  Real-world complex systems are often modelled by sets of equations with
endogenous and exogenous variables. What can we say about the causal and
probabilistic aspects of variables that appear in these equations without
explicitly solving the equations? We make use of Simon's causal ordering
algorithm (Simon, 1953) to construct a causal ordering graph and prove that it
expresses the effects of soft and perfect interventions on the equations under
certain unique solvability assumptions. We further construct a Markov ordering
graph and prove that it encodes conditional independences in the distribution
implied by the equations with independent random exogenous variables, under a
similar unique solvability assumption. We discuss how this approach reveals and
addresses some of the limitations of existing causal modelling frameworks, such
as causal Bayesian networks and structural causal models.
