Toward a Unified Mathematics of Concepts

Excerpt

arXiv:2609.24554v1 Announce Type: new Abstract: Concepts are commonly defined as abstract, compact representations of knowledge and treated as basic units of intelligent behavior. Yet, cognition, psychology, and AI lack a shared mathematical language for them. Modern systems represent concepts as vectors, distributions, symbols, graphs, and other structures, but these formalisms are typically treated as competing rather than as solutions to a common problem. We propose an operation-based view th