Article

Foundations of Science

, Volume 3, Issue 1, pp 151-182

First online:

An Axiomatic Characterization of Causal Counterfactuals

  • David GallesAffiliated withCognitive Systems Laboratory Computer Science Department, University of California
  • , Judea PearlAffiliated withCognitive Systems Laboratory Computer Science Department, University of California

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Abstract

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