From Ethical Declarations to Provable Independence: An Ontology-Driven Optimal-Transport Framework for Certifiably Fair AI Systems

TL;DR

This work addresses algorithmic bias in high-stakes AI by reframing fairness as exact independence from a formally specified set of sensitive information. It introduces an ontology-driven, measure-theoretic pipeline that compiles OWL 2-QL ontologies into a bias $\sigma$-algebra $\mathcal{G}$ and uses Delbaen–Majumdar optimal transport to construct a fair representation $Y$ with $Y \perp\!\!\!\perp \mathcal{G}$ while minimizing $\mathbb{E}[\|X-Y\|^2]$. The framework yields a certifiable, auditable approach to fairness, addressing the proxy problem (e.g., ZIP codes or institutions) by exhaustively capturing proxies through ontology reasoning and closed-form measure-theoretic constructs. A detailed implementation blueprint outlines ontology authoring, sigma-algebra generation, a PyTorch-based OT solver, and a JSON-LD certificate with HSIC-based independence testing, enabling end-to-end practice and regulatory verification. The contributions span formal bias modeling, principled integration of symbolic and probabilistic knowledge, and a practical, auditable path toward trustworthy AI in lending and other domains.

Abstract

This paper presents a framework for provably fair AI that overcomes the limits of current bias mitigation methods by systematically removing all sensitive information and its proxies. Using ontology engineering in OWL 2 QL, it formally defines sensitive attributes and infers their proxies through logical reasoning, constructing a sigma algebra G that captures the full structure of biased patterns. Fair representations are then obtained via Delbaen Majumdar optimal transport, which generates variables independent of G while minimizing L2 distance to preserve accuracy. This guarantees true independence rather than mere decorrelation. By modeling bias as dependence between sigma algebras, compiling ontological knowledge into measurable structures, and using optimal transport as the unique fair transformation, the approach ensures complete fairness in tasks like loan approval, where proxies such as ZIP code reveal race. The result is a certifiable and mathematically grounded method for trustworthy AI.

Figures (2)

• Figure 1: Ontology-guided $\sigma$-algebra construction and robustness in AI fairness. Sensitive and proxy classes $S_{\text{onto}}$ are identified in the ontology, extended to measurable events $\llbracket C \rrbracket$, and generate the bias $\sigma$-algebra $\mathcal{G}_O \subseteq F$. A fair representation $Y$ is then constructed such that $Y \perp\!\!\!\perp \mathcal{G}_O$ and is optimal in $L^2$, ensuring debiased loan approval decisions while guaranteeing completeness, transparency, and mathematical rigor.
• Figure 2: Planned implementation pipeline: sensitive and proxy classes $S_{\text{onto}}$ are declared in the ontology, compiled into measurable events $\llbracket C \rrbracket$, and aggregated into the bias $\sigma$-algebra $\mathcal{G}_O$. Optimal transport then constructs a fair representation $Y \perp\!\!\!\perp \mathcal{G}_O$, and certification provides auditability.

Theorems & Definitions (1)

• definition thmcounterdefinition: Ontology-Guided $\sigma$-Algebra of Bias