A Lewisian Logic of Causal Counterfactuals

Minds and Machines 23 (1):77-93 (2013)
Abstract
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
Keywords Causal models  Causal reasoning  Conditional logic  Counterfactual  Intervention
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    James Woodward (2004). Counterfactuals and Causal Explanation. International Studies in the Philosophy of Science 18 (1):41 – 72.
    James Woodward (2011). Psychological Studies of Causal and Counterfactual Reasoning. In Christoph Hoerl, Teresa McCormack & Sarah R. Beck (eds.), Understanding Counterfactuals, Understanding Causation. Oxford University Press. 16.
    Peter Menzies, Counterfactual Theories of Causation. Stanford Encyclopedia of Philosophy.
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