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From 2-Sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics

Abstract : We extend to natural deduction the approach of Linear Nested Sequents and of 2-Sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction: only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalization, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (à la Scott) for formulating sound deduction rules.
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https://hal.inria.fr/hal-03342394
Contributor : Simone Martini Connect in order to contact the contributor
Submitted on : Wednesday, September 15, 2021 - 7:20:39 AM
Last modification on : Friday, July 8, 2022 - 10:06:06 AM
Long-term archiving on: : Thursday, December 16, 2021 - 6:02:11 PM

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Simone Martini, Andrea Masini, Margherita Zorzi. From 2-Sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics. ACM Transactions on Computational Logic, 2021, 22 (3), pp.1-29. ⟨10.1145/3461661⟩. ⟨hal-03342394⟩

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