Semantic Library Relationship Ontology

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

flow "SemanticLibraryRelationshipOntology" v1.0 {
  ontology:
    id: "semantic-library-relationship-ontology"
    parent: "ai-semantic-library-relationships"
    purpose: "Represent, validate and trace typed relationships among semantic library resources, concepts, ontologies and evidence."

  types:
    LibraryResource: {id: string, uri: string, kind: enum[book, chapter, page, dataset, ontology, flow, document, other], version: string?}
    Concept: {id: string, label: string, definition: string?, ontology_id: string?}
    Ontology: {id: string, uri: string, version: string}
    Assertion: {id: string, subject: string, predicate: string, object: string, context: string?, evidence: string[], confidence: number}
    Evidence: {id: string, source_uri: string, retrieved_at: datetime?, provenance: string}
    Relationship: {id: string, source_id: string, target_id: string, kind: string, context: string?, evidence_ids: string[], confidence: number}

  predicates:
    contains(parent: LibraryResource, child: LibraryResource)
    describes(resource: LibraryResource, concept: Concept)
    defined_in(concept: Concept, ontology: Ontology)
    references(source: LibraryResource, target: LibraryResource)
    maps_to(source: Concept, target: Concept)
    equivalent_to(source: Concept, target: Concept)
    broader_than(parent: Concept, child: Concept)
    derived_from(resource: LibraryResource, source: LibraryResource)
    supported_by(assertion: Assertion, evidence: Evidence)
    supersedes(newer: LibraryResource, older: LibraryResource)

  constraints:
    - "Every relationship endpoint must resolve to a typed entity."
    - "Relationship confidence must lie within [0,1]."
    - "Preserve ontology versions, resource URIs, context and evidence identifiers."
    - "Do not treat references, similarity, mappings or shared labels as identity."
    - "Do not infer transitivity for arbitrary relationships."
    - "Containment and broader-than hierarchies must be cycle-checked where acyclicity is required."
    - "Equivalence requires documented meaning and scope compatibility."
    - "Derived assertions must retain an auditable inference path."

  inference:
    rule containment_ancestry:
      if contains(a,b) and contains(b,c) and acyclic_hierarchy(a,b,c)
      then indirectly_contains(a,c)
      confidence: "preserve supporting edges and their contexts"
    rule concept_mapping:
      if equivalent_to(a,b) and equivalent_to(b,c) and compatible_scope(a,b,c)
      then candidate_equivalence(a,c)
      confidence: "requires validation before promotion to asserted equivalence"
    rule evidence_trace:
      if supported_by(assertion,evidence) and valid(evidence)
      then traceable_to(assertion,evidence)
      confidence: "evidence quality dependent"
    rule version_lineage:
      if supersedes(a,b) and supersedes(b,c) and same_resource_lineage(a,b,c)
      then supersedes_transitively(a,c)
      confidence: "retain all intermediate versions"

  SEMANTIC_EQUIVALENCE:
    - "Normalise identifiers using versioned ontology and catalogue mappings."
    - "Distinguish exact equivalence, close match, broader match, reference and alias."
    - "Preserve language, domain, definition, context and temporal validity."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, evidence_quality, semantic_alignment, contextual_fit, version_consistency, independent_confirmation]
    policy: "Never increase certainty merely by chaining relationships or repeating evidence."

  VALIDATION:
    - "Check entity types, resolvable URIs, predicates, versions and provenance."
    - "Detect broken references, contradictory mappings, invalid cycles and unsupported identity merges."
    - "Retain competing interpretations and flag unresolved conflicts."
    - "Ensure inferred links can be traced to source assertions and rules."

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

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

  AI_CONSUMPTION:
    representation: "typed semantic knowledge graph with evidence-backed edges"
    outputs: [resource_links, concept_mappings, ontology_links, inference_paths, confidence_annotations, provenance_records]
    safeguards: [no_unsupported_identity_merges, no_unjustified_transitivity, preserve_versions_and_context, evidence_traceability]
}

END FLOW ALGEBRA