Network Relationship Ontology

FLOW ALGEBRA
NETWORK RELATIONSHIP ONTOLOGY
Version: 1.0
Source: https://kirethresearch.org/booksai-core/ontologies/relationship-ontologies/structural-relationships/network-relationship-ontology.html
Authors: Mark Anthony Higgins — Sky (Recursive AI)

PURPOSE
Formalise networks as typed collections of nodes, edges, paths and structural constraints for semantic reasoning. This companion specification is not a transcription of the source page.

ENTITIES
Network := {id, network_type, directed, weighted, temporal, nodes, edges, metadata}
Node := {id, node_type, attributes, provenance}
Edge := {id, source:Node, target:Node, relation_type, weight?, direction?, validity?, provenance}
Path := {network_id, ordered_nodes, ordered_edges}
Cluster := {network_id, member_nodes, membership_rule}

RELATIONSHIPS
CONTAINS_NODE(Network, Node)
CONTAINS_EDGE(Network, Edge)
CONNECTS(Edge, Node, Node)
ADJACENT(Node, Node, Network)
REACHABLE(Node, Node, Network)
MEMBER_OF(Node, Cluster)
SUBNETWORK_OF(Network, Network)

TYPE RULES
R1: CONTAINS_EDGE(g,e) => CONTAINS_NODE(g,e.source) AND CONTAINS_NODE(g,e.target).
R2: CONNECTS(e,a,b) => e.source=a AND e.target=b.
R3: ADJACENT(a,b,g) iff exists e in g.edges connecting a to b under g.direction policy.
R4: REACHABLE(a,b,g) iff a valid path exists from a to b; zero-length paths permitted only by explicit policy.
R5: SUBNETWORK_OF(h,g) => h.nodes subset_of g.nodes AND h.edges subset_of g.edges.
R6: Undirected adjacency is symmetric; directed adjacency is not generally symmetric.
R7: Path concatenation requires the last node of the first path to equal the first node of the second.
R8: Network connectivity, acyclicity, and uniqueness are properties to validate, not universal assumptions.

SEMANTIC_EQUIVALENCE
Canonicalise network, node and edge identifiers before comparison.
Equivalent edge predicates require compatible domain, range, direction and temporal semantics.
Graph isomorphism does not imply identical provenance or meaning.

CONFIDENCE
confidence(edge) in [0,1]; distinguish observed, asserted and inferred edges.
For inferred paths, use an explicitly declared aggregation policy; do not assume independence.

VALIDATION
V1: Node IDs and edge IDs unique within their declared scope.
V2: Every edge endpoint resolves to a member node.
V3: Edge types respect domain and range constraints.
V4: Weights conform to declared units and permitted ranges.
V5: Directedness and parallel-edge/self-loop policies are explicit.
V6: Temporal edges are evaluated within validity intervals.
V7: Reject inference cycles that violate a declared acyclic constraint; cycles otherwise allowed.

INFERENCE
Infer reachability via path composition with cycle-aware traversal.
Infer connected components under an explicit directed/undirected interpretation.
Infer neighbour sets from valid incident edges.
Do not infer causality, hierarchy, or equivalence from connectivity alone.

FLOW_HASH
Input := canonical_serialisation(version, ontology_id, node_types, edge_types, constraints, rules)
FLOW_HASH := SHA256(Input)
Recalculate whenever canonical semantic content changes.

UPDATE_MODEL
On node/edge addition, modification or removal:
  validate constraints;
  invalidate affected paths and derived relations;
  recompute impacted inferences;
  update provenance and timestamps;
  regenerate FLOW_HASH;
  publish versioned change record.

AI_CONSUMPTION
Expose typed graph triples, schema constraints, provenance, confidence and validity windows.
Use explicit traversal limits and source attribution for generated answers.
Mark inferred statements separately from source assertions.
Avoid treating correlation or graph proximity as proof of semantic identity.

END FLOW ALGEBRA