Semigraphoids Are Two-Antecedental Approximations of Stochastic Conditional Independence Models

Abstract

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.