Axiomatizing Causal Reasoning

TL;DR

This paper provides axiomatizations for various classes of causal models based on equations, extending existing languages and analyzing decision procedure complexities for causal reasoning.

Contribution

It introduces axiomatizations for three classes of causal models and extends the language for the most general class, advancing formal understanding of causal reasoning.

Findings

Axiomatizations for recursive theories and theories with unique solutions.

Extension of language needed for arbitrary theories.

Complexity analysis of decision procedures for different model 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 characterized for all the languages and classes of models considered.