Generalized Rules of Probabilistic Independence

Probabilistic independence, as a fundamental concept of probability, enables probabilistic inference to become computationally feasible for increasing numbers of variables. By adding five more rules to an existing sound, yet incomplete, system of rules of independence, Studený completed it for the class of structural semi-graphoid independence relations over four variables. In this paper, we generalize Studený’s rules to larger numbers of variables. We thereby contribute enhanced insights in the structural properties of probabilistic independence. In addition, we are further closing in on the class of probabilistic independence relations, as the class of relations closed under the generalized rules is a proper subclass of the class closed under the previously existing rules.