A Lewisian Logic of Causal Counterfactuals
In the artificial intelligence literature a promising approach to counterfactual reasoning is to interpret counterfactual conditionals based on causal models. Different logics of such causal counterfactuals have been developed with respect to different classes of causal models. In this paper I characterize the class of causal models that are Lewisian in the sense that they validate the principles in Lewiss well-known logic of counterfactuals. I then develop a system sound and complete with respect to this class. The resulting logic is the weakest logic of causal counterfactuals that respects Lewiss principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearls logic in the same fashion as Lewiss stands to Stalnakers.
counterfactual causal models causal reasoning conditional logic intervention