Axiomatizing Causal Reasoning

TL;DR

This paper axiomatizes causal reasoning in models defined by equations, covering recursive, unique-solution, and general theories, and explores the complexity of reasoning procedures across these classes.

Contribution

It provides the first comprehensive axiomatizations for various classes of causal models, extending the language for the most general class, and analyzes reasoning complexity.

Findings

Axiomatizations for recursive, unique-solution, and arbitrary causal models.

Extended language needed for general models with non-unique solutions.

Complexity results for decision procedures across classes.

Abstract

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those without feedback), (2) the class of theories where the solutions to the equations are unique, (3) arbitrary theories (where the equations may not have solutions and, if they do, they are not necessarily unique). It is shown that to reason about causality in the most general third class, we must extend the language used by Galles and Pearl. In addition, the complexity of the decision procedures is examined for all the languages and classes of models considered.