Library / First Principles Framework (FPF) - Core Conceptual Specification
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Source changed 2026-10-03 10:39:28 UTC · snapshot created 2026-10-03 10:40:04 UTC · last check 2026-10-03 10:45:12 UTC

A.2.7:4.4 - Monotonic Kind Order and Residual Qualification

When one exact system-role kind appears to narrow another, test C.3.1 U.SubkindOf first. Use that relation only when the paired classification judgments satisfy monotonicity under the exact aligned editions and effective-reference-scheme edition required by C.3.1:

for every candidate x in the defined comparison domain:
  judgment(x, NarrowerSystemRoleKind) = true
  implies judgment(x, BroaderSystemRoleKind) = true

The proposed U.SubkindOf edge is never a premise for either membership judgment. Direct feature criteria must establish both judgments independently. A known narrower true with broader false refutes the relation. An unavailable broader dependency yields unknown and leaves the order unresolved.

When the restriction is useful but non-monotonic, use a separate residual relation rather than weakening U.SubkindOf:

<exact context-local residual qualification relation species> : U.Relation
RelationSignature:
  QualifiedSystemRoleKindSlot: exact local qualified-kind domain, ByValue
  ReferenceSystemRoleKindSlot: exact local reference-kind domain, ByValue
  ResidualQualificationPredicateSlot:
    exact context-local residual-qualification-predicate kind, ByValue

The residual predicate names the exact restriction, applicability, orientation, and only meaning-changing semantic-basis editions. A receiving Method needing substitution must establish that separate directional relation.