Foundations of Science

, Volume 3, Issue 1, pp 151–182

An Axiomatic Characterization of Causal Counterfactuals

  • David Galles
  • Judea Pearl

DOI: 10.1023/A:1009602825894

Cite this article as:
Galles, D. & Pearl, J. Foundations of Science (1998) 3: 151. doi:10.1023/A:1009602825894


This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback-less) models are considered. Composition and effectiveness also hold in Lewis's closest-world semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but not in Lewis's closest-world semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models.

causality counterfactuals interventions structural equations policy analysis graphical models 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • David Galles
    • 1
  • Judea Pearl
    • 1
  1. 1.Cognitive Systems Laboratory Computer Science DepartmentUniversity of CaliforniaLos Angeles

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