C.40:5.11 - An editable rule acquires an exception, then a proposed improvement fails

A workshop is constructing a rule that sends small jobs either to quick preparation or to manual setup. In this finite constructed case, job size n is one of 1, 2, 3 or 4, and a special-material flag is observable before the choice. The practitioner states that special-material jobs require manual setup. Ordinary jobs of sizes 1 and 2 are known to work with quick preparation; sizes 3 and 4 currently use manual setup. The task is to preserve those conditions while making an affordable rule, not to infer workshop performance from a model’s confidence.

An existing program supplies four ordinary-job outputs. Searching the five threshold rules quick if n <= t, otherwise manual, for t in {0,1,2,3,4}, gives zero disagreement at t=2. That establishes agreement on the four supplied cases. The rule has no way to express the special-material exception. A high imitation score cannot recover it.

The practitioner supplies the missing condition. The representation is extended to inspect the flag, and the execution rule becomes: first, if special material, return manual; otherwise apply the size threshold. This first condition is protected from the threshold search. Enumerating the eight admitted size/flag combinations confirms the required routing: four special-material cases return manual; the four ordinary cases keep their earlier actions. The construction now implements the stated exception. Successful routing does not establish the quality of the resulting workshop work.

For readability, suppose the ordinary quick condition was written n <= 2 AND n <= 3. Removing its second clause preserves behavior for the stated integer domain because the first implies the second. Removing the special-material guard merely because no special jobs appeared in the original four examples would be a different change. Its first counterexample is a special-material job of size 1.

The practitioner next proposes increasing the threshold to 3 to save setup effort. It changes one of the eight outputs: an ordinary size-3 job now takes quick preparation. The workshop compares permitted actual attempts on that case, retaining the previous rule. In the stipulated trial, quick preparation yields an unacceptable finish; manual setup meets the existing requirement. The proposal is rejected and t=2 retained. This observation does not require changing the already-correct special-material guard or pretending that the human suggestion was a verified target. If a different material later permits quick preparation, that new observation can reopen its own case.

Finally, remove the flag from the later input while retaining the special-material requirement. The formerly successful rule is no longer executable as specified. Obtain the flag before routing, use an adequate permitted fallback such as manual setup when it is actually available, or return the missing input. Further fitting of thresholds cannot distinguish jobs whose inputs have been made identical. The affordable answer may be this small explicit procedure; no neural network or population search is required.