Edge Relationship Ontology

FLOW ALGEBRA
TITLE: Edge Relationship Ontology
VERSION: 1.0
SOURCE: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/structural-relationships/edge-relationship-ontology.html
AUTHORS: Mark Anthony Higgins — Sky (Recursive AI)
STATUS: Companion formalisation; source page not independently verified.

flow "EdgeRelationshipOntology" v1.0

ONTOLOGY:
  id: kireth:EdgeRelationshipOntology
  domain: Structural Relationships
  purpose: Represent and validate connections between graph nodes with explicit direction, type, evidence and constraints.

TYPES:
  Node: {id: IRI, label: string?, node_type: string?}
  Edge: {id: IRI, source: Node, target: Node, predicate: IRI, directed: bool, weight: float?, confidence: float, provenance: IRI?, valid_from: datetime?, valid_until: datetime?}
  Graph: {id: IRI, nodes: set<Node>, edges: set<Edge>}

RELATIONSHIPS:
  CONNECTS(edge: Edge, source: Node, target: Node)
  INCIDENT_TO(edge: Edge, node: Node)
  OUTGOING_FROM(edge: Edge, node: Node)
  INCOMING_TO(edge: Edge, node: Node)
  ADJACENT(source: Node, target: Node, graph: Graph)
  MEMBER_OF(edge: Edge, graph: Graph)
  HAS_PREDICATE(edge: Edge, predicate: IRI)

CONSTRAINTS:
  C1: every edge has exactly one source and one target.
  C2: edge endpoints must belong to its graph.
  C3: edge identifiers are unique within the graph.
  C4: confidence is in [0,1].
  C5: valid_from <= valid_until when both are present.
  C6: self-loops, parallel edges and negative weights are governed by graph policy, not universally prohibited.

INFERENCE:
  R1: CONNECTS(e,a,b) => INCIDENT_TO(e,a) and INCIDENT_TO(e,b).
  R2: CONNECTS(e,a,b) and e.directed => OUTGOING_FROM(e,a) and INCOMING_TO(e,b).
  R3: CONNECTS(e,a,b) and MEMBER_OF(e,g) => ADJACENT(a,b,g).
  R4: CONNECTS(e,a,b) and not e.directed => ADJACENT(b,a,g) when MEMBER_OF(e,g).
  R5: directed edges do not imply reverse adjacency without a separately supported reverse edge.
  R6: transitive reachability is distinct from direct adjacency.

SEMANTIC_EQUIVALENCE:
  compare: [predicate, source_identity, target_identity, directed, context, validity_interval]
  rule: Equivalent labels alone do not establish equivalent edges.
  undirected_normalisation: endpoint order is immaterial only for undirected edges.

CONFIDENCE:
  range: [0,1]
  default: unknown
  aggregation: preserve supporting evidence and dependence; do not assume independent probabilities.

VALIDATION:
  verify: [endpoint_integrity, predicate_definition, directionality, graph_membership, temporal_consistency, confidence_range, provenance_integrity]
  result: [valid, invalid, indeterminate]

FLOW_HASH:
  algorithm: SHA-256
  input: canonical_serialisation(ontology_id, version, types, relationships, constraints, inference_rules)
  purpose: detect changes to formal ontology definition

UPDATE_MODEL:
  strategy: versioned_incremental
  on_change: [revalidate_affected_edges, recompute_affected_adjacency, invalidate_dependent_inferences, regenerate_flow_hash]
  preserve: [previous_versions, provenance, audit_trail]

AI_CONSUMPTION:
  formats: [typed_triples, property_graph, JSON-LD_compatible_mapping]
  tasks: [knowledge_graph_construction, relationship_reasoning, graph_navigation, semantic_retrieval, consistency_checking]
  safeguards: [do_not_invent_edges, retain_provenance, distinguish_asserted_from_inferred, respect_direction_and_time]

end flow