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Game Semantics for Constructive Modal Logic

Abstract : In this paper we provide the first game semantics for the constructive modal logic CK. We first define arenas encoding modal formulas, we then define winning innocent strategies for games on these arenas, and finally we characterize the winning strategies corresponding to proofs in the logic CK. To prove the full-completeness of our semantics, we provide a sequentialization procedure of winning strategies. We conclude the paper by proving their compositionality and showing how our results can be extend to the constructive modal logic CD.
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https://hal.inria.fr/hal-03369819
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Submitted on : Thursday, October 7, 2021 - 3:48:29 PM
Last modification on : Friday, October 22, 2021 - 3:07:18 PM

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Matteo Acclavio, Davide Catta, Lutz Straßburger. Game Semantics for Constructive Modal Logic. Automated Reasoning with Analytic Tableaux and Related Methods, 12842, Springer International Publishing, pp.428-445, 2021, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-86059-2_25⟩. ⟨hal-03369819⟩

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