Coordinate System Ontology

FLOW ALGEBRA

Ontology: Coordinate System Ontology
Domain: Metadata Ontologies > Spatial Metadata
Canonical URL: https://kirethresearch.org/booksai-core/ontologies/metadata-ontologies/spatial-metadata/coordinate-system-ontology.html

Authors: Mark Anthony Higgins — Sky (Recursive AI)

flow "CoordinateSystemOntology" v1.0

# ---------- DOMAIN ----------
domain:
  class: MetadataOntology
  category: SpatialMetadata
  subject: CoordinateSystem
  purpose:
    - represent systems used to express spatial positions
    - define coordinate axes, dimensions, units, and origins
    - provide machine-readable spatial reference context
    - support coordinate interpretation and transformation
    - prevent ambiguity in spatial data exchange and reasoning

# ---------- CORE ENTITY ----------
entity CoordinateSystem:
  type: SpatialReferenceStructure
  defines:
    - dimensions
    - axes
    - axis_order
    - units
  may_include:
    - origin
    - orientation
    - handedness
    - datum
    - projection
    - identifier
    - coordinate_domain
    - provenance

entity Coordinate:
  type: PositionTuple
  belongs_to: CoordinateSystem
  composed_of: CoordinateValue

entity CoordinateValue:
  type: NumericOrOrdinalSpatialValue
  associated_with: CoordinateAxis
  expressed_in: Unit

entity CoordinateAxis:
  type: SpatialAxis
  properties:
    - axis_name
    - axis_direction
    - axis_unit
    - axis_order

entity Origin:
  type: ReferencePoint
  defines: CoordinateSystemZeroReference

entity Dimension:
  type: StructuralProperty
  represents: NumberOfIndependentCoordinateAxes

entity Unit:
  type: MeasurementUnit
  applies_to: CoordinateAxis

entity Datum:
  type: ReferenceDefinition
  anchors: CoordinateSystem

entity Projection:
  type: SpatialTransformationModel
  maps:
    - source_surface
    - coordinate_plane

# ---------- COORDINATE SYSTEM TYPES ----------
coordinate_system_types:
  - CartesianCoordinateSystem
  - GeographicCoordinateSystem
  - ProjectedCoordinateSystem
  - PolarCoordinateSystem
  - CylindricalCoordinateSystem
  - SphericalCoordinateSystem
  - VerticalCoordinateSystem
  - LocalCoordinateSystem

entity CartesianCoordinateSystem:
  subtype_of: CoordinateSystem
  axes:
    - x
    - y
    - optional_z

entity GeographicCoordinateSystem:
  subtype_of: CoordinateSystem
  typical_axes:
    - latitude
    - longitude
    - optional_ellipsoidal_height

entity ProjectedCoordinateSystem:
  subtype_of: CoordinateSystem
  derived_from: GeographicCoordinateSystem
  uses: Projection

entity PolarCoordinateSystem:
  subtype_of: CoordinateSystem
  typical_components:
    - radial_distance
    - angle

entity SphericalCoordinateSystem:
  subtype_of: CoordinateSystem
  typical_components:
    - radial_distance
    - angular_coordinate_1
    - angular_coordinate_2

# ---------- RELATIONSHIPS ----------
relationships:
  CoordinateSystem -> DEFINES -> CoordinateAxis
  CoordinateSystem -> HAS_DIMENSION -> Dimension
  CoordinateSystem -> MAY_HAVE_ORIGIN -> Origin
  CoordinateSystem -> MAY_USE -> Datum
  CoordinateSystem -> MAY_USE -> Projection
  Coordinate -> EXPRESSED_IN -> CoordinateSystem
  Coordinate -> HAS_COMPONENT -> CoordinateValue
  CoordinateValue -> CORRESPONDS_TO -> CoordinateAxis
  CoordinateAxis -> USES -> Unit
  ProjectedCoordinateSystem -> DERIVED_FROM -> GeographicCoordinateSystem
  Projection -> TRANSFORMS -> SpatialRepresentation
  CoordinateSystem -> MAY_HAVE_IDENTIFIER -> Identifier
  CoordinateSystem -> MAY_REFERENCE -> Provenance

