One-to-One Relationship Ontology

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

flow "OneToOneRelationshipOntology" v1.0 {
  ontology:
    id: "one-to-one-relationship-ontology"
    parent: "database-relationships"
    purpose: "Model, constrain and validate one-to-one associations between database entities."

  types:
    EntityType: {id: string, name: string, primary_key: string[]}
    EntityRecord: {id: string, entity_type: string, key_values: map}
    KeyConstraint: {id: string, fields: string[], kind: enum[primary, unique, foreign], nullable: boolean}
    OneToOneRelationship: {id: string, left_type: string, right_type: string, left_min: integer, left_max: integer, right_min: integer, right_max: integer, enforcement: string, provenance: string?, confidence: number}
    Association: {id: string, left_record: string, right_record: string, evidence: string[]}

  predicates:
    linked_to(a: EntityRecord, b: EntityRecord)
    has_unique_key(t: EntityType, key: KeyConstraint)
    references(a: EntityRecord, b: EntityRecord)
    participates_in(record: EntityRecord, relationship: OneToOneRelationship)

  constraints:
    - "Each participating left record is linked to at most one right record, and vice versa."
    - "Minimum participation is 0 for optional and 1 for mandatory participation; maximum participation is 1 on both sides."
    - "Foreign-key-based implementations require uniqueness on the referencing key and referential integrity against the referenced key."
    - "Nullable foreign keys represent optional participation where the database permits them; uniqueness and NULL behaviour are DBMS-specific."
    - "A UNIQUE foreign key alone does not guarantee mandatory participation on the referenced side."
    - "Shared-primary-key designs require matching key domains and valid foreign-key enforcement."
    - "Do not equate a one-to-one database association with real-world identity."
    - "Confidence lies within [0,1] and does not replace hard integrity constraints."

  inference:
    rule unique_partner:
      if linked_to(a,b) and linked_to(a,c) and valid_one_to_one(a,b,c)
      then same_database_record(b,c)
      note: "Applies only when both targets are in the same constrained entity type and referential integrity is enforced."
    rule reverse_navigation:
      if linked_to(a,b) and inverse_relationship_declared(a,b)
      then linked_from(b,a)
      note: "Navigation inverse is not entity identity."
    rule cardinality_violation:
      if linked_to(a,b) and linked_to(a,c) and distinct_keys(b,c)
      then flag_violation("one-to-one cardinality")

  SEMANTIC_EQUIVALENCE:
    - "Map one-to-one, 1:1 and max-cardinality-one to the same constrained cardinality concept only in compatible contexts."
    - "Keep optional one-to-one distinct from mandatory one-to-one."
    - "Preserve differences between conceptual associations and physical key implementations."

  CONFIDENCE:
    range: [0,1]
    factors: [schema_evidence, key_validation, referential_integrity, provenance, migration_state]
    policy: "Report uncertain schema mappings separately from enforced database constraints."

  VALIDATION:
    - "Resolve entity types, records, key definitions and data types."
    - "Check UNIQUE or PRIMARY KEY enforcement for the referencing side."
    - "Check foreign-key targets, orphan records and duplicate associations."
    - "Check optionality and mandatory participation in both directions."
    - "Test update, deletion and migration behaviour against declared referential actions."

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

  UPDATE_MODEL:
    strategy: "versioned, integrity-preserving schema and assertion updates"
    steps: [ingest, normalise, validate, compare, migrate, recheck_cardinality, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed database relationship graph with enforced cardinality annotations"
    outputs: [entity_links, key_constraints, participation_bounds, validation_findings, provenance_records]
    safeguards: [no_unverified_identity_merges, preserve_optionality, distinguish_schema_from_data, enforce_referential_integrity]
}

END FLOW ALGEBRA