Geometric Algebra Proposed as New Foundation for Natural Language Semantics

A recent publication on arXiv introduces Functional Geometric Algebra (FGA) as a mathematically enhanced substitute for traditional linear algebra in the realm of natural language semantics. The author contends that existing distributional and neural methodologies relying on vectors, matrices, and tensors encounter ongoing challenges regarding compositional semantics, type sensitivity, and interpretability. The study highlights geometric algebra, particularly Clifford algebras, as a robust basis that advances typed, compositional semantics, facilitating inference, transformation, and interpretability, while also aligning with distributional learning and contemporary neural frameworks. It establishes formal foundations and pinpoints three essential features unique to geometric algebra that linear algebra lacks. This research is documented in arXiv:2604.25902v1.