Mathematical foundations of matrix syntax
This work addresses the challenge of formalizing language syntax for linguists and researchers, but it is incremental as it builds on existing mathematical structures without introducing a new paradigm.
The paper tackles the problem of modeling syntactic relations in language by developing matrix syntax, a formal model with mathematical foundations, and shows that it can describe difficult language phenomena like linguistic chains more economically than existing theories.
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.