C.3.1:4 - Core Objects
| Object | Meaning | Boundary |
|---|---|---|
U.Kind | The admitted meta-kind whose individuals are reusable intensional classification distinctions. One individual is recovered through its candidate domain, operative membership condition, intended member/non-member distinction, and continuity rule. | A KindSignature, label, source boundary, reference scheme, current extension, or receiving use is not the kind. |
U.SubkindOf | The admitted direct relation kind whose occurrences relate exact narrower and broader U.Kind participants within declared applicability. Its obtaining facts form a preorder. | It is not a predicate expression, assertion episteme, dependency, part-whole relation, construction, system-role assignment, or admission relation. |
SubkindOfObtains(k1, k2) | The relation-obtaining condition. It holds either because the exact membership criterion for k1 entails the criterion for k2 under an aligned interpretation and applicability, or because every candidate in a deliberately closed finite domain has been evaluated and every admissible true result for k1 is also true for k2. | The first branch is criterion-based. The second is explicitly domain-bounded. Non-exhaustive observations support a separate assertion but do not make the relation obtain. |
R_sub : U.SubkindOf | One obtaining relation occurrence between exact narrower kind k1 and broader kind k2. | Use a designator only when a receiver needs it. The ordered kind participants determine occurrence identity; schemes, signatures, evidence, assertions, and publications do not. |
| subkind assertion episteme | A C.2.1 episteme that affirms, denies, or leaves unresolved the obtaining condition and cites its interpretation, applicability, branch, and support. | The assertion does not make the relation obtain; a negative or unresolved assertion designates no obtaining occurrence. |
| classification equivalence for an alignment | Mutual obtaining U.SubkindOf facts between two kinds within the same declared applicability. | It says that the two membership distinctions classify alike there. It does not identify the kinds. A consumer that needs a partial order may order these equivalence groups. |
KindSignature edition | The C.3.2 declaration episteme used to interpret and evaluate one kind. | It is neither the kind nor the subkind relation. |
C.3.1:4.1 - Direct U.SubkindOf Relation Boundary
A readable sentence such as CoolingPumpKind is a subkind of PumpKind for this declared plant use states that the direct relation obtains. It needs no occurrence identifier when no receiver distinguishes or refers to the occurrence.
The relation obtains under the criterion-entailment branch when the exact narrower membership condition entails the broader one under the aligned interpretation and applicability. Under the closed-domain branch, it obtains only when the candidate domain is deliberately finite and closed, every candidate’s admissibility has been checked, and exhaustive evaluation leaves no narrower true without a broader true. A counterexample refutes either proposal. A missing dependency or unknown judgment cannot establish either branch; a not-applicable request is outside the comparison.
When a receiver needs one occurrence, R_sub is participant-determined by the ordered pair of kind identities. The effective scheme, aligned signatures, and applicability qualify how obtaining is tested and asserted. A scheme-edition change therefore prompts an alignment and renewed test; it does not create another relation occurrence. If the same participants still satisfy the condition, the same relation continues to obtain. If they no longer do, the prior obtaining claim is no longer current; another assertion may record that change without inventing a scheme-keyed occurrence.