A Lie-algebraic perspective on Tree-Adjoining Grammars
This work provides a foundational mathematical perspective for computational linguistics, potentially simplifying and unifying TAG frameworks, though it appears incremental in applying Lie algebra to an existing grammar model.
The paper tackles the mathematical formalization of Tree-Adjoining Grammars (TAG) by introducing a novel implementation using combinatorial graph definitions, showing that the adjoining operation forms a Lie algebra. It demonstrates utility by capturing TAG properties like null-adjoining constraints without additional components.
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.