Abduction is the process of generating the best explanation as to why a fact is observed given what is already known. A real problem in this area is the selective generation of hypotheses that have some reasonable prospect of being valid. In this paper, we propose the notion of skeptical abduction as a model to face this problem. Intuitively, the hypotheses pointed out by skeptical abduction are all the explanations that are consistent with the given knowledge and that are minimal, i.e. not unnecessarily general. Our contribution is twofold. First, we present a formal characterization of skeptical abduction in a logical framework. On this ground, we address the problem of mechanizing skeptical abduction. A new method to compute minimal and consistent hypotheses in propositional logic is put forward. The extent to which skeptical abduction can be mechanized in first—order logic is also investigated. In particular, two classes of first-order formulas in which skeptical abduction is effective are provided. As an illustration, we finally sketch how our notion of skeptical abduction applies as a theoretical tool to some artificial intelligence problems (e.g. diagnosis, machine learning).