From Causal Models To Counterfactual Structures
  Galles and Pearl claimed that "for recursive models, the causal model
framework does not add any restrictions to counterfactuals, beyond those
imposed by Lewis's [possible-worlds] framework." This claim is examined
carefully, with the goal of clarifying the exact relationship between causal
models and Lewis's framework. Recursive models are shown to correspond
precisely to a subclass of (possible-world) counterfactual structures. On the
other hand, a slight generalization of recursive models, models where all
equations have unique solutions, is shown to be incomparable in expressive
power to counterfactual structures, despite the fact that the Galles and Pearl
arguments should apply to them as well. The problem with the Galles and Pearl
argument is identified: an axiom that they viewed as irrelevant, because it
involved disjunction (which was not in their language), is not irrelevant at
all.
