B.5.RR:4 - Solution

Start with the receiving question, follow the affected reasoning and derive the result that can now be used. A useful reminder is:

Changed question or condition → affected reasoning → retained or replacement contribution → revised conclusion → receiving use.

B.5.RR:4.1 - Say what changed and what is needed now

Compare the earlier question with the present one. State the result needed and the changed condition in terms that can be used in the reasoning. For a calculation, that may be a new range or an input that is now an unknown. For an empirical conclusion, it may be an observation, a changed population or an operating condition.

Distinguish a change in the situation from a correction to your account of it. A measurement taken yesterday can remain a sound report of yesterday while being insufficient for today’s operation. A proposed condition can be explored hypothetically without replacing the account of what has happened.

Keep the meanings of the quantities and claims visible. If the same term now denotes a different quantity, translate the question before substituting its value. If only the spelling or presentation changed and the established application still fits, no reasoning revision is needed.

B.5.RR:4.2 - Recover the dependence that matters

Begin at the changed premise and at the desired conclusion. Find which intermediate claims or constructions connect them. At each relevant transition, ask what is needed together, what is produced and why that transition is allowed.

Keep a sufficient alternative separately. For example, recovering a file may require either a readable local copy or an available remote copy. If both are encrypted with one unavailable key, the two storage locations leave the same prerequisite unresolved.

Use an established lemma at the level its receiving use needs. Open its proof when the change reaches a condition of the lemma or the way its result is obtained. Do the same for an established measurement or computation: inspect the part whose application the change calls into question.

A sketch or a few statements can hold these dependencies. Use B.1.1 when a dependency representation needs its relation clarified. A reasoning dependency says which premise or operation supports a conclusion; physical causation and temporal order require their own relations.

If the needed dependence is missing from the account, recover it through B.5.RA or ask for that contribution. Treat a supposedly unaffected part as reusable only when its independence from the change is adequately understood for this use.

B.5.RR:4.3 - Derive what follows after the change

Work from available premises through the affected transitions. Reuse a contribution whose conditions and required result still fit. Where they do not, derive the replacement, select an adequate alternative or identify the unresolved step.

Withdrawing a premise removes that premise as a basis for asserting the conclusion. Another sufficient argument may still support it. To assert the opposite conclusion, obtain a reason for that assertion. The conditional argument can remain available for situations in which its premises hold.

Follow the change through each needed use of a shared prerequisite. Keep the premises of an alternative argument together: pieces from two incompatible situations do not form a supported argument for either situation. If conclusions refer back to one another, recover the grounding of that reasoning, such as an initial case and induction step. Mutual repetition alone cannot replace the starting support.

A changed requested result can require working backward as well. Identify what the new conclusion would need, reuse the earlier contributions that supply it, and produce the remaining contribution. Release a former fixed value when the question now asks you to determine it.

Compare the work of recovering and repairing the affected reasoning with the work of obtaining a fresh sufficient answer. A short new calculation can be cheaper and clearer. A maintained dependency account is useful when repeated revisions repay its cost; it is optional for an ordinary one-off question.

B.5.RR:4.4 - Choose the result the present reasoning supports

Relate the revised conclusion to the result requested in §4.1. It may supply the requested answer, a conditional answer, a bound or an obstruction. Say what the receiver can do with that result.

For a mathematical argument, carry the domain and assumptions into its conclusion. For an empirical application, examine the changed observation or applicability premise using the relevant subject method. Recomputing a model can establish its new consequence while leaving its correspondence with the physical situation unresolved.

If the original target is unattainable under the retained conditions, use the obstruction to propose a changed condition or a different question. Keep that proposal visible as a choice. A weaker result can be useful without silently replacing the requested result.

Obtain further evidence or checking when its possible outcomes can change this use. C.11.DUA helps compare that contribution with its cost. The method can finish with an explicitly conditional result when conditional use is sufficient.

B.5.RR:4.5 - Apply the result and carry the change to its users

Perform the receiving use, or give its next contributor the revised conclusion and the condition that governs it. When others rely on the earlier result, tell the affected users what changed and which application must change with it. Their unchanged uses need no new argument merely because a nearby result was revised.

Check the changed transition by the method appropriate to its claim. A small instance can reveal a substitution error; a proof establishes its stated general conclusion; an observation can test a physical consequence. Choose the check for the result actually being relied on.

Stop when the receiving question is answered at the required level, or when the remaining contribution has been located well enough to obtain it. A useful new question can begin another inquiry under B.5.