Semigraphoids are Two-Antecedental Approximations of Stochastic Conditional Independence Models

The semigraphoid closure of every couple of CI-statements (CI=conditional independence) is a stochastic CI-model. As a consequence of this result it is shown that every probabilistically sound inference rule for CI-models, 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. 1 INTRODUCTION Many reasoning tasks arising in AI can be considerably simplified if a suitable concept of relevance or irrelevance of variables is utilized. The conditional irrelevance in probabilistic reasoning is modelled by means of the concept of stochastic conditional independence (CI) -- details about the probabilistic approach to uncertainty handling in AI are in Pearl's book (1988). The fact that every CI-statement can be interpreted as certain qualitative re..