Game Semantics for Constructive Modal Logic

Matteo Acclavio (1) , Davide Catta (2) , Lutz Strassburger (3)

1 Uni.lu - Université du Luxembourg
2 TEXTE - Exploration et exploitation de données textuelles
3 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion

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.

Domaines: Logique en informatique [cs.LO]

Matteo Acclavio, Davide Catta, Lutz Strassburger. Game Semantics for Constructive Modal Logic. TABLEAUX 2021 - 30th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Sep 2021, Birmingham, United Kingdom. pp.428-445, ⟨10.1007/978-3-030-86059-2_25⟩. ⟨hal-03369819⟩