On the Logic of Causal Models
  This paper explores the role of Directed Acyclic Graphs (DAGs) as a
representation of conditional independence relationships. We show that DAGs
offer polynomially sound and complete inference mechanisms for inferring
conditional independence relationships from a given causal set of such
relationships. As a consequence, d-separation, a graphical criterion for
identifying independencies in a DAG, is shown to uncover more valid
independencies then any other criterion. In addition, we employ the Armstrong
property of conditional independence to show that the dependence relationships
displayed by a DAG are inherently consistent, i.e. for every DAG D there exists
some probability distribution P that embodies all the conditional
independencies displayed in D and none other.
