube in a modular fashion. We present an internal cut-elimination procedure for the focused system which in turn is used to show its completeness.
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https://hal.inria.fr/hal-01417603
Contributor : Lutz Straßburger <>
Submitted on : Thursday, December 15, 2016 - 5:15:06 PM
Last modification on : Thursday, January 7, 2021 - 3:40:14 PM

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Kaustuv Chaudhuri, Sonia Marin, Lutz Straßburger. Modular Focused Proof Systems for Intuitionistic Modal Logics. FSCD 2016 - 1st International Conference on Formal Structures for Computation and Deduction, Jun 2016, Porto, Portugal. ⟨10.4230/LIPIcs.FSCD.2016.16⟩. ⟨hal-01417603⟩

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