Cross-Ontology Relationship Ontology

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

flow "CrossOntologyRelationshipOntology" v1.0 {
  ontology:
    id: "cross-ontology-relationship-ontology"
    parent: "ai-semantic-library-relationships"
    purpose: "Represent evidence-backed mappings and dependencies between independently versioned ontologies without conflating identity, similarity and equivalence."

  types:
    Ontology: {id: string, iri: string, version: string, provenance: string}
    Term: {iri: string, ontology_id: string, kind: enum[class, property, individual, concept], label: string?}
    Mapping: {id: string, source: Term, target: Term, kind: enum[exact_match, close_match, broader_match, narrower_match, related_match, equivalent_class, equivalent_property, sub_class, sub_property, disjoint, transformation], context: string?, confidence: number, evidence: string[], provenance: string, valid_from: datetime?, valid_to: datetime?}
    Import: {importer: string, imported: string, version_constraint: string?, provenance: string}
    Alignment: {id: string, source_ontology: string, target_ontology: string, mappings: string[], status: enum[draft, reviewed, approved, deprecated]}

  predicates:
    maps_to(source: Term, target: Term, mapping: Mapping)
    imports(source: Ontology, target: Ontology)
    equivalent_class(a: Term, b: Term)
    equivalent_property(a: Term, b: Term)
    broader_than(a: Term, b: Term)
    conflicts_with(a: Mapping, b: Mapping)
    supersedes(new_mapping: Mapping, old_mapping: Mapping)

  constraints:
    - "Every mapped term must resolve to a versioned source ontology."
    - "Mapping confidence must be within [0,1] and carry provenance."
    - "Similarity and close_match do not establish logical identity or equivalence."
    - "Equivalent-class and equivalent-property mappings require compatible term kinds and explicit semantic justification."
    - "Imports do not imply equivalence between ontology terms."
    - "Do not infer global equivalence from context-limited mappings."
    - "Check disjointness, domain, range and cardinality conflicts before applying mappings."
    - "Mapping composition requires compatible semantics and cannot automatically increase confidence."

  inference:
    rule equivalent_class_symmetry:
      if equivalent_class(a,b) and validated(a,b)
      then equivalent_class(b,a)
      confidence: "retain supporting evidence"
    rule subclass_bridge:
      if subclass_of(a,b) and equivalent_class(b,c) and approved_mapping(b,c)
      then subclass_of(a,c)
      confidence: "dependent on ontology versions and mapping validity"
    rule import_dependency:
      if imports(a,b) and imports(b,c)
      then depends_on(a,c)
      confidence: "dependency only; not direct import assertion"
    rule mapping_conflict:
      if maps_to(a,b,m1) and maps_to(a,c,m2) and incompatible(b,c)
      then review_required(m1,m2)
      confidence: "flag; do not silently merge"

  SEMANTIC_EQUIVALENCE:
    - "Separate owl:equivalentClass, owl:equivalentProperty and owl:sameAs from SKOS-style matches."
    - "Preserve namespace, version, language, context and modelling assumptions."
    - "Record directionality for broader, narrower and transformation mappings."

  CONFIDENCE:
    range: [0,1]
    factors: [source_quality, semantic_compatibility, mapping_evidence, expert_review, version_stability, context_match]
    policy: "Do not manufacture certainty by chaining mappings or repeating dependent evidence."

  VALIDATION:
    - "Resolve ontology and term IRIs; verify version compatibility."
    - "Check term kinds, logical constraints, mapping direction and provenance."
    - "Flag contradictory alignments and cyclic import dependencies."
    - "Keep unreviewed mappings separate from asserted ontology axioms."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, mappings, constraints, rules and provenance"
    note: "Compute at execution; no precomputed digest is claimed."

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental alignment"
    steps: [ingest, resolve_versions, normalise, propose_mappings, validate, review_conflicts, publish, monitor_drift]
    rollback: true

  AI_CONSUMPTION:
    representation: "version-aware cross-ontology knowledge graph"
    outputs: [aligned_terms, mapping_edges, dependency_links, uncertainty_annotations, conflict_reports, provenance_records]
    safeguards: [no_unreviewed_identity_merges, no_similarity_as_equivalence, preserve_source_context, detect_schema_conflicts]
}

END FLOW ALGEBRA