NOT.1:4 - Solution

Choose a working operation → find a consequential difference → locate what carries that difference → try a notation choice → compare the work it enables and displaces → retain or revise the requirement.

NOT.1:4.1 - Choose an operation and the conditions for performing it

Describe what the user starts with, what they do and what they need to obtain. Prefer a question such as “after exchanging these two operations, what changes in the result?” to an aim such as “make the notation intuitive”. The former exposes what an expression must support.

Specify the preparation and access on which the operation relies. A mathematician may use established algebraic conventions; a performer may recognize a learned gesture; a program may receive only serialized text. An AI agent’s access to a rendered page, a text extraction and an editor’s internal structure are different conditions. Include the context that is actually available, rather than assuming that every reader receives the designer’s view.

For a small task, one operation is enough to begin. If the notation will be used for a family of operations, choose cases that exercise materially different demands. For example, interpreting a completed expression and changing a shared component can need different support. Do not turn this selection into an inventory of every conceivable use.

NOT.1:4.2 - Find cases whose difference changes the work

Construct or recover a pair of cases that require different answers, permitted changes or actions. Explain the difference in the practice before deciding how to write it. Two arrangements of the same components can have different outputs; two performances with the same starting times can have different sustained intervals.

Attempt to express both cases with the candidate notation and its allowed context. If they become indistinguishable while the required answers differ, something needed by that operation has been omitted. Recover it through an expression rule, an accessible annotation, a query to another representation or a narrower declared use. The choice depends on how the expression will be used.

Conversely, two visibly different cases may be interchangeable for the present operation. Keep their shared representation if that simplification preserves the needed result. The question determines which differences matter.

A deliberately unfinished choice can itself matter. If the work permits an unspecified order or duration, retain a way to leave it unspecified and a way to recognize when the next operation needs it settled. A convention that silently chooses a value would change the work being described.

NOT.1:4.3 - Locate the information and operations behind the marks

Follow the user through the proposed operation. Which part of the expression identifies a participant, establishes a relation or permits a transformation? Which part is supplied by a convention, the surrounding account or an interaction with a tool?

This examination can reveal three different needs:

• The difference is known but cannot be expressed or recovered under the available rules. Design a way to carry it.
• The expression carries the difference, but obtaining or changing it is too costly. Change the arrangement or the supported operation; NOT.7 develops that redesign.
• The practice has not supplied the needed distinction or inference. Obtain that contribution from the relevant practitioner or method before prescribing how it must be expressed.

Test the whole expression and its usable context. A symbol may be ambiguous in isolation yet clear in a composition. A diagram may be clear to a prepared human reader while its plain-text export loses the grouping on which that reading depends. Preserve the effective context or revise the notation for the receiving conditions.

NOT.1:4.4 - Try a design choice through use

Propose a small change capable of supporting the selected operation. Examples include marking operand groups, adding a reference to a shared component, exposing event duration, or making an unresolved alternative visible. Construct the contrasting cases with that change and carry out the operation using the proposed reading rule.

Where modification matters, change an input, component or relation and follow the resulting edits. A notation that displays one finished example well may make the required family of changes error-prone or laborious. Include a contrasting case that challenges the same rule, rather than polishing the first example until it looks convincing.

Separate the notation’s contribution from supplied subject knowledge. In a diagram for composing functions, arrows can expose the order of application; the functions and the ability to apply them supply the numerical result. If the result cannot be obtained because an algorithm or physical law is missing, return that question to the corresponding practice.

An expert walkthrough can establish an explicit loss or a useful candidate change. When it remains uncertain whether the intended reader can recover or perform the operation, use C.2.8 to choose a bounded reading probe with the intended preparation and access. Obtain further evidence only when its outcome could change the design or the permitted use.

NOT.1:4.5 - Compare the work enabled and the work displaced

Compare candidate notations on the selected operations under comparable conditions. Look for a practical trade-off: a shared definition may make one update cheap while requiring the reader to follow references; expanded expressions may be easy to read locally while repeating changes in several places.

Keep both alternatives when they serve different necessary operations and the correspondence between them can be maintained. NOT.6 develops that arrangement. For a choice among alternatives, compare only characteristics that affect the work and state the selection criterion. A simple contrast can settle the local choice: one notation loses an answer that the other preserves.

When the comparison must be reused across alternatives or design iterations, A.19.CPM governs comparison under a declared comparator; A.19.SelectorMechanism governs selecting a set from those results under stated criteria. A Pareto criterion can retain alternatives that are not dominated on the chosen characteristics. It does not by itself resolve a trade-off between reading and editing effort. Keep that trade-off visible until the work supplies a reason to choose, or retain both notations for their different uses. A vocabulary of design trade-offs can help notice a difficulty, but a vocabulary or weighted checklist cannot establish that a user can perform the operation.

Trying a candidate can reveal that the original question was incomplete. Revise the selected operations or cases when the newly visible distinction changes a useful next move. Then test the affected requirement again. This is a development of the problem and its proposed solution, for which C.40.CD supplies the common method.

NOT.1:4.6 - Retain the decision at the scale needed for the next construction

State the operation to support, the distinction it needs, how a candidate carries it and the burden or unresolved choice that remains. A short explanation beside the candidate can suffice. Keep the contrasting cases when they will help construct, teach or revise the rule; no separate requirements document is necessary for an ordinary small use.

Stop when the next notation construction or choice is clear enough to undertake. Detailed expression formation, interpretation and transformation can then be developed where needed. Do not reopen every design choice merely because a new example is available; reopen the choice whose supported operation or conditions changed.