Causes and explanations: A structural-model approach

In Proceedings of the Seventeenth Conference on Uncertainy in Artiﬁcial Intelligence, San Francisco, CA: Morgan Kaufmann, 194–202, 2001. TECHNICAL REPORT R-266-UAI June 2001 Causes and Explanations: A Structural-Model Approach— Part I: Causes Joseph Y. Halpern Judea Pearl Cornell University Dept. of Computer Science Dept. of Computer Science University of California, Los Angeles Ithaca, NY 14853 Los Angeles, CA 90095 halpern@cs.cornell.edu judea@cs.ucla.edu http://www.cs.cornell.edu/home/halpern http://www.cs.ucla.edu/ judea Abstract We propose a new deﬁnition of actual causes, using structural equations to model counterfac- tuals. We show that the deﬁnition yields a plausi- ble and elegant account of causation that handles well examples which have caused problems for other deﬁnitions and resolves major difﬁculties in the traditional account. 1 Introduction What does it mean that an event actually causes event ? This is a question that goes beyond mere philosophical speculation. As Good [1993] argues persuasively, in many legal settings, what needs to be established (for determin- ing responsibility) is not a counterfactual kind of causation, but “cause in fact. ” A typical example considers two ﬁres advancing toward a house. If ﬁre burned the house be- fore ﬁre , we (and many juries nationwide) would con- sider ﬁre “the actual cause” for the damage, even sup- posing the house would have deﬁnitely burned down by ﬁre , if it were not for . Actual causation is also im- portant 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 automatic generation of adequate explanations, a task essential in planning, diag- nosis and natural language processing, therefore requires a formal analysis of the concept of actual cause. Giving a precise and useful deﬁnition of actual causality is notoriously difﬁcult. The philosophical literature has been struggling with this notion since the days of Hume [1739]. (See [Sosa and Tooley 1993], [Hall 1998], and [Pearl 2000] for some recent discussions.) To borrow just one example from Hall [1998], suppose a bolt lightning hits a tree and Supported in part by NSF under grant IRI-96-25901 Supported in part by grants from NSF, ONR, AFOSR, and MICRO. starts a forest ﬁre. It seems reasonable to say that the light- ning bolt is a cause of the ﬁre. (Indeed, the description “the lightning bolt . . . starts a forest ﬁre” can be viewed as say- ing this.) But what about the oxygen in the air and the fact that the wood was dry? Presumably, if there has not been oxygen or the wood was wet there would not have been a ﬁre. Carrying this perhaps to the point of absurdity, what about the Big Bang? This problem is relatively easy to deal with, but there are a host of other, far more subtle, difﬁcul- ties that have been raised over the years. Here we give a deﬁnition of actual causality based on the language of structural equations; in a companion paper ([Halpern and Pearl 2001]; see also the full paper [Halpern and Pearl 2000]), we give a deﬁnition of (causal) explana- tion using the deﬁnition of causality. The use of structural equations as a model for causal relationships is standard in the social sciences, and seems to go back to the work of Se- wall Wright in the 1920s (see [Goldberger 1972] for a dis- cussion); the framework we use here is due to Pearl [1995], and is further developed in [Galles and Pearl 1997; Halpern 2000; Pearl 2000]. While it is hard to argue that our deﬁ- nition (or any other deﬁnition, for that matter) is the “right deﬁnition”, we show that it deals well with the difﬁculties that have plagued other approaches in the past, especially those exempliﬁed by the rather extensive compendium of Hall [1998]. There has been extensive discussion about causality in the literature, particularly in the philosophy literature. To keep this paper to manageable length, we spend only minimal time describing other approaches and comparing ours to them. We refer the reader to [Hall 1998; Pearl 2000; Sosa and Tooley 1993; Spirtes, Glymour, and Scheines 1993] for details and criticism of the probabilistic and logical ap- proaches to causality in the philosophy literature. (We do try to point out where our deﬁnition does better than per- haps the best known approach, due to Lewis [1986, 2000] in the course of discussing the examples.) There has also been work in the AI literature on causality. Perhaps the closest to this are papers by Pearl and his col- leagues that use the structural-model approach. The def-