Child Relationship Ontology

FLOW ALGEBRA
Title: Child Relationship Ontology
Source: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/structural-relationships/child-relationship-ontology.html
Authors: Mark Anthony Higgins — Sky (Recursive AI)
Version: 1.0
Date: 2026-10-08

ONTOLOGY ChildRelationshipOntology
DOMAIN StructuralRelationships
PURPOSE Model immediate child-to-parent structural relationships with explicit direction, evidence, constraints and safe inference.

ENTITY Node { id: IRI; label: String?; type: IRI? }
ENTITY ChildRelationship { id: IRI; child: Node; parent: Node; context: IRI?; provenance: IRI?; confidence: Real[0,1]; valid_from: DateTime?; valid_to: DateTime? }
ENTITY Hierarchy { id: IRI; nodes: Set<Node>; edges: Set<ChildRelationship>; tree_mode: Boolean }

RELATION child_of(child: Node, parent: Node) : Boolean
RELATION parent_of(parent: Node, child: Node) : Boolean
RELATION descendant_of(descendant: Node, ancestor: Node) : Boolean
RELATION ancestor_of(ancestor: Node, descendant: Node) : Boolean
RELATION sibling_of(a: Node, b: Node) : Boolean

AXIOM A1: child_of(c,p) => parent_of(p,c)
AXIOM A2: child_of(c,p) => descendant_of(c,p)
AXIOM A3: child_of(c,p) => ancestor_of(p,c)
AXIOM A4: child_of(c,p) AND descendant_of(p,a) => descendant_of(c,a)
AXIOM A5: child_of(a,p) AND child_of(b,p) AND a != b => sibling_of(a,b)
AXIOM A6: child_of(c,p) => c != p
AXIOM A7: child_of(c,p) AND descendant_of(p,c) => INVALID_CYCLE
AXIOM A8: child_of(c,p) does NOT imply child_of(p,c)
AXIOM A9: descendant_of(c,p) does NOT imply child_of(c,p)
AXIOM A10: tree_mode(h) => each non-root node has exactly one parent within h

TYPE_RULE R1: child_of: Node × Node -> Boolean
TYPE_RULE R2: confidence ∈ [0,1]
TYPE_RULE R3: valid_from <= valid_to when both are present

SEMANTIC_EQUIVALENCE:
  child_of(c,p) <=> parent_of(p,c)
  direct_subordinate_of(c,p) <=> child_of(c,p) ONLY when direct structural hierarchy is intended
  descendant_of(c,p) != child_of(c,p) in general

CONFIDENCE:
  explicit_assertion: preserve source confidence
  inferred_inverse: inherit supporting assertion confidence
  multi_hop_descendant: combine evidence conservatively; never increase confidence without independent evidence
  conflicting_assertions: retain provenance and flag for review

VALIDATION:
  - enforce node identifiers and typed endpoints
  - reject self-parent links and cycles in acyclic hierarchies
  - enforce single-parent constraint only when hierarchy is declared tree_mode
  - permit multiple parents in directed acyclic graphs when tree_mode is false
  - distinguish immediate child edges from transitive descendant paths
  - track context and validity periods to avoid false cross-context inference

INFERENCE:
  INPUT: child_of(C,P)
  OUTPUT: parent_of(P,C), descendant_of(C,P), ancestor_of(P,C)
  INPUT: child_of(C,P), descendant_of(P,A)
  OUTPUT: descendant_of(C,A)
  INPUT: child_of(A,P), child_of(B,P), A != B
  OUTPUT: sibling_of(A,B)

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(ontology_id, version, typed_entities, relationships, axioms, rules)
  note: compute hash during publication; no uncomputed digest is asserted

UPDATE_MODEL:
  strategy: versioned_incremental
  operations: [ADD_NODE, REMOVE_NODE, ADD_CHILD_EDGE, REMOVE_CHILD_EDGE, UPDATE_PROVENANCE, UPDATE_CONFIDENCE, UPDATE_VALIDITY]
  on_change: [REVALIDATE_CONSTRAINTS, RECOMPUTE_AFFECTED_INFERENCES, REBUILD_FLOW_HASH]
  retain_history: true

AI_CONSUMPTION:
  representation: typed_graph
  supported_tasks: [hierarchy_navigation, graph_reasoning, structural_search, knowledge_graph_inference, explainable_relationship_tracing]
  safeguards: [preserve_edge_direction, distinguish_direct_and_transitive_links, retain_provenance, respect_context, avoid_unjustified_inference]

END ONTOLOGY