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

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.