Boundary Relationship Ontology

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

flow "BoundaryRelationshipOntology" v1.0 {
  ontology:
    id: "boundary-relationship-ontology"
    parent: "spatial-relationships"
    purpose: "Represent and validate boundaries, boundary contact, separation and topological relationships among spatial entities."

  types:
    SpatialEntity: {id: string, geometry_id: string, dimension: integer, crs: string, valid_time: string?}
    Boundary: {id: string, owner_id: string, geometry_id: string, dimension: integer, kind: enum[interior, exterior, administrative, physical, conceptual, other], crs: string}
    Geometry: {id: string, type: enum[point, line, polygon, multipolygon, surface, solid, other], coordinates_ref: string, crs: string, precision: number?}
    Observation: {id: string, method: string, timestamp: datetime?, uncertainty: number?, provenance: string}
    Relationship: {id: string, subject: string, predicate: string, object: string, context: string?, confidence: number, evidence: string[]}

  predicates:
    boundary_of(b: Boundary, e: SpatialEntity)
    touches(a: SpatialEntity, b: SpatialEntity)
    shares_boundary_with(a: SpatialEntity, b: SpatialEntity)
    intersects_boundary_of(a: SpatialEntity, b: SpatialEntity)
    inside(a: SpatialEntity, b: SpatialEntity)
    contains(a: SpatialEntity, b: SpatialEntity)
    disjoint_from(a: SpatialEntity, b: SpatialEntity)
    separates(b: Boundary, a: SpatialEntity, c: SpatialEntity)
    derived_from(b: Boundary, o: Observation)

  constraints:
    - "All relationship endpoints must resolve to typed spatial entities or boundaries."
    - "Confidence must lie within [0, 1]."
    - "Geometry comparisons require compatible coordinate reference systems and dimensional models."
    - "Specify boundary convention and tolerance before classifying contact or intersection."
    - "Boundary contact alone does not imply overlap of interiors."
    - "Administrative and conceptual boundaries must not be treated as physical barriers."
    - "Temporal validity must be preserved when boundaries change."
    - "Do not infer containment solely from shared boundary contact."

  inference:
    rule touch_symmetry:
      if touches(a,b)
      then touches(b,a)
      confidence: "retain source evidence and geometry context"
    rule shared_boundary_symmetry:
      if shares_boundary_with(a,b)
      then shares_boundary_with(b,a)
      confidence: "retain source evidence and boundary convention"
    rule containment_inverse:
      if contains(a,b)
      then inside(b,a)
      confidence: "preserve containment definition and temporal context"
    rule disjoint_symmetry:
      if disjoint_from(a,b)
      then disjoint_from(b,a)
      confidence: "retain original evidence"
    rule no_contact_transitivity:
      if touches(a,b) and touches(b,c)
      then do_not_infer(touches(a,c))
      confidence: "topological contact is not transitive"

  SEMANTIC_EQUIVALENCE:
    - "Normalise equivalent boundary and topology terms against versioned spatial vocabularies."
    - "Distinguish touches, overlaps, intersects, contains and shares_boundary_with."
    - "Preserve geometry model, CRS, precision, temporal validity and boundary convention."

  CONFIDENCE:
    range: [0,1]
    factors: [geometry_accuracy, measurement_uncertainty, source_reliability, crs_transform_quality, boundary_definition, temporal_validity]
    policy: "Do not increase confidence solely by chaining spatial inferences."

  VALIDATION:
    - "Check entity and geometry identifiers, geometry validity, coordinate systems and provenance."
    - "Check dimensional compatibility and topological consistency under the selected boundary model."
    - "Flag conflicting boundary definitions and uncertain or disputed boundaries."
    - "Retain competing boundary interpretations where evidence is inconclusive."

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

  UPDATE_MODEL:
    strategy: "versioned, provenance-preserving incremental update"
    steps: [ingest, normalise, transform_crs, validate, compare, reconcile, recompute_inferences, publish]
    rollback: true

  AI_CONSUMPTION:
    representation: "typed spatial knowledge graph with geometry-backed boundary relationships"
    outputs: [boundary_entities, spatial_relation_triples, topology_annotations, uncertainty_annotations, inferred_edges, provenance_records]
    safeguards: [no_unqualified_topological_inference, preserve_crs_and_precision, distinguish_legal_and_physical_boundaries, retain_temporal_context]
}

END FLOW ALGEBRA