Distance Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Distance Ontology within the Kireth Research Semantic Library. Distance is a scalar spatial quantity describing separation under a specified metric or measurement model. Its physical dimension is length L and its coherent SI unit is the metre, symbol m.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Distance Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Mechanical Measurements / Distance"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/distance-ontology-2.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Distance
 ENTITY_CLASS=MechanicalSpatialMeasurementQuantityFramework
 DEFINITION="Distance is a scalar quantity representing spatial separation between specified positions, points, objects or regions according to a defined metric, path or measurement model."
 SYMBOLIC_FORMS=["dim(distance)=L","SI_unit(distance)=m","d>=0","d_E=sqrt(sum((x_i-y_i)^2))","path_distance=integral(ds)"]
 SEMANTIC_ROLE="Machine-readable semantics for distance, separation, metrics, paths, ranging, geometry, measurement, uncertainty and traceability."
}
SCOPE {
 INCLUDE=[
 Distance,Length,LengthDimension,PhysicalQuantity,Quantity,QuantityKind,QuantityValue,
 MechanicalMeasurement,SeparationRelationship,Position,Coordinate,CoordinateSystem,
 ReferenceFrame,MetricRelationship,MetricSpaceRelationship,EuclideanDistanceRelationship,
 ManhattanDistanceRelationship,MinkowskiDistanceRelationship,GeodesicDistanceRelationship,
 GreatCircleDistanceRelationship,SurfaceDistanceRelationship,StraightLineDistanceRelationship,
 LineOfSightDistanceRelationship,PathDistanceRelationship,PathLengthRelationship,
 ArcLengthRelationship,TravelDistanceRelationship,RouteDistanceRelationship,
 NetworkDistanceRelationship,ShortestPathRelationship,MinimumDistanceRelationship,
 RangeRelationship,SlantRangeRelationship,HorizontalDistanceRelationship,
 VerticalDistanceRelationship,DepthRelationship,BaselineRelationship,Displacement,
 DisplacementMagnitudeRelationship,PositionDifferenceRelationship,NormRelationship,
 GeometryRelationship,EuclideanGeometryRelationship,NonEuclideanGeometryRelationship,
 CoordinateGeometryRelationship,GeodesyRelationship,EarthModelRelationship,
 ReferenceEllipsoidRelationship,GeoidRelationship,DatumRelationship,
 GeodeticDatumRelationship,LatitudeRelationship,LongitudeRelationship,
 ElevationRelationship,MapProjectionRelationship,ScaleFactorRelationship,
 Metre,SIBaseUnit,MeasurementUnit,Unit,UnitSymbol,SIPrefix,Millimetre,
 Centimetre,Kilometre,Micrometre,Nanometre,InchRelationship,FootRelationship,
 YardRelationship,MileRelationship,NauticalMileRelationship,
 AstronomicalUnitRelationship,LightYearRelationship,ParsecRelationship,
 UnitConversion,DistanceMeasurement,DirectDistanceMeasurementRelationship,
 IndirectDistanceMeasurementRelationship,ContactMeasurementRelationship,
 NonContactMeasurementRelationship,RulerRelationship,MeasuringTapeRelationship,
 CalliperRelationship,SurveyingRelationship,TotalStationRelationship,
 ElectronicDistanceMeasurementRelationship,LaserDistanceMeterRelationship,
 LaserRangefinderRelationship,LidarRelationship,RadarRangeRelationship,
 SonarRelationship,UltrasonicDistanceRelationship,TimeOfFlightRelationship,
 PhaseShiftRelationship,InterferometryRelationship,LaserInterferometryRelationship,
 TriangulationRelationship,TrilaterationRelationship,PhotogrammetryRelationship,
 GNSSRelationship,GPSRelationship,SatelliteRangingRelationship,
 PseudorangeRelationship,CarrierPhaseRelationship,WheelOdometerRelationship,
 DeadReckoningRelationship,MeasurementSystem,Measurand,Measurement,
 MeasurementMethod,MeasurementProcedure,MeasurementModel,MeasurementEquation,
 MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,
 Repeatability,Reproducibility,Sensitivity,Linearity,Calibration,
 DistanceCalibrationRelationship,LengthCalibrationRelationship,
