From Contrastive to Abductive Explanations and Back Again

Explanations of Machine Learning (ML) models often address a `Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that address a `Why Not?' question, i.e. finding a change of feature values that guarantee a change of prediction. Given their goals, these two forms of explaining predictions of ML models appear to be mostly unrelated. However, this paper demonstrates otherwise, and establishes a rigorous formal relationship between `Why?' and `Why Not?' explanations. Concretely, the paper proves that, for any given instance, `Why?' explanations are minimal hitting sets of `Why Not?' explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.