# A Lie-algebraic perspective on Tree-Adjoining Grammars

arXiv: https://arxiv.org/abs/2507.03234 · HTML: https://mlsanity.com/paper/2507.03234/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 1 of 1)

- [The categorical contours of the Chomsky-Sch"utzenberger representation theorem](https://mlsanity.com/paper/2405.14703/) (2023)

## Abstract (arXiv)

We provide a novel mathematical implementation of tree-adjoining grammars using two combinatorial definitions of graphs. With this lens, we demonstrate that the adjoining operation defines a pre-Lie operation and subsequently forms a Lie algebra. We demonstrate the utility of this perspective by showing how one of our mathematical formulations of TAG captures properties of the TAG system without needing to posit them as additional components of the system, such as null-adjoining constraints and feature TAG.