Problem
Research questions and friction points this paper is trying to address.
Base-extension Semantics
Game Semantics
Proof-theoretic Semantics
Fully Abstract Correspondence
Intensional Meaning
Inferentialist Game Semantics (Extended Abstract)
🤖 AI Summary
This work establishes a fully abstract correspondence between base-extension semantics (B-eS) in proof-theoretic semantics and Hyland–Ong game semantics, aiming to unify intensional accounts of meaning for logical systems. By linking the dynamic, interactive nature of logical inference with atom-based provability, the study develops an intensional semantic framework grounded in proof computation and integrates Sandqvist-style completeness techniques. It presents the first fully abstract connection between B-eS and Hyland–Ong game semantics, yielding a sound and complete semantic characterization for intuitionistic propositional logic. The expressiveness and applicability of the framework are further demonstrated through a case study on a 4×4 Sudoku puzzle.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Game Semantics
Base-extension Semantics
Proof-theoretic Semantics
Fully Abstract Correspondence
Intensional Meaning
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