# ---------- DIMENSION RULES ----------
rule dimension_consistency:
  number_of_coordinate_components SHOULD equal CoordinateSystem.dimension
  unless optional dimensions are explicitly supported

rule axis_uniqueness:
  each CoordinateAxis within CoordinateSystem MUST have a distinct semantic role

rule axis_order:
  coordinate values MUST be interpreted according_to declared axis order

# ---------- AXIS RULES ----------
rule axis_definition:
  each axis SHOULD declare:
    - name
    - direction
    - unit
    - order

rule axis_direction:
  axis direction MUST be semantically compatible with CoordinateSystem type

rule axis_unit:
  coordinate value MUST use axis-compatible unit
  OR be transformed to compatible unit before comparison

# ---------- ORIGIN AND ORIENTATION ----------
rule origin:
  IF CoordinateSystem depends on explicit Origin
  THEN Origin MUST be available for deterministic position interpretation

rule orientation:
  IF orientation affects coordinate interpretation
  THEN orientation MUST be declared

rule handedness:
  IF CoordinateSystem is directional Cartesian 3D
  THEN handedness SHOULD be declared where ambiguity is possible

# ---------- DATUM ----------
rule datum_requirement:
  IF CoordinateSystem represents Earth-referenced coordinates
  AND datum materially affects position
  THEN Datum MUST be explicit or unambiguously implied by declared reference system

rule datum_difference:
  coordinates using different datums MUST NOT be assumed spatially identical

# ---------- PROJECTION ----------
rule projection:
  IF CoordinateSystem.type = ProjectedCoordinateSystem
  THEN Projection MUST be defined

rule projection_source:
  ProjectedCoordinateSystem SHOULD reference source GeographicCoordinateSystem

rule projection_distortion:
  projection MAY introduce:
    - distance_distortion
    - area_distortion
    - angle_distortion
    - shape_distortion
  therefore projected measurements MUST be interpreted in projection context

# ---------- COORDINATE TRANSFORMATION ----------
operation transform_coordinate(source_coordinate, target_system):
  require:
    - source_coordinate
    - source_coordinate_system
    - target_system
    - valid_transformation_path

  process:
    1. validate source coordinate
    2. resolve source axes and units
    3. resolve datum if required
    4. resolve projection if required
    5. transform into target reference
    6. validate target coordinate

  preserve:
    - source_coordinate
    - source_coordinate_system
    - transformation_method
    - transformation_parameters
    - provenance

  output:
    - transformed_coordinate
    - target_coordinate_system
    - confidence

# ---------- COMPATIBILITY ----------
rule direct_comparison:
  coordinates MAY be directly compared
  ONLY IF coordinate systems are semantically compatible

rule conversion:
  IF units differ but axes and reference semantics are compatible
  THEN convert units before comparison

rule transformation_required:
  IF coordinate systems differ in datum, projection, origin, orientation, or axis semantics
  THEN explicit transformation MAY be required

# ---------- VALIDATION ----------
validation:
  require:
    - identifiable_coordinate_system
    - defined_dimensions
    - interpretable_axes

  validate_if_present:
    - axis_order
    - units
    - origin
    - datum
    - projection
    - orientation
    - handedness
    - identifier

  reject:
    - coordinate_dimension_mismatch
    - undefined_axis_semantics
    - incompatible_axis_unit
    - missing_required_projection
    - unresolved_reference_context
    - invalid_direct_coordinate_comparison

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE:
  "coordinate system" ~= "coordinate framework" WHEN defining positional axes
  "coordinate axis" ~= "axis" WHEN context = coordinate_system
  "coordinate tuple" ~= "coordinate" WHEN tuple represents one spatial position
  "projected coordinate system" ~= "projected CRS component" ONLY WHEN reference semantics match
  "geographic coordinate system" ~= "geodetic coordinate system" WHEN geodetic semantics apply

