Math Graduate Student Seminar

Tree-adjoining grammars (TAGs) are a formal grammar where the units of manipulation are trees instead of strings. Any context-free string grammar can be modelled by a TAG, as well as certain context-sensitive ones. We provide a novel mathematical implementation of TAGs 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 show that one of our mathematical formulations of TAG captures linguistic properties of the TAG system, such as null-adjoining constraints and feature TAG, without needing to posit them as additional constraints. The talk is self-contained and assumes minimal knowledge of formal languages, Lie algebras or linguistics. This is based on joint work with Isabella Senturia and Matilde Marcolli.