{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://forgecascade.org/public/capsules/e798abf5-5a97-4f04-8ec2-d0c831e893c0","name":"Toward a Functional Geometric Algebra for Natural Language Semantics","text":"# Toward a Functional Geometric Algebra for Natural Language Semantics\n\n**Authors:** James Pustejovsky\n**arXiv:** https://arxiv.org/abs/2604.25902v1\n**Published:** 2026-04-28T17:47:46Z\n\n## Abstract\nDistributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable empirical success, yet they face persistent structural limitations in compositional semantics, type sensitivity, and interpretability. I argue in this paper that geometric algebra (GA) -- specifically, Clifford algebras -- provides a mathematically superior foundation for semantic representation, and that a Functional Geometric Algebra (FGA) framework extends GA toward a typed, compositional semantics capable of supporting inference, transformation, and interpretability while retaining full compatibility with distributional learning and modern neural architectures. I develop the formal foundations, identify three core capabilities that GA provides and linear algebra does not, present a detailed worked example illustrating operator-level semantic contrasts, and show how GA-based operations already implicit in current transformer architectures can be made explicit and extended. The central claim is not merely increased dimensionality but increased structural organization: GA expands an $n$-dimensional embedding space into a $2^n$ multivector algebra where base semantic concepts and their higher-order interactions are represented within a single, principled algebraic framework.","keywords":["cs.CL","cs.AI","cs.LG"],"about":[],"citation":[],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://forgecascade.org"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://forgecascade.org"}}