Ontology Relationship Ontology

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

flow "OntologyRelationshipOntology" v1.0 {
  ontology:
    id: "ontology-relationship-ontology"
    parent: "ai-semantic-library-relationships"
    purpose: "Represent, validate and trace relationships among ontologies, their versions, classes, properties and cross-ontology mappings."

  types:
    Ontology: {id: iri, title: string, version: string?, namespace: iri?, provenance: string}
    OntologyElement: {id: iri, ontology_id: iri, kind: enum[class, property, individual, axiom, concept]}
    Mapping: {id: string, source: iri, target: iri, kind: enum[exact, equivalent, broader, narrower, related, incompatible], confidence: number, evidence: string[]}
    OntologyVersion: {ontology_id: iri, version: string, published_at: datetime?, predecessor: string?}
    Relationship: {id: string, subject: iri, predicate: string, object: iri, context: string?, confidence: number, provenance: string}

  predicates:
    imports(source: Ontology, target: Ontology)
    extends(source: Ontology, target: Ontology)
    maps_to(source: OntologyElement, target: OntologyElement)
    equivalent_to(source: OntologyElement, target: OntologyElement)
    broader_than(source: OntologyElement, target: OntologyElement)
    depends_on(source: Ontology, target: Ontology)
    supersedes(new_version: OntologyVersion, old_version: OntologyVersion)
    defined_in(element: OntologyElement, ontology: Ontology)

  constraints:
    - "Every relationship endpoint must resolve to an identified ontology or typed ontology element."
    - "Confidence values must lie within [0, 1]."
    - "Distinguish owl:imports semantics from informal references or dependencies."
    - "Do not infer element identity from similar labels, shared namespaces or related concepts."
    - "Do not automatically treat broader, narrower or related mappings as equivalence."
    - "Version-specific mappings must retain source and target versions."
    - "Cycles in imports and dependencies must be reported and handled according to their semantics."

  inference:
    rule equivalent_symmetry:
      if equivalent_to(a,b) and verified_equivalence(a,b)
      then equivalent_to(b,a)
      confidence: "preserve supporting evidence"
    rule equivalent_transitivity:
      if equivalent_to(a,b) and equivalent_to(b,c) and compatible_context(a,b,c)
      then candidate_equivalence(a,c)
      confidence: "requires validation before assertion"
    rule import_dependency:
      if imports(a,b)
      then depends_on(a,b)
      confidence: "structural relationship, not semantic identity"
    rule version_lineage:
      if supersedes(v3,v2) and supersedes(v2,v1)
      then historical_successor(v3,v1)
      confidence: "retain version history and provenance"

  SEMANTIC_EQUIVALENCE:
    - "Normalise IRIs and identifiers without erasing ontology version boundaries."
    - "Distinguish exact identity, logical equivalence, lexical similarity and mapping correspondence."
    - "Record alignment context, assumptions and evidence."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, mapping_evidence, logical_consistency, version_compatibility, independent_validation]
    policy: "Do not increase confidence merely by chaining mappings or importing ontologies."

  VALIDATION:
    - "Resolve ontology and element identifiers; check class/property type compatibility."
    - "Check mapping consistency, import resolution, version constraints and provenance."
    - "Flag conflicting alignments, unsatisfiable classes and unsupported equivalence claims."
    - "Preserve unresolved alternatives instead of silently merging concepts."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed relationships, 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_versions, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed, version-aware ontology relationship graph"
    outputs: [ontology_links, alignment_assertions, dependency_edges, inference_traces, confidence_annotations, provenance_records]
    safeguards: [no_unsupported_identity_merges, preserve_version_context, validate_imports, expose_uncertainty]
}

END FLOW ALGEBRA