An Axiomatic Characterization of Causal Counterfactuals

This paper studies the causal interpretation of counterfactual sentences using a mod-iiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and eeectiveness, are sound and complete relative to this interpretation , when recursive (i.e., feedback-less) models are considered. Composition and eeectiveness also hold in Lewis's closest-world semantics, which implies that for recur-sive 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 exempliied and compared to those based on graphical models.