  Recent years have witnessed the widespread use of artificial intelligence
(AI) algorithms and machine learning (ML) models. Despite their tremendous
success, a number of vital problems like ML model brittleness, their fairness,
and the lack of interpretability warrant the need for the active developments
in explainable artificial intelligence (XAI) and formal ML model verification.
The two major lines of work in XAI include feature selection methods, e.g.
Anchors, and feature attribution techniques, e.g. LIME and SHAP. Despite their
promise, most of the existing feature selection and attribution approaches are
susceptible to a range of critical issues, including explanation unsoundness
and out-of-distribution sampling. A recent formal approach to XAI (FXAI)
although serving as an alternative to the above and free of these issues
suffers from a few other limitations. For instance and besides the scalability
limitation, the formal approach is unable to tackle the feature attribution
problem. Additionally, a formal explanation despite being formally sound is
typically quite large, which hampers its applicability in practical settings.
Motivated by the above, this paper proposes a way to apply the apparatus of
formal XAI to the case of feature attribution based on formal explanation
enumeration. Formal feature attribution (FFA) is argued to be advantageous over
the existing methods, both formal and non-formal. Given the practical
complexity of the problem, the paper then proposes an efficient technique for
approximating exact FFA. Finally, it offers experimental evidence of the
effectiveness of the proposed approximate FFA in comparison to the existing
feature attribution algorithms not only in terms of feature importance and but
also in terms of their relative order.
