We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those without feedback), (2) the class of theories where the solutions to the equations are unique, (3) arbitrary theories (where the equations may not have solutions and, if they do, they are not necessarily unique). It is shown that to reason about causality in the most general third class, we must extend the language used by Galles and Pearl (1997, 1998). In addition, the complexity of the decision procedures is characterized for all the languages and classes of models considered. 1. Introduction The important role of causal reasoning---in prediction, explanation, and counterfactual reasoning---has been argued eloquently in a number of recent papers and books (Chajewska & Halpern, 1997; Heckerman & Shachter, 1995; Henrion & Druzdzel, 1990; Druzdz...

The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.

This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback-less) models are considered. Composition and effectiveness also hold in Lewis's closest-world semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but not in Lewis's closest-world semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models.

This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI-99, and is intended to supplement the lecture with technical details and pointers to more elaborate discussions in the literature. The ruling conception will be to treat causation as a computational schema devised to identify the invariant relationships in the environment, so as to facilitate reliable prediction of the effect of actions. This conception, as well as several of its satellite principles and tools, has been guiding paradigm for several research communities in AI, most notably those connected with causal discovery, troubleshooting, planning under uncertainty and modeling the behavior of physical systems. My hopes are to encourage a broader and more effective usage of causal modeling by explicating these common principles in simple and familiar mathematical form. Af...

This paper investigates Walley’s concepts of epistemic irrelevance and epistemic independence for imprecise probability models. We study the mathematical properties of irrelevance and independence, and their relation to the graphoid axioms. Examples are given to show that epistemic irrelevance can violate the symmetry, contraction and intersection axioms, that epistemic independence can violate contraction and intersection, and that this accords with informal notions of irrelevance and independence.

We analyze the computational complexity of causal relationships in Pearl's structural models, where we focus on causality between variables, event causality, and probabilistic causality. In particular, we analyze the complexity of the sophisticated notions of weak and actual causality by Halpern and Pearl. In the course of this, we also prove an open conjecture by Halpern and Pearl, and establish other semantic results. To our knowledge, no complexity aspects of causal relationships have been considered so far, and our results shed light on this issue. 1

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This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excess-risk-ratio could be used for assessing attributional quantities such as the probability of causation. 1