M. Studeny: Semigraphoids are two-antecedental approximations of stochastic conditional independence models. In Uncertainty in Artificial Intelligence. Proceedings of the Tenth Conference (R.L. de Mantaras, D. Poole eds.), Morgan Kaufmann, San Francisco CA 1994, pp. 546-552.

The paper describes in a simple way the results published later in the paper:
M. Studeny: Semigraphoids and structures of probabilistic conditional independence. Annals of Mathematics and Artificial Intelligence 21 (1997), n. 1, pp. 71-98.
and illustrates them by examples and pictures.
The semigraphoid closure of every couple of conditional independence statements is a stochastic conditional independence model. As a consequence of this result, it is shown that every probabilistically sound inference rule for conditional independence models, having at most two antecedents, is derivable from the semigraphoid inference rules. This justifies the use of semigraphoids as approximations of stochastic conditional independence models in probabilistic reasoning. The list of all nineteen potential dominant elements of the mentioned semigraphoid closure is given as a byproduct. However, the proof of the crucial lemma was beyond the scope of a conference paper; it is proved in the journal paper mentioned above.

AMS classification 68T30 (03B30)

probabilistic reasoning
stochastic conditional independence
inference rule
dependency model

A scanned pdf copy (1119kB) is available.