MMP.Preface:3.3 - Construct change and observation together when they interact

For an evolving situation, A.3.3.TR constructs a state-change rule from the contributing relations, including simultaneous constraints, alternatives and events. If situations assigned the same state need different continuations under the same modeled inputs, revise the state or retain the alternatives. The computation’s chosen solution order need not be the represented order of physical change.

MMP.7 derives a probability law for the record produced by an observing procedure. Compose the source and recording laws, retain shared unknowns, sum or integrate unrecorded alternatives, and account for selection. The resulting law can supply a statistical inference or prediction method. C.16.IR addresses what a supplied observation relation resolves, including bounds and consequential ambiguity.

MMP.12 constructs recovery from a forward relation. Find which changes to the unknown leave the records unchanged or change them too little for stable recovery. A restriction or penalty can make a useful reconstruction possible; derive both the error it suppresses and the target detail it may remove. A bound that already settles the question can end the work before regularization.

MMP.13 constructs the inferential claim. Choose whether the use needs a repeated-sampling guarantee, a posterior probability or a prediction for a new outcome; derive that result under the record law and the additional assumptions it requires. Propagate joint uncertainty to the quantity the receiver actually needs. A regularized optimum alone supplies neither a posterior distribution nor a coverage guarantee.

Observation can also change the situation. C.28 and C.28.MR help formulate that intervention and replace the affected mechanism. MMP.15 asks whether its requested consequence is determined by the available laws and causal assumptions. It derives an identifying expression, a sufficient bound or an unresolved difference between compatible causal accounts. MMP.13 can then estimate an identified quantity from finite records; an observational fit alone does not identify it.

A question about the same case under another action needs a further connection. MMP.19 constructs the underlying conditions shared by its alternatives, uses MMP.7/.13 to recover what the factual record says about them, then applies the changed mechanisms. Separately known intervention distributions can leave their same-case relation ambiguous. The result can be a conditional response or a bound; a choice based only on expected outcomes can remain settled without resolving that ambiguity.