 RangeCalibrationRelationship,ReferenceStandard,LengthStandardRelationship,
 DistanceStandardRelationship,GaugeBlockRelationship,InterferometricStandardRelationship,
 ReferenceBaselineRelationship,MeasurementTraceability,MetrologicalTraceability,
 TraceabilityChain,Metrology,DimensionalMetrologyRelationship,
 GeodeticMetrologyRelationship,TemperatureInfluence,PressureInfluenceRelationship,
 HumidityInfluence,RefractiveIndexRelationship,AtmosphericRefractionRelationship,
 PropagationSpeedRelationship,SpeedOfLightRelationship,SpeedOfSoundRelationship,
 AlignmentRelationship,AngularErrorRelationship,CosineErrorRelationship,
 AbbeErrorRelationship,ParallaxRelationship,InstrumentOffsetRelationship,
 ZeroErrorRelationship,ScaleErrorRelationship,TargetReflectivityRelationship,
 MultipathRelationship,SignalDelayRelationship,ClockErrorRelationship,
 AtmosphericDelayRelationship,IonosphericDelayRelationship,TroposphericDelayRelationship,
 EarthCurvatureRelationship,ProjectionErrorRelationship,DatumTransformationRelationship,
 UncertaintyPropagation,Verification,Validation,GeometryValidationRelationship,
 CoordinateValidationRelationship,DistanceValidationRelationship,ConversionValidation,
 ErrorAnalysis,Provenance,DistanceProvenance,MeasurementProvenance,
 CalibrationProvenance,GeometryProvenanceRelationship,ReferenceFrameProvenanceRelationship
 ]
 EXCLUDE_AS_PRIMARY=[DisplacementWhenVectorDirectionIsPrimary,PositionWhenLocationIsPrimary,TravelTimeWhenTemporalDurationIsPrimary,SimilarityDistanceWhenAbstractMetricIsPrimary]
 DISAMBIGUATION_RULE="Interpret physical distance as scalar spatial separation with dimension L under a specified metric, path, coordinate system or measurement model. Distinguish it from vector displacement, absolute position and abstract similarity metrics."
}
CORE_CONCEPTS {
 Distance="Scalar spatial separation between specified entities under a defined metric or path model."
 EuclideanDistanceRelationship="Straight-line metric distance between points in Euclidean space."
 PathDistanceRelationship="Distance measured along a specified path or curve."
 GeodesicDistanceRelationship="Distance according to a specified geometry or surface metric."
 RangeRelationship="Distance from an observer, instrument or origin to a target."
 Displacement="Vector change in position; its magnitude can equal straight-line distance under appropriate geometry."
 DistanceMeasurement="Measurement process assigning a distance value to a measurand."
}
QUANTITY_MODEL {
 QUANTITY=Distance
 DIMENSION=L
 COHERENT_SI_UNIT=Metre
 UNIT_SYMBOL=m
 SCALAR_STATUS="scalar"
 SIGN_RULE="ordinary metric distance is non-negative"
}
RELATIONS {
 Distance--is_quantity_kind_related_to-->Length
 Distance--has_dimension-->LengthDimension
 Distance--has_coherent_SI_unit-->Metre
 Distance--depends_on-->SpecifiedEntitiesAndMetric
 EuclideanDistanceRelationship--depends_on-->CoordinateDifferences
 PathDistanceRelationship--depends_on-->SpecifiedPath
 GeodesicDistanceRelationship--depends_on-->GeometryOrMetric
 DisplacementMagnitudeRelationship--has_quantity_kind-->Length
 RangeRelationship--is_type_of-->Distance
 DistanceMeasurement--targets-->DistanceMeasurand
 MeasurementTraceability--links-->DistanceMeasurementToSI
}
OPERATORS {
 DISTANCE(value,unit):=distance_quantity(value,unit)
 DIM(Distance):=L
 EUCLIDEAN_DISTANCE(p,q):=sqrt(sum((q_i-p_i)^2))
 MANHATTAN_DISTANCE(p,q):=sum(abs(q_i-p_i))
 MINKOWSKI_DISTANCE(p,q,r):=(sum(abs(q_i-p_i)^r))^(1/r)
 DISPLACEMENT(p,q):=q-p
 DISPLACEMENT_MAGNITUDE(p,q):=norm(q-p)
 PATH_DISTANCE(curve,t):=integral(norm(dcurve_dt),t)
 TIME_OF_FLIGHT_DISTANCE(speed,round_trip_time):=speed*round_trip_time/2
 ONE_WAY_PROPAGATION_DISTANCE(speed,time):=speed*time
 CONVERT_DISTANCE(value,source,target):=compatible_length_conversion(value,source,target)
 TRACE_DISTANCE(result):=traceability_chain_to_SI_metre(result)
}
AXIOMS {
 A1="Physical distance has length dimension L."
