Towards Functorial 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.Comment: In Proceedings CAPNS 2018, arXiv:1811.0270

Fibrational linguistics: Language acquisition

In this work we show how FibLang, a category-theoretic framework concerned with the interplay between language and meaning, can be used to describe vocabulary acquisition, that is the process with which a speaker $p$ acquires new vocabulary (through experience or interaction). We model two different kinds of vocabulary acquisition, which we call `by example' and `by paraphrasis'. The former captures the idea of acquiring the meaning of a word by being shown a witness representing that word, as in `understanding what a cat is, by looking at a cat'. The latter captures the idea of acquiring meaning by listening to some other speaker rephrasing the word with others already known to the learner. We provide a category-theoretic model for vocabulary acquisition by paraphrasis based on the construction of free promonads. We draw parallels between our work and Wittgenstein's dynamical approach to language, commonly known as 'language games'.Comment: ACT2022 version; FibLang chapter 0 is at arXiv:2201.0113

Towards functorial 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