  PRESERVE distinctions:
    coordinate_system != coordinate_reference_system
    coordinate_system != datum
    coordinate_system != projection
    coordinate != coordinate_system
    axis_order != axis_direction
    unit_conversion != coordinate_transformation

# ---------- CONFIDENCE ----------
CONFIDENCE:
  explicit_coordinate_system:
    score: 1.00

  explicit_axis_definition:
    score: 1.00

  explicit_reference_identifier:
    score: 1.00

  validated_coordinate_transformation:
    score: 0.95

  inferred_axis_order:
    score: 0.75

  inferred_coordinate_system:
    score: 0.70

  ambiguous_reference_context:
    score: <= 0.60
    action: preserve uncertainty

# ---------- UPDATE MODEL ----------
UPDATE_MODEL:
  on_axis_change:
    - preserve previous axis definition
    - update coordinate interpretation rules
    - revalidate stored coordinates
    - update provenance

  on_unit_change:
    - preserve original units
    - transform values where valid
    - revalidate coordinates
    - record conversion provenance

  on_datum_change:
    - preserve original datum
    - require valid transformation
    - transform affected coordinates
    - revalidate spatial relationships
    - update provenance

  on_projection_change:
    - preserve original projection
    - recalculate projected coordinates where required
    - preserve source geographic coordinates
    - update provenance

# ---------- FLOW HASH ----------
FLOW_HASH:
  inputs:
    - ontology
    - coordinate_system_entities
    - relationships
    - dimension_rules
    - axis_rules
    - transformation_rules
    - validation
    - semantic_equivalence
    - confidence
    - update_model

  canonicalisation:
    - normalise_whitespace
    - preserve_case_sensitive_identifiers
    - sort_unordered_property_sets
    - preserve_rule_order

  output:
    deterministic_semantic_hash

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION:
  interpret_as:
    - coordinate ontology
    - spatial reference model
    - coordinate validation model
    - transformation reasoning structure

  operations:
    - identify coordinate systems
    - interpret coordinate tuples
    - resolve axes
    - resolve units
    - validate dimensions
    - determine coordinate compatibility
    - transform coordinates
    - distinguish datum and projection semantics
    - preserve provenance
    - expose uncertainty

  constraints:
    - do_not_assume_axis_order_without evidence
    - do_not_assume_units_without evidence
    - do_not_assume_datum_without evidence
    - do_not_compare_incompatible_coordinates directly
    - do_not_discard_original_coordinates_after transformation
    - preserve coordinate-system semantics

# ---------- QUERY MODEL ----------
query:
  input:
    - coordinate
    - coordinate_system
    - axis
    - unit
    - datum
    - projection
    - target_coordinate_system

  resolve:
    1. identify CoordinateSystem
    2. resolve dimensions
    3. resolve axes and axis order
    4. resolve units
    5. resolve origin and orientation
    6. resolve datum where applicable
    7. resolve projection where applicable
    8. determine transformation requirements
    9. validate result

  output:
    - interpreted_coordinate
    - coordinate_system
    - reference_context
    - compatibility_state
    - transformation_path
    - confidence
    - provenance

# ---------- INFERENCE ----------
inference:
  IF coordinate has explicit system identifier
  THEN resolve CoordinateSystem
  WITH confidence = 1.00

  IF axes, units, datum, and projection uniquely identify system
  THEN infer CoordinateSystem
  WITH confidence >= 0.90

  IF source and target systems differ only by compatible units
  THEN infer unit_conversion_required

  IF source and target systems differ in spatial reference semantics
  THEN infer coordinate_transformation_required

  IF reference context remains ambiguous
  THEN do_not_force_coordinate_system_resolution
  AND preserve candidate interpretations

# ---------- OUTPUT CONTRACT ----------
output:
  ontology_entity: CoordinateSystem
  coordinate_structure: machine_interpretable
  dimensions: explicit
  axes: explicit
  units: explicit
  spatial_reference_context: preserved
  transformations: traceable
  provenance: preserved
  uncertainty: explicit
  semantic_retrieval: enabled

end flow