  We introduce a logical approach to formalizing statistical properties of
machine learning. Specifically, we propose a formal model for statistical
classification based on a Kripke model, and formalize various notions of
classification performance, robustness, and fairness of classifiers by using
epistemic logic. Then we show some relationships among properties of
classifiers and those between classification performance and robustness, which
suggests robustness-related properties that have not been formalized in the
literature as far as we know. To formalize fairness properties, we define a
notion of counterfactual knowledge and show techniques to formalize conditional
indistinguishability by using counterfactual epistemic operators. As far as we
know, this is the first work that uses logical formulas to express statistical
properties of machine learning, and that provides epistemic (resp.
counterfactually epistemic) views on robustness (resp. fairness) of
classifiers.