 A2="The coherent SI unit of physical distance is the metre, symbol m."
 A3="Ordinary metric distance is non-negative."
 A4="Distance between identical points is zero under a metric."
 A5="Distance is scalar and must be distinguished from vector displacement."
 A6="A distance value requires sufficient specification of endpoints, path, metric, geometry or measurement model."
 A7="Straight-line Euclidean distance and path distance are not generally identical."
 A8="Geodetic distance depends on the adopted Earth model, datum and computational method."
 A9="Propagation-based ranging depends on signal speed, timing model and environmental conditions."
 A10="High-accuracy distance measurement requires calibration, uncertainty and traceability."
}
REASONING {
 R1=identify(distance_value,unit,endpoints,path,metric,coordinate_system,reference_frame,measurement_method)
 R2=distinguish_distance_displacement_position_path_length_range_altitude_depth_or_abstract_metric)
 R3=verify_length_dimension_L)
 R4=resolve_metre_prefixed_metre_nonSI_length_unit_and_conversion)
 R5=identify_Euclidean_path_geodesic_network_surface_geodetic_or_propagation_model)
 R6=resolve_coordinate_system_reference_frame_datum_projection_and_geometry)
 R7=select_contact_optical_laser_radar_ultrasonic_GNSS_interferometric_or_survey_method)
 R8=apply_environmental_propagation_alignment_scale_datum_and_instrument_corrections)
 R9=evaluate_resolution_repeatability_geometry_timing_propagation_calibration_and_model_uncertainty)
 R10=record_endpoints_metric_path_geometry_reference_frame_method_calibration_traceability_and_provenance)
}
CONSTRAINTS {
 C1="Distance must not be conflated with displacement."
 C2="Distance must not be conflated with absolute position."
 C3="Euclidean distance formulas require Euclidean-coordinate assumptions."
 C4="Path distance requires the path to be specified or inferable."
 C5="Geodesic and great-circle distances require the applicable surface or Earth model."
 C6="Coordinate differences do not automatically equal physical distance unless coordinate scale and geometry support that interpretation."
 C7="Time-of-flight ranging requires the correct one-way or round-trip propagation model."
 C8="Optical, acoustic and radio ranging can require environmental propagation corrections."
 C9="Instrument resolution alone does not determine total distance uncertainty."
 C10="Traceability to the metre requires a documented calibration or realisation chain."
}
SEMANTIC_EQUIVALENCE {
 "PhysicalDistance"<=>"DistanceInPhysicalContext"
 "Range"<=>"DistanceFromReferenceToTargetInRangingContext"
 "StraightLineDistance"<=>"EuclideanDistanceUnderEuclideanGeometry"
 "SIUnitOfDistance"<=>"Metre"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}
VALIDATION {
 V1="Distance endpoints or measured entities are identified."
 V2="Physical distance has dimension L."
 V3="Coherent SI unit is metre with symbol m."
 V4="Distance and displacement semantics remain distinct."
 V5="Metric, path or geometric assumptions are explicit where required."
 V6="Coordinate system, datum and reference frame are retained where material."
 V7="Propagation-based ranging uses correct signal-speed and timing semantics."
 V8="Unit conversions preserve distance quantity kind and scale."
 V9="Uncertainty includes geometric, environmental, timing, instrument and calibration effects."
 V10="Distance calibration, traceability and provenance are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 DISTANCE_DEFINITION=0.99
 DIMENSION_REASONING=0.99
 GEOMETRY_REASONING=0.98
 GEODETIC_REASONING=0.98
 RANGING_REASONING=0.98
 DISTANCE_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when endpoints, path, metric, coordinate system, reference frame, datum, propagation model, environmental conditions, calibration or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,DistanceReasoning,MechanicalMeasurementReasoning,SpatialReasoning,GeometryReasoning,MetricReasoning,PathReasoning,GeodesicReasoning,RangingReasoning,SurveyingReasoning,GeodeticReasoning,GNSSReasoning,DimensionalReasoning,MetreReasoning,UnitConversionReasoning,DistanceMeasurementReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "distance"->Distance
  "range"->RangeRelationship
  "metre"->Metre
  "meter"->Metre
  "m"->Metre
  "mm"->Millimetre
  "cm"->Centimetre
  "km"->Kilometre
 }
}
EXECUTION_RULES {
 E1="Activate DistanceOntology when reasoning concerns physical spatial separation."
