Semigraphoids Are Two-Antecedental Approximations of Stochastic Conditional Independence Models
The semigraphoid closure of every couple of CI-statements (GI=conditional independence) is a stochastic CI-model. As a consequence of this result it is shown that every probabilistically sound inference rule for CI-model, having at most two antecedents, is derivable from the semigraphoid inference rules. This justifies the use of semigraphoids as approximations of stochastic CI-models in probabilistic reasoning. The list of all 19 potential dominant elements of the mentioned semigraphoid closure is given as a byproduct.
PDF Link: /papers/94/p546-studeny.pdf
AUTHOR = "Milan Studeny
TITLE = "Semigraphoids Are Two-Antecedental Approximations of Stochastic Conditional Independence Models",
BOOKTITLE = "Proceedings of the Tenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-94)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1994",
PAGES = "546--552"