Towards Functorial Language-Games

TL;DR

This paper develops a compositional semantics for natural language using category theory, specifically functors to open games, enabling a game-theoretic interpretation of language with modifications to existing grammatical categories.

Contribution

It introduces a novel approach combining categorical semantics with open games, extending the functorial framework to model language-games.

Findings

Successfully models Wittgenstein's language-games

Adapts grammatical categories for open game semantics

Provides a foundation for functorial language-games

Abstract

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.