C.3.4:5 - Solution — Declaration, Correspondence, and Judgment

A KindUseAdaptationDeclaration is a named, versioned C.2.1 declaration episteme about one local use. The base kind is its EntityOfConcern; its effective scheme gives meaning to declaration names and predicates. Its claim content states:

1. the exact base kind and pinned base KindSignature edition;
2. the receiving use and adaptation type: constraint, vocabulary, or composite;
3. additional directly governed candidate conditions, when any;
4. vocabulary or notation bindings;
5. exact candidate and slice applicability plus dependencies;
6. scope expectations routed separately through A.2.6; and
7. intended guard use and this declaration episteme’s formality, when current.

First evaluate adaptation admissibility. A candidate rejected by the base signature’s ValueKind, an adaptation-specific candidate requirement needed merely to form the question, or the declared slice applicability is not-applicable; no adaptation judgment is formed. For an admissible request, use:

J_kindUse(candidate, kind, kindSignatureEdition, adaptationDeclarationEdition, slice) ∈ {true, false, unknown}

The judgment conjoins the base C.3.2 judgment with every added candidate-condition predicate. A known false gives false; all known true gives true; unresolved required facts give unknown. A vocabulary-only declaration adds no predicate and preserves the base judgment. A guard may decline use on not-applicable or unknown without rewriting either.

An optional pinned-edition representation may list admissible candidates judged true. It is not U.EntitySet, A.14 membership, another kind, or a direct classification relation. Scope conditions stay under A.2.6 rather than becoming kind identity.

When a use moves to another practice, source, or team, compare the base-kind membership distinctions first:

• if the same kind continues, use the declaration and signature edition selected for the receiving use and make a fresh receiving judgment; no KindBridge exists merely because locality changed;
• if independently identified kinds are distinct and the use claims a directional correspondence, establish the C.3.3 KindBridge; use the receiving signature and adaptation declaration and make a fresh receiving judgment; and
• if two adaptation declarations differ in constraints or bindings, a separate KindUseAdaptationCorrespondenceDeclaration may name source declaration as EntityOfConcern and state target, direction, deterministic rule, definedness, loss, and effective scheme. It creates no bridge or target truth.

A stable conceptual refinement may justify another kind and an obtaining C.3.1 subkind fact. A declaration, correspondence, judgment, catalog row, or representation creates neither.