AI Semantic Library Relationships

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

FLOW ALGEBRA
TITLE: AI Semantic Library Relationships
DOMAIN: Relationship Ontologies / AI Semantic Library
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/ai-semantic-library-relationships.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "AISemanticLibraryRelationships" v1.0 {
  ontology:
    id: "ai-semantic-library-relationships"
    parent: "relationship-ontologies"
    purpose: "Represent traceable relationships among library resources, ontologies, concepts, assertions, evidence, and AI reasoning artefacts."

  types:
    LibraryResource: {id: string, uri: string, title: string, version: string?, media_type: string?}
    Ontology: {id: string, uri: string, version: string, domain: string}
    Concept: {id: string, label: string, ontology_id: string, definition: string?}
    Assertion: {id: string, subject: string, predicate: string, object: string, context: string?, confidence: number, evidence: string[]}
    Evidence: {id: string, source_uri: string, locator: string?, retrieved_at: datetime?, reliability: number?}
    Inference: {id: string, premises: string[], conclusion: string, rule_id: string, provenance: string[]}
    Relationship: {id: string, source: string, predicate: string, target: string, context: string?, confidence: number, provenance: string[]}

  predicates:
    contains(collection: LibraryResource, item: LibraryResource)
    defines(ontology: Ontology, concept: Concept)
    references(source: LibraryResource, target: LibraryResource)
    maps_to(source: Concept, target: Concept)
    broader_than(parent: Concept, child: Concept)
    equivalent_to(a: Concept, b: Concept)
    supports(evidence: Evidence, assertion: Assertion)
    contradicts(a: Assertion, b: Assertion)
    derived_from(result: Inference, premise: Assertion)
    supersedes(newer: LibraryResource, older: LibraryResource)

  constraints:
    - "All relationship endpoints must resolve to typed identifiers."
    - "Confidence and evidence reliability, when present, must lie in [0,1]."
    - "Equivalence must not be inferred from similarity, shared labels or cross-references alone."
    - "Broader-than, contains, references and maps-to have distinct semantics."
    - "No automatic transitivity for references, mappings, evidence support or provenance."
    - "Preserve ontology versions, domain contexts and source attribution."
    - "Do not merge conflicting assertions without an explicit reconciliation policy."
    - "Protect access-controlled and personal information from unrestricted AI consumption."

  inference:
    rule concept_hierarchy:
      if broader_than(a,b) and broader_than(b,c) and compatible_context(a,b,c)
      then broader_than(a,c)
      confidence: "retain the weakest relevant evidence and provenance"
    rule resource_navigation:
      if contains(collection,item) and references(item,target)
      then discoverable_via(target,collection)
      confidence: "navigation only; not semantic equivalence"
    rule evidence_trace:
      if supports(e,a) and derived_from(i,a)
      then evidence_candidate_for(e,i)
      confidence: "requires validation of the inference rule and premises"
    rule version_link:
      if supersedes(newer,older) and validated_version_lineage(newer,older)
      then historical_version_of(older,newer)
      confidence: "provenance-backed"

  SEMANTIC_EQUIVALENCE:
    - "Normalise identifiers using canonical URI and version-aware aliases."
    - "Distinguish exact equivalence, close match, broader/narrower match and mere reference."
    - "Record scope and provenance of each cross-ontology alignment."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, evidence_quality, ontology_alignment, contextual_fit, temporal_validity, independent_confirmation]
    policy: "Do not manufacture certainty through chained or repeated assertions."

  VALIDATION:
    - "Validate identifiers, predicate domains and ranges, versions and provenance."
    - "Detect broken links, cycles in strict hierarchies, inconsistent equivalences and conflicting claims."
    - "Preserve unresolved ambiguity and conflicting evidence."
    - "Check access permissions before publication or AI retrieval."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed assertions, rules and provenance"
    note: "Compute hash at execution; no hash value is claimed here."

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental update"
    steps: [ingest, normalise, validate, align, compare, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed, version-aware semantic knowledge graph"
    outputs: [resource_links, concept_mappings, relationship_triples, evidence_trails, inference_records, confidence_annotations]
    safeguards: [source_attribution, no_unsupported_identity_merges, permission_checks, version_awareness, uncertainty_preservation]
}

END FLOW ALGEBRA