Towards Functorial Language-Games

Jules Hedges
(University of Oxford)
Martha Lewis
(ILLC, University of Amsterdam)

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.

In Martha Lewis, Bob Coecke, Jules Hedges, Dimitri Kartsaklis and Dan Marsden: Proceedings of the 2018 Workshop on Compositional Approaches in Physics, NLP, and Social Sciences (CAPNS 2018), Nice, France, 2-3rd September 2018, Electronic Proceedings in Theoretical Computer Science 283, pp. 89–102.
Published: 8th November 2018.

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