  This paper proposes a novel framework for certifying the fairness of
predictive models trained on biased data. It draws from query answering for
incomplete and inconsistent databases to formulate the problem of consistent
range approximation (CRA) of fairness queries for a predictive model on a
target population. The framework employs background knowledge of the data
collection process and biased data, working with or without limited statistics
about the target population, to compute a range of answers for fairness
queries. Using CRA, the framework builds predictive models that are certifiably
fair on the target population, regardless of the availability of external data
during training. The framework's efficacy is demonstrated through evaluations
on real data, showing substantial improvement over existing state-of-the-art
methods.
