One-to-Many Relationship Ontology

FLOW ALGEBRA
TITLE: One-to-Many Relationship Ontology
DOMAIN: Database Relationships / Relational Data Modelling
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/database-relationships/one-to-many-relationship-ontology.html
VERSION: 1.0
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source-page specification not independently verified.

flow "OneToManyRelationshipOntology" v1.0 {
  ontology:
    id: "one-to-many-relationship-ontology"
    parent: "database-relationships"
    purpose: "Model, validate and reason about one-to-many associations between relational entities and their instances."

  types:
    EntityType: {id: string, name: string, primary_key: string[]}
    EntityInstance: {id: string, entity_type: string, key_values: map}
    ForeignKey: {id: string, child_entity: string, child_columns: string[], parent_entity: string, parent_columns: string[], nullable: boolean}
    Cardinality: {min: integer, max: integer?}
    OneToManyRelationship: {id: string, parent: string, child: string, foreign_key: string, parent_to_children: Cardinality, child_to_parent: Cardinality, confidence: number, provenance: string[]}
    ConstraintEvidence: {id: string, source: string, timestamp: datetime?, verified: boolean}

  predicates:
    references(child: EntityInstance, parent: EntityInstance)
    has_child(parent: EntityInstance, child: EntityInstance)
    has_parent(child: EntityInstance, parent: EntityInstance)
    defines_foreign_key(child_type: EntityType, parent_type: EntityType)
    participates_in(instance: EntityInstance, relationship: OneToManyRelationship)

  constraints:
    - "The child foreign-key columns must reference a candidate key or primary key of the parent entity."
    - "A non-null child foreign-key tuple must match an existing parent key, unless a documented deferred constraint is pending."
    - "For a conventional one-to-many relationship, each child has at most one parent through the specified foreign key."
    - "Parent participation may be zero-to-many or one-to-many, according to declared minimum cardinality."
    - "Child participation may be optional or mandatory, according to foreign-key nullability and additional constraints."
    - "Composite foreign keys must be validated as tuples; SQL NULL semantics and MATCH rules must be respected."
    - "Relationship direction must not be confused with cascade delete or update behaviour."
    - "Confidence values must lie within [0,1]."

  inference:
    rule inverse_parent_child:
      if references(child,parent) and valid_foreign_key(child,parent)
      then has_parent(child,parent) and has_child(parent,child)
      confidence: "inherit verified assertion evidence"
    rule parent_children_collection:
      if has_parent(c1,p) and has_parent(c2,p)
      then related_by_shared_parent(c1,c2,p)
      confidence: "retain source provenance; do not imply identity"
    rule referential_integrity_failure:
      if non_null_foreign_key(child) and not exists_matching_parent(child)
      then flag_integrity_violation(child)
      confidence: "requires a complete authoritative snapshot and appropriate transaction visibility"

  SEMANTIC_EQUIVALENCE:
    - "Align parent, owner and referenced entity only when their schema roles and context match."
    - "Distinguish one-to-many from many-to-many and one-to-one relationships."
    - "Do not infer semantic identity from shared foreign-key values across unrelated schemas."

  CONFIDENCE:
    range: [0,1]
    factors: [schema_authority, key_integrity, provenance_quality, transaction_consistency, constraint_enforcement]
    policy: "Schema constraints are deterministic when enforced; uncertain mappings must retain uncertainty."

  VALIDATION:
    - "Verify primary/candidate keys, foreign-key targets, types and column ordering."
    - "Check nullable columns, minimum cardinalities and uniqueness constraints."
    - "Detect orphan references, duplicate parent keys and inconsistent schema declarations."
    - "Respect deferred constraints, soft deletion, temporal validity and transaction isolation."
    - "Do not assert that every parent has a child unless this is explicitly enforced or verified."

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

  AI_CONSUMPTION:
    representation: "typed relational schema and evidence-backed knowledge graph"
    outputs: [parent_child_edges, cardinality_constraints, key_mappings, integrity_findings, inferred_relations, provenance_records]
    safeguards: [no_unverified_cardinality_claims, preserve_null_semantics, no_unsupported_identity_merges, enforce_referential_integrity]
}

END FLOW ALGEBRA