  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. In addition, the
complexity of the decision procedures is characterized for all the languages
and classes of models considered.
