Different conditional independence models have been proposed in literature; in this paper we consider models induced by conditional probabilities based on the definition of conditional cs-independence. These models need not comply with the symmetry property, so that they have not the graphoid structure. Hence, the well-known d-separation criterion for directed acyclic graphs may not be able to represent such independence models. Therefore, we introduce a new separation criterion called L-separation. We study its main properties and show how it allows to represent the above-mentioned independence models through directed acyclic graphs. © 2002 Elsevier Science Inc. All rights reserved.
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