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 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...

Counterfactual quantities representing path-specific effects arise in cases where we are interested in computing the effect of one variable on another only along certain causal paths in the graph (in other words by excluding a set of edges from consideration). A recent paper [7] details a method by which such an exclusion can be specified formally by fixing the value of the parent node of each excluded edge. In this paper we derive simple, graphical conditions for experimental identifiability of path-specific effects, namely, conditions under which path-specific effects can be estimated consistently from data obtained from controlled experiments. 1

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

A stratified view of causal reasoning is set forth; one in which the identification of counterfactual dependencies plays an important role in determining what sort of causal connection, if any, exists between two events named by a given pair of partial descriptions. A semantics for temporal counterfactuals in which events are represented at the object level is then formalized based on a syntactic form of belief updating. Counterfactuals are evaluated relative to an agent's information state, taken to include a set of initial beliefs together with additional assumptions to handle the frame problem. Inertial inferences emerge as a side-effect of requiring minimal information change between states of the world in some chronicle. A chronicle is, in addition, assumed minimal with respect to an explanatory preference that minimizes the set of beliefs that are not part of an agent's initial set of beliefs or are not supported by some body of law-like knowledge. A number of epistemic preferenc...

In this paper we present a new approach to reasoning about actions and causation which is based on a conditional logic. The conditional implication is interpreted as causal implication. This makes it possible to formalize in a uniform way causal dependencies between actions and their immediate and indirect effects. The proposed approach also provides a natural formalization of concurrent actions and of the dependency (and independency) relations between actions. The properties of causality are formalized as axioms of the conditional connectives and a nonmonotonic (abductive) semantics is adopted for dealing with the frame problem. 1

According to common judicial standard, judgment in favor of plaintiff should be made if and only if it is "more probable than not" that the defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models of counterfactuals, for the probability that event x was a necessary or sufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient) causation can be learned from statistical data, and shows how data from both experimental and nonexperimental studies can be combined to yield information that neither study alone can provide. Finally,weshow that necessity and sufficiency are two independent aspects of causation, and that both should be invoked in the construction of causal explanations for specific scenarios.