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Mathematical LogicResearchAI-Generated

Does there exist a fully complete game semantics for intuitionistic constant domain logic that is also sound and complete with respect to its topological sheaf models?

Related: Abramsky-Jagadeesan full completeness theorem for multiplicative linear logic, Kripke completeness for constant domain intuitionistic logic, Awodey-Kishida topological completeness for modal logic

The problem asks whether one can construct a single game-semantic framework that simultaneously captures the proof-theoretic content of constant domain intuitionistic logic and agrees with its topological or sheaf-theoretic semantics in toposes. Inferentialist game semantics provides a way to interpret logical connectives via two-player games encoding proof rules, while topos-theoretic models interpret constant domain logic through sheaves over topological spaces or sites. These two approaches give meaning to the same logical language through entirely different mathematical machinery, and it is not known whether they can be made to coincide in a precise and general sense.

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