4 research outputs found
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 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