On the Logic of Causal Models

TL;DR

This paper investigates the use of Directed Acyclic Graphs (DAGs) for representing and inferring causal and conditional independence relationships, demonstrating their soundness, completeness, and inherent consistency in causal modeling.

Contribution

It proves that DAGs provide polynomially sound and complete inference mechanisms for conditional independence and establishes the Armstrong property for DAGs, ensuring their displayed dependencies are consistent.

Findings

DAGs enable polynomially sound and complete inference of conditional independencies.

D-separation identifies more valid independencies than other criteria.

Every DAG corresponds to some probability distribution embodying its independencies.

Abstract

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.