Towards Functorial Language-Games
This work addresses a theoretical challenge in computational linguistics by integrating game theory into categorical semantics, though it appears incremental as it builds on existing categorical frameworks.
The paper tackled the problem of compositionally building game-theoretic semantics for natural language by using open games as the semantic category, requiring modifications to the grammar category due to structural mismatches. It illustrated the approach with simple examples from Wittgenstein's language-games.
In categorical compositional semantics of natural language one studies functors from a category of grammatical derivations (such as a Lambek pregroup) to a semantic category (such as real vector spaces). We compositionally build game-theoretic semantics of sentences by taking the semantic category to be the category whose morphisms are open games. This requires some modifications to the grammar category to compensate for the failure of open games to form a compact closed category. We illustrate the theory using simple examples of Wittgenstein's language-games.