Containment Ontology

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

flow "ContainmentOntology" v1.0 {
  ontology:
    id: "containment-ontology"
    parent: "spatial-relationships"
    purpose: "Represent and validate topological and geographic containment relationships with explicit boundary, reference-frame and temporal semantics."

  types:
    SpatialEntity: {id: string, kind: enum[point, line, polygon, solid, region, geographic_feature, other], geometry_id: string?, crs: string?, valid_time: string?}
    Geometry: {id: string, geometry_type: string, coordinates: string, crs: string, precision: number?}
    ContainmentAssertion: {id: string, contained: string, container: string, predicate: string, boundary_policy: string, timestamp: datetime?, confidence: number, evidence: string[], provenance: string}
    Observation: {id: string, method: string, timestamp: datetime, uncertainty: number?, provenance: string}

  predicates:
    contains(container: SpatialEntity, contained: SpatialEntity)
    strictly_contains(container: SpatialEntity, contained: SpatialEntity)
    within(contained: SpatialEntity, container: SpatialEntity)
    covers(container: SpatialEntity, contained: SpatialEntity)
    covered_by(contained: SpatialEntity, container: SpatialEntity)
    intersects(a: SpatialEntity, b: SpatialEntity)
    touches(a: SpatialEntity, b: SpatialEntity)
    disjoint(a: SpatialEntity, b: SpatialEntity)

  constraints:
    - "Resolve all relationship endpoints to typed spatial entities and valid geometries."
    - "Transform geometries into a compatible coordinate reference system before topological evaluation."
    - "Specify whether boundary contact is allowed: strict containment and boundary-inclusive coverage differ."
    - "Use one declared topology convention consistently; do not equate contains with covers."
    - "Containment is not generally symmetric; inverse assertions must reverse the argument order."
    - "Do not infer containment from bounding-box overlap, geographic names or proximity alone."
    - "Validate geometry, dimensionality, measurement precision and temporal applicability."
    - "Confidence must lie within [0, 1]."

  inference:
    rule inverse_contains:
      if contains(a,b)
      then within(b,a)
      confidence: "preserve source confidence, topology and evidence"
    rule inverse_covers:
      if covers(a,b)
      then covered_by(b,a)
      confidence: "preserve source confidence, topology and evidence"
    rule containment_transitivity:
      if contains(a,b) and contains(b,c) and compatible_topology(a,b,c) and same_valid_time(a,b,c)
      then contains(a,c)
      confidence: "conservative propagation with recorded inference path"
    rule coverage_transitivity:
      if covers(a,b) and covers(b,c) and compatible_topology(a,b,c) and same_valid_time(a,b,c)
      then covers(a,c)
      confidence: "conservative propagation with recorded inference path"
    rule strict_containment_implies_disjoint_boundaries:
      if strictly_contains(a,b) and valid_geometry(a,b)
      then boundaries_do_not_intersect(a,b)
      confidence: "dependent on strict-containment definition"

  SEMANTIC_EQUIVALENCE:
    - "Map contains/within and covers/covered_by as inverse pairs, not interchangeable predicates."
    - "Distinguish topological containment from administrative jurisdiction, ownership and organisational membership."
    - "Normalise place identifiers and coordinate reference systems while retaining source geometry and epoch."

  CONFIDENCE:
    range: [0,1]
    factors: [geometry_accuracy, boundary_uncertainty, source_reliability, temporal_validity, topology_consistency]
    policy: "Do not manufacture certainty by chaining inferred relationships."

  VALIDATION:
    - "Check geometry validity, CRS compatibility, dimensions, topology convention and boundary policy."
    - "Flag incompatible contains/disjoint assertions for the same entities and time."
    - "Retain uncertain or competing boundaries with provenance instead of forcing a single answer."
    - "Test inverse and transitive rules using valid spatial fixtures."

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

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

  AI_CONSUMPTION:
    representation: "typed spatial knowledge graph with topology-aware, evidence-backed edges"
    outputs: [containment_triples, inverse_relations, inferred_relations, boundary_annotations, uncertainty_annotations, provenance_records]
    safeguards: [no_unverified_containment, preserve_boundary_semantics, preserve_crs_and_time, no_unjustified_identity_merges]
}

END FLOW ALGEBRA