What does it mean that an event C "actually caused'' event E? The problem of defining actual causation goes beyond mere philosophical speculation. For example, in many legal arguments, it is precisely what needs to be established in order to determine responsibility. (What exactly was the actual cause of the car accident or the medical problem?) Actual causation is also important in artificial intelligence applications. Whenever we undertake to explain a set of events that unfold in a specific scenario, the explanation produced must acknowledge the actual cause of those events.

The philosophy literature has been struggling with the problem of defining causality since the days of Hume, in the 1700s. Many of the definitions have been couched in terms of counterfactuals. (C is a cause of E if, had C not happened, then E would not have happened.) However, all the previous definitions have been shown (typically by example) to be problematic. We propose here new definitions of actual cause and (causal) explanation, using Pearl's notion of structural equations to model counterfactuals. We show that these definitions yield a plausible and elegant account of causation and explanation that handles well examples which have caused problems for other definitions and resolve major difficulties in the traditional account. This is joint work with Judea Pearl.