Spatial Relationships

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

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

flow "SpatialRelationships" v1.0 {
  ontology:
    id: "spatial-relationships"
    parent: "relationship-ontologies"
    purpose: "Represent spatial location, topology, orientation, proximity and containment with explicit reference systems and evidence."

  types:
    SpatialEntity: {id: string, class: string, geometry_id: string?, provenance: string}
    Geometry: {id: string, kind: enum[point, line, polygon, volume, collection], coordinates: any, crs: string, epoch: datetime?, precision: number?}
    SpatialRegion: {id: string, geometry_id: string, provenance: string}
    SpatialObservation: {id: string, timestamp: datetime, method: string, uncertainty: number?, provenance: string}
    Distance: {value: number, unit: string, method: string, uncertainty: number?}
    SpatialRelationship: {id: string, subject: string, predicate: string, object: string, crs: string?, valid_time: string?, confidence: number, evidence: string[]}

  predicates:
    located_in(entity: SpatialEntity, region: SpatialRegion)
    contains(region: SpatialRegion, entity: SpatialEntity)
    intersects(a: SpatialEntity, b: SpatialEntity)
    disjoint_from(a: SpatialEntity, b: SpatialEntity)
    overlaps(a: SpatialEntity, b: SpatialEntity)
    touches(a: SpatialEntity, b: SpatialEntity)
    adjacent_to(a: SpatialEntity, b: SpatialEntity)
    north_of(a: SpatialEntity, b: SpatialEntity, frame: string)
    east_of(a: SpatialEntity, b: SpatialEntity, frame: string)
    near(a: SpatialEntity, b: SpatialEntity, threshold: Distance)
    distance_between(a: SpatialEntity, b: SpatialEntity, distance: Distance)

  constraints:
    - "All relationship endpoints must resolve to typed spatial entities."
    - "Confidence values must lie within [0,1]."
    - "Coordinates require an explicit coordinate reference system (CRS)."
    - "Compare or transform geometries to compatible CRS before spatial inference."
    - "Distances require units and a declared measurement method."
    - "Near is threshold- and context-dependent, not an intrinsic absolute relation."
    - "Topological relationships must use declared boundary/interior semantics."
    - "Directional relations depend on the chosen coordinate frame and geometry representation."
    - "Do not treat overlapping, touching, adjacency and containment as interchangeable."
    - "Spatial relationships may change over time; retain observation epoch and validity interval."

  inference:
    rule containment_inverse:
      if contains(r,e) and valid_geometry(r,e)
      then located_in(e,r)
      confidence: "preserve original evidence and spatial interpretation"
    rule intersection_symmetry:
      if intersects(a,b)
      then intersects(b,a)
      confidence: "retain source confidence"
    rule disjoint_symmetry:
      if disjoint_from(a,b)
      then disjoint_from(b,a)
      confidence: "retain source confidence"
    rule proximity_symmetry:
      if near(a,b,d) and symmetric_distance_metric(d.method)
      then near(b,a,d)
      confidence: "retain threshold and metric"
    rule nested_containment:
      if contains(a,b) and contains(b,c) and compatible_geometry(a,b,c)
      then contains(a,c)
      confidence: "propagate uncertainty; do not manufacture certainty"

  SEMANTIC_EQUIVALENCE:
    - "Resolve place aliases using versioned geographic identifiers."
    - "Distinguish same place, nearby place, shared boundary and overlapping extent."
    - "Preserve CRS, geometry precision, epoch and scale when comparing spatial assertions."

  CONFIDENCE:
    range: [0,1]
    factors: [source_reliability, positional_accuracy, geometry_quality, temporal_validity, scale, independent_confirmation]
    policy: "Inference chaining must not increase confidence without independent evidence."

  VALIDATION:
    - "Check geometry validity, coordinate dimensions, CRS and units."
    - "Check endpoint types, evidence, temporal applicability and predicate compatibility."
    - "Flag inconsistent topology and contradictory spatial assertions."
    - "Retain competing interpretations when measurement uncertainty prevents resolution."

  FLOW_HASH:
    algorithm: "SHA-256"
    input: "canonicalised ontology version, typed assertions, 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 geospatial knowledge graph with evidence-backed relationships"
    outputs: [spatial_entities, geometry_references, relation_triples, uncertainty_annotations, inferred_edges, provenance_records]
    safeguards: [no_unqualified_location_merges, preserve_crs_and_units, preserve_temporal_context, no_unsupported_spatial_inference]
}

END FLOW ALGEBRA