Abstract

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...

Citations

8882	Computers and Intractability: A Guide to the Theory of NP-completeness - Garey, Johnson - 1979
743	First-Order Dynamic Logic - Harel - 1997
384	Causation, prediction and search - Spirtes, Glymour, et al. - 1993
175	TS: A theory of inferred causation - Pearl, Verma
84	Causality - Pearl - 2000
46	Axioms of causal relevance - Galles, Pearl - 1997
40	Decision-theoretic foundations for causal reasoning - Heckerman, Shachter - 1995
40	Qualitative propagation and scenario-based approaches to explanation in probabilistic reasoning - Henrion, Druzdzel - 1991
37	Causality in Bayesian belief networks - Druzdzel, Simon - 1993
37	An axiomatic characterization of causal counterfactuals - Galles, Pearl - 1998
20	Defining explanation in probabilistic systems - Chajewska, Halpern - 1997
18	Structural Equation Methods in the Social Sciences. Econometrica 40:979–1001. / The Econometricians’ Statisticians 149 - Goldberger - 1972
1	Axiomatizing Causal Structures - Pearl - 1995
1	to appear - Galles, Pearl - 1998