A Lie-algebraic perspective on Tree-Adjoining Grammars
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913926627721216 |
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| author | Senturia, Isabella Xiao, Elizabeth Marcolli, Matilde |
| author_facet | Senturia, Isabella Xiao, Elizabeth Marcolli, Matilde |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lie-algebraic perspective on Tree-Adjoining Grammars Senturia, Isabella Xiao, Elizabeth Marcolli, Matilde Computation and Language Quantum Algebra Rings and Algebras 91F20, 17B60, 17D25, 18M60 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. |
| title | A Lie-algebraic perspective on Tree-Adjoining Grammars |
| topic | Computation and Language Quantum Algebra Rings and Algebras 91F20, 17B60, 17D25, 18M60 |
| url | https://arxiv.org/abs/2507.03234 |