Explanation of Pseudo-Boolean Functions Using Cooperative Game Theory and Prime Implicants.

Explanation methods can be formal or heuristic-based. Many explanation methods have been developed. Formal methods provide principles to derive sufficient reasons (prime implicants) or necessary reasons (counterfactuals, causes). These approaches are appealing but require to discretize the input and output spaces. Heuristic-based approaches such as feature attribution (such as the Shapley value) work in any condition but the relation to explanation is less clear. We show that they cannot distinguish between conjunction and disjunction, which is not the case with sufficient explanations. This work is an initial work that aims at combining some idea of prime implicants into feature attribution, in order to measure sufficiency of the features. We apply it to two values - the proportional division and the Shapley value.