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Communication Dans Un Congrès Année : 2023

Intuitionistic S4 is decidable

Résumé

In this paper we demonstrate decidability for the intuitionistic modal logic S4 first formulated by Fischer Servi. This solves a problem that has been open for almost thirty years since it had been posed in Simpson's PhD thesis in 1994. We obtain this result by performing proof search in a labelled deductive system that, instead of using only one binary relation on the labels, employs two: one corresponding to the accessibility relation of modal logic and the other corresponding to the order relation of intuitionistic Kripke frames. Our search algorithm outputs either a proof or a finite counter-model, thus, additionally establishing the finite model property for intuitionistic S4, which has been another long-standing open problem in the area.
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hal-04267899 , version 1 (02-11-2023)

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Marianna Girlando, Roman Kuznets, Sonia Marin, Marianela Morales, Lutz Strassburger. Intuitionistic S4 is decidable. LICS 2023- 38th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2023, Boston, United States. pp.1-13, ⟨10.1109/LICS56636.2023.10175684⟩. ⟨hal-04267899⟩
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