用李代数重新诠释树附着语法，揭示其内在代数结构。
A Lie-algebraic perspective on Tree-Adjoining Grammars
- 基于图的组合定义构建树附着语法新模型
- 证明了附着操作构成预李代数并生成李代数
- 无需额外假设即可自然捕获空附着与特征语法特性
我们提出一种基于两种图的组合定义的新数学实现方式，用于树附着语法（TAG）。通过这一视角，我们证明附着操作构成一个预李代数，并进一步形成李代数。该方法的实用性体现在：其中一个数学表述能自然捕捉标签系统中的属性，无需额外引入如空附着约束或特征标签等附加组件。
原文摘要 · Abstract (English)
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.
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