C.28.MR:4.4 - Solve what the intervention query requires

For an acyclic model, evaluate the retained and replaced functions in dependency order. For a time-stepped model, propagate from its initial conditions through the selected horizon. For simultaneous equations or continuous dynamics, use the solution method and conditions appropriate to those relations.

Check the transformed relations themselves when a replacement can change existence or select among several solutions. A solver’s first returned branch may leave other admitted answers. If all admitted solutions agree on the queried quantity, that agreement can answer the question. If their answers differ, retain the possible answers, derive a useful bound, or expose the condition needed to choose among them. If the model has no relevant solution for inputs the query includes, return that obstruction and repair the model or question.

For probabilistic results, the selected solutions must define the requested random quantity under the input law. Existence of one numerical trace supplies less than a uniquely determined distribution. A general proof is unnecessary when a direct finite calculation settles the present query.

For a dynamically triggered jump, recover the event-order or flow/jump choice if it changes the result. A model’s steady-state solution alone does not determine what happens during a transient. The hybrid-system approach discussed in :11 supplies one current treatment with explicit conditions; the subject model still determines which treatment is appropriate.