Thomas Verma and Judea Pearl,
Causal Networks: Semantics and Expressiveness,
In Uncertainty in Artificial Intelligence-4,
New York, NY, USA, pp. 69-76, Elsevier Science Publishing Company, Inc., 1988.
Thomas Verma and Judea Pearl,
Causal Networks: Semantics and Expressiveness,
In Uncertainty in Artificial Intelligence-4,
New York, NY, USA, pp. 69-76, Elsevier Science Publishing Company, Inc., 1988.Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with graphical structures such as undirected graphs and directed acyclic graphs (DAGs). In this paper we show that the graphical criterion called d-separation is a sound rule for reading independencies from any DAG based on a causal input list drawn from a graphoid. The rule may be extended to cover DAGs that represent functional dependencies as well as conditional dependencies.