Many-to-Many Relationship Ontology

FLOW ALGEBRA
TITLE: Many-to-Many Relationship Ontology
DOMAIN: Relationship Ontologies / Database Relationships
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/database-relationships/many-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 "ManyToManyRelationshipOntology" v1.0 {
  ontology:
    id: "many-to-many-relationship-ontology"
    parent: "database-relationships"
    purpose: "Model, enforce and explain many-to-many associations between typed database entities through explicit relationship records."

  types:
    EntityType: {id: string, name: string, primary_key: string}
    EntityInstance: {id: string, type_id: string, key: string}
    JunctionTable: {id: string, name: string, left_fk: string, right_fk: string, uniqueness: string[]}
    Association: {id: string, left: string, right: string, junction_id: string, attributes: map?, provenance: string?, confidence: number?}
    Cardinality: {min: integer, max: integer?}
    Constraint: {id: string, kind: enum[foreign_key, unique, not_null, check, cascade_policy], expression: string}

  predicates:
    many_to_many(left_type: EntityType, right_type: EntityType)
    mediated_by(left_type: EntityType, right_type: EntityType, junction: JunctionTable)
    references(association: Association, entity: EntityInstance)
    associated_with(left: EntityInstance, right: EntityInstance)
    has_cardinality(entity_type: EntityType, role: string, cardinality: Cardinality)

  constraints:
    - "Each junction row references one valid instance on each side unless an explicitly documented staging policy permits unresolved references."
    - "A composite UNIQUE(left_fk, right_fk) or equivalent key prevents duplicate pairs when the relationship is set-valued."
    - "Repeated pairs are allowed only when an additional discriminator is explicitly part of the association identity."
    - "Foreign keys and referenced primary or candidate keys must have compatible types and enforce referential integrity."
    - "Many-to-many cardinality permits multiple partners on both sides; minimum participation (zero or one) must be specified separately."
    - "Deleting a referenced entity must follow an explicit RESTRICT, CASCADE or other supported referential action policy."
    - "Association does not imply equality, causality or transitivity."

  inference:
    rule association_from_junction:
      if valid(junction_row) and references_left(junction_row,a) and references_right(junction_row,b)
      then associated_with(a,b)
      confidence: "retain source-row provenance; no invented certainty"
    rule reverse_navigation:
      if associated_with(a,b) and relation_is_bidirectionally_navigable(a,b)
      then navigable_from(b,a)
      confidence: "same evidence, inverse role semantics preserved"
    rule participation_count:
      if valid_associations_for(entity, role, rows)
      then participation(entity,role,count_distinct(rows))
      confidence: "computed from validated rows and query snapshot"

  SEMANTIC_EQUIVALENCE:
    - "Map junction-table and associative-entity representations only when keys, roles, attributes and constraints are preserved."
    - "Distinguish relation direction and role names from semantic symmetry."
    - "Never merge entities based only on shared associations."

  CONFIDENCE:
    range: [0,1]
    factors: [referential_integrity, provenance_quality, temporal_validity, source_reliability]
    policy: "Schema constraints are deterministic; confidence annotations apply to uncertain source assertions, not to proven key checks."

  VALIDATION:
    - "Verify endpoint existence, key compatibility, uniqueness policy and cardinality bounds."
    - "Detect orphan junction rows, duplicate pairs, unexpected null keys and inconsistent role mappings."
    - "Test insert, update and delete behaviour against declared referential actions."
    - "Retain junction attributes and provenance during graph conversion."

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

  UPDATE_MODEL:
    strategy: "versioned, integrity-preserving incremental updates"
    steps: [ingest, normalise, validate_keys, enforce_constraints, reconcile, update_associations, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed relational associations with knowledge-graph projection"
    outputs: [entity_links, junction_records, role_aware_edges, cardinality_metadata, integrity_reports, provenance_records]
    safeguards: [no_unverified_entity_merges, no_automatic_transitivity, preserve_junction_attributes, enforce_referential_integrity]
}

END FLOW ALGEBRA