Logical Properties of Stable Conditional Independence

We utilize recent results concerning a complete axiomatization of stable conditional independence (CI) relative to discrete probability measures to derive perfect model properties of stable CI structures. We show that stable CI can be interpreted as a generalization of undirected graphical models and establish a connection between sets of stable CI statements and propositional formulae in conjunctive normal form. Consequently, we derive that the implication problem for stable CI is coNP-complete. Finally, we show that SAT solvers can be employed to efficiently decide the implication problem and to compute nonredundant representations of stable CI, even for instances involving hundreds of variables.