Fibrational linguistics: First concepts

TL;DR

This paper introduces FibLang, a general mathematical framework for linguistics based on fibrations, which models the interaction between language and cognition in a flexible, axiomatization-agnostic way, enabling the application of category theory tools.

Contribution

It presents the first fibrational framework for linguistics that is compatible with existing categorical models and emphasizes conceptual motivation over specific axiomatizations.

Findings

Provides a formal fibrational model for linguistics

Ensures compatibility with existing categorical language models

Facilitates the use of categorical logic in linguistic analysis

Abstract

We define a general mathematical framework for linguistics based on the theory of fibrations, called FibLang. We start by modelling the interaction between linguistics and cognition in the most general way possible, with a heavy focus on conceptually motivating any assumption we make. The advantage is that FibLang remains agnostic with respect to any particular axiomatization of grammar one may choose. As such, it is compatible with already existing categorical models of language (such as for example, DisCoCat), providing a formally sound framework to apply mathematical tools developed in the context of category theory, mainly categorical logic, to the study of language