We address the fundamental task of computing rigorous, sample-based abductive explanations for machine learning predictions. In this setting, we propose a new class of explanations derived from a generalization of the consensus operation in propositional logic. We prove that these explanations are precisely those that satisfy a monotonicity property ensuring they remain valid as the sample grows. Furthermore, we show that their computation can be performed efficiently. As a direct application, we also show how these explanations can be used to identify necessary and relevant features. The proposed framework provides a robust and scalable approach to formal model-agnostic XAI.

We address the problem of attributing responsibility to individual clauses for the unsatisfiability of a propositional formula. Recent work adopted the Shapley-Shubik power index, proposing a probabilistic approximation algorithm. However, although polynomial, the required number of SAT solver calls becomes impractical when the input formula is not easy to solve. In such cases, it is often possible to enumerate a partial set of minimal unsatisfiable subsets (MUSes) and minimal correction subsets (MCSes). In this paper, we demonstrate that these subsets can be leveraged to efficiently bound and approximate the Shapley-Shubik index. We introduce a framework that exploits the structural information provided by the available sets to derive useful attribution explanations.