M. Studeny:
Semigraphoids are twoantecedental 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. 546552.
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. 7198.
 and illustrates them by examples and pictures.
 Abstract
 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)
 Keywords
 probabilistic reasoning
 stochastic conditional independence
 inference rule
 dependency model
 semigraphoid

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