A Lewisian Logic of Causal Counterfactuals
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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 Lewis’s 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 Lewis’s principles, sits in between the logic developed by Galles and Pearl and the logic developed by Halpern, and stands to Galles and Pearl’s logic in the same fashion as Lewis’s stands to Stalnaker’s.
KeywordsCausal models Causal reasoning Conditional logic Counterfactual Intervention
I thank Lam Wai Yin for helpful discussions on issues related to this article, and the audiences of a seminar at Carnegie Mellon University for useful feedback. My research was supported in part by the Research Grants Council of Hong Kong under the General Research Fund LU341910.
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