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.