Mathematical foundations of matrix syntax

TL;DR

This paper presents the mathematical foundations of matrix syntax, a formal model of linguistic relations, using axiomatic structures that resemble quantum mechanics, offering a potentially more economical approach to language modeling.

Contribution

It introduces an axiomatic mathematical framework for matrix syntax, linking linguistic phenomena to structures similar to quantum mechanics.

Findings

Describes sentences as vectors in a Hilbert space.

Models linguistic chains using tensor products.

Proposes a more economical language theory.

Abstract

Matrix syntax is a formal model of syntactic relations in language. The purpose of this paper is to explain its mathematical foundations, for an audience with some formal background. We make an axiomatic presentation, motivating each axiom on linguistic and practical grounds. The resulting mathematical structure resembles some aspects of quantum mechanics. Matrix syntax allows us to describe a number of language phenomena that are otherwise very difficult to explain, such as linguistic chains, and is arguably a more economical theory of language than most of the theories proposed in the context of the minimalist program in linguistics. In particular, sentences are naturally modelled as vectors in a Hilbert space with a tensor product structure, built from 2x2 matrices belonging to some specific group.