The new approach to mathematical description of structures of stochastic conditional independence from [Studený, 1993a-c] is related to the classical approach by means of the notion of structural semigraphoid. It is shown how to realize the corresponding deductive mechanism to infer probabilistically valid consequences of input information about CI-structure, called facial implication. In the case of 4 attributes (random variables), structural semigraphoids are characterized in terms of inference rules.
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Milan Studený (1993) studied this question.
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