Class Relationship Ontology

FLOW ALGEBRA
TITLE: Class Relationship Ontology
DOMAIN: Relationship Ontologies / Knowledge Graph Relationships
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/knowledge-graph-relationships/class-relationship-ontology.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "ClassRelationshipOntology" v1.0 {
  ontology:
    id: "class-relationship-ontology"
    parent: "knowledge-graph-relationships"
    purpose: "Represent and validate class definitions, subclass relationships, class equivalence, disjointness and instance membership in RDF/OWL knowledge graphs."

  types:
    Class: {iri: string, label: string?, definition: string?, ontology_version: string?}
    Individual: {id: string, iri: string?, provenance: string?}
    Property: {iri: string, kind: enum[object, datatype, annotation], domain: string?, range: string?}
    ClassAxiom: {id: string, subject_class: string, relation: enum[subclass_of, equivalent_to, disjoint_with, intersects_with], object_class: string, evidence: string[], confidence: number}
    Membership: {individual: string, class_iri: string, asserted: bool, provenance: string, confidence: number}
    Evidence: {id: string, source: string, timestamp: datetime?, method: string?}

  predicates:
    subclass_of(child: Class, parent: Class)
    equivalent_class(a: Class, b: Class)
    disjoint_class(a: Class, b: Class)
    instance_of(entity: Individual, class: Class)
    domain_of(property: Property, class: Class)
    range_of(property: Property, class: Class)
    defined_in(class: Class, ontology: string)

  constraints:
    - "All class and property IRIs must be valid and resolvable within a declared namespace policy."
    - "Class membership is distinct from subclass membership."
    - "Class equivalence must not be inferred from similar labels alone."
    - "Disjoint classes must not share a satisfiable instance in a consistent OWL interpretation."
    - "Subclass and equivalent-class reasoning must respect the selected entailment regime."
    - "RDFS domain and range statements support type inference; they are not closed-world validation constraints."
    - "Confidence values lie within [0,1] and annotate evidence, not OWL truth values."

  inference:
    rule subclass_transitivity:
      if subclass_of(a,b) and subclass_of(b,c)
      then subclass_of(a,c)
      confidence: "retain derivation provenance"
    rule membership_inheritance:
      if instance_of(x,a) and subclass_of(a,b)
      then instance_of(x,b)
      confidence: "retain premises and entailment regime"
    rule equivalence_symmetry:
      if equivalent_class(a,b)
      then equivalent_class(b,a)
      confidence: "retain original axiom"
    rule equivalence_subsumption:
      if equivalent_class(a,b)
      then subclass_of(a,b) and subclass_of(b,a)
      confidence: "logical entailment under OWL semantics"
    rule disjointness_conflict:
      if instance_of(x,a) and instance_of(x,b) and disjoint_class(a,b)
      then flag_inconsistency(x,a,b)
      confidence: "explain conflicting assertions; do not silently delete"

  SEMANTIC_EQUIVALENCE:
    - "Use explicit owl:equivalentClass or justified bidirectional subsumption."
    - "Keep lexical similarity, SKOS mapping and formal logical equivalence separate."
    - "Record vocabulary versions, namespaces and alignment evidence."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, mapping_evidence, ontology_consistency, version_alignment, independent_validation]
    policy: "Do not treat inferred axioms as independently verified evidence or increase confidence solely by chaining."

  VALIDATION:
    - "Check IRI syntax, typed endpoints, axiom provenance and ontology version."
    - "Run an OWL reasoner for satisfiability and disjointness conflicts where applicable."
    - "Use SHACL or an explicit closed-world profile for operational cardinality and data-quality checks."
    - "Preserve alternative mappings and flag unsupported identity merges."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, class axioms, instance 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, classify, detect_inconsistencies, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed RDF/OWL knowledge graph with class hierarchy and evidence-backed axioms"
    outputs: [class_hierarchy, class_memberships, equivalent_classes, disjointness_conflicts, inference_traces, provenance_records]
    safeguards: [no_label_only_equivalence, no_unsupported_identity_merges, preserve_open_world_semantics, report_inconsistencies]
}

END FLOW ALGEBRA