Axiomatizing Causal Reasoning

J. Y. Halpern
2000 The Journal of Artificial Intelligence Research  
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
more » ... most general third class, we must extend the language used by Galles and Pearl. In addition, the complexity of the decision procedures is characterized for all the languages and classes of models considered.
doi:10.1613/jair.648 fatcat:gem3lkijqfhg5epzyj4cr7xt5y