Inferentialist Game Semantics (Extended Abstract)
arXiv:2607.13855
The paper establishes a fully abstract correspondence between base‑extension proof‑theoretic semantics and Hyland‑Ong game semantics, demonstrating how games can model intensional meaning of logical systems and illustrating the approach with a 4×4 Sudoku example.
Abstract
Game semantics is an elegant approach to the formal semantics of reasoning and computation that grounds model-theoretic concepts of truth and validity in game-theoretic concepts that emphasize the dynamic and interactive aspects of logical reasoning. In Hyland-Ong games, plays are traces of interactions between a player and an environment and such games provide a naturally appealing semantics for computation that is derived from proof-search in logical systems. Such a semantics can be seen as providing an intensional theory of meaning for systems of logic in terms of (the computation of) proofs. In logic, an intensional theory of meaning for systems of logic is offered by proof-theoretic semantics; in particular, by base-extension semantics (B-eS), in which the model-theoretic interpretation of atomic propositions in a satisfaction relation is replaced by a validity relation which uses provability in `bases' of atomic rules. We establish a fully abstract correlation between B-eS and Hyland-Ong game semantics, employing techniques similar to those used by Sandqvist to give a sound and complete B-eS for intuitionistic propositional logic. We illustrate our semantics through the example of 4x4 Sudoku.