Fibrational Linguistics (FibLang): Language Acquisition

TL;DR

This paper introduces FibLang, a category-theoretic framework for modeling vocabulary acquisition processes like learning by example and paraphrasis, linking linguistic theory with formal mathematical structures.

Contribution

It provides a novel category-theoretic model for vocabulary acquisition, especially by paraphrasis, using free promonads, and connects this to Wittgenstein's language games.

Findings

Model of vocabulary acquisition by paraphrasis using free promonads

Formal connection between language games and category theory

Framework for describing language learning processes

Abstract

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'.