A Lie-algebraic perspective on Tree-Adjoining Grammars
arXiv:2507.03234
Abstract
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.
14 pages, 7 figures. To appear in the proceedings of the 18th Meeting on the Mathematics of Language (MOL 2025)