The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated. We utilize recent results concerning a complete axiomatization of stable conditional independence relative to discrete probability measures to derive perfect model properties of stable conditional independence structures. We show that stable CI can be interpreted as a generalization of Markov networks and establish a connection between sets of stable CI statements and propositional formulas in conjunctive normal form. Consequently, we derive that the implication problem for stable CI is coNP-complete. Finally, we show that Boolean satisfiability (SAT) solvers can be employed to efficiently decide the implication problem and to compute concise, non-redundant representations of stable CI, even for instances involving hundreds of random variables. © 2010 Elsevier Inc. All rights reserved.
Niepert, M., Gucht, D. V., & Gyssens, M. (2010). Logical and algorithmic properties of stable conditional independence. In International Journal of Approximate Reasoning (Vol. 51, pp. 531–543). https://doi.org/10.1016/j.ijar.2010.01.011