A Set-Theoretic Framework for Enterprise Risk Taxonomy Classification with Categorical Semantics

Enterprise risk taxonomies face a persistent classification challenge: deciding which candidate concepts belong in a vertical risk hierarchy and which operate as cross-cutting drivers that overlay many categories. This article presents a reproducible, auditable classification methodology that uses set-theoretic operations over attributed structures, while using categorical concepts as a semantic organizing language. The framework defines three quantitative tests— Relevance (Concentration Ratio), Distinction (factorization), and Materiality (Herfindahl–Hirschman Index)—and a simple decision rule to classify taxonomy candidate concepts as hierarchical sub-risks or cross-cutting drivers. We demonstrate the approach with a worked application to geopolitical risk and validate behavior on representative edge cases (model risk, climate risk). The method is computationally tractable for typical enterprise taxonomies and supports governance-ready documentation of classification decisions.