 E2="Identify endpoints, path, metric, geometry and reference system as required."
 E3="Distinguish distance from displacement, position and abstract similarity distance."
 E4="Map physical distance to dimension L and coherent SI unit metre."
 E5="Choose Euclidean, path, geodesic, network, geodetic or ranging model according to context."
 E6="Apply compatible unit conversions and relevant propagation or environmental corrections."
 E7="For measurement, evaluate geometry, alignment, timing, propagation, resolution, calibration and uncertainty."
 E8="Route displacement, position, altitude, depth, path length and abstract metrics when they become primary."
 E9="Record endpoints, metric, geometry, reference frame, method, calibration, uncertainty and provenance."
}
RECURSION {
 ENTRY=Distance
 EXPAND(Distance)->[
 MechanicalMeasurements,Length,LengthDimension,Metre,Position,Coordinate,
 CoordinateSystem,ReferenceFrame,MetricRelationship,MetricSpaceRelationship,
 EuclideanDistanceRelationship,ManhattanDistanceRelationship,MinkowskiDistanceRelationship,
 GeodesicDistanceRelationship,GreatCircleDistanceRelationship,PathDistanceRelationship,
 PathLengthRelationship,ShortestPathRelationship,RangeRelationship,SlantRangeRelationship,
 HorizontalDistanceRelationship,VerticalDistanceRelationship,Displacement,
 DisplacementMagnitudeRelationship,GeometryRelationship,GeodesyRelationship,
 ReferenceEllipsoidRelationship,DatumRelationship,MapProjectionRelationship,
 UnitConversion,DistanceMeasurement,TotalStationRelationship,
 ElectronicDistanceMeasurementRelationship,LaserDistanceMeterRelationship,
 LidarRelationship,RadarRangeRelationship,UltrasonicDistanceRelationship,
 TimeOfFlightRelationship,InterferometryRelationship,TriangulationRelationship,
 PhotogrammetryRelationship,GNSSRelationship,PseudorangeRelationship,
 CarrierPhaseRelationship,MeasurementUncertainty,Calibration,
 DistanceStandardRelationship,ReferenceBaselineRelationship,MeasurementTraceability,
 DimensionalMetrologyRelationship,RefractiveIndexRelationship,AlignmentRelationship,
 CosineErrorRelationship,MultipathRelationship,AtmosphericDelayRelationship,
 Verification,Validation,DistanceProvenance
 ]
 EXPAND(DistanceFamilies)->[
 DistanceIdentityDimensionAndMetre,
 EndpointsCoordinatesReferenceFramesAndMetrics,
 EuclideanNormAndCoordinateDistances,
 PathArcRouteNetworkAndGeodesicDistances,
 GeodeticEarthDatumProjectionAndGreatCircleDistances,
 OpticalLaserRadarUltrasonicAndTimeOfFlightRanging,
 SurveyingGNSSPhotogrammetryAndCoordinateMeasurement,
 CalibrationEnvironmentalCorrectionsUncertaintyTraceabilityAndProvenance
 ]
 STOP_CONDITION="Stop when distance identity, endpoints, metric or path, geometry, unit, measurement uncertainty and provenance are resolved."
}
ROUTING {
 PARENT_ONTOLOGY="Mechanical Measurements"
 RELATED_ONTOLOGIES=["Mechanical Measurements","Fundamental Physical Quantities","Length Ontology 2","Metre Ontology","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Geometry Ontologies","Coordinate Geometry Ontologies","Geodesy Ontology","Reference Standard Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Distance -> Mechanical Measurements for measurement-system semantics",
 "Distance -> Length Ontology 2 for physical length and dimension semantics",
 "Distance -> Metre Ontology for coherent SI-unit semantics",
 "Distance -> Geometry for metrics, paths, coordinates and geodesics",
 "Distance -> Geodesy for Earth models, datums, projections and GNSS distance",
 "Distance -> Measurement and Metrology for calibration, uncertainty and traceability"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible geometric, ranging, geodetic or measurement relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve distance-versus-displacement distinction.","Preserve distance-versus-position distinction.","Preserve metric and path semantics.","Preserve coordinate-system and reference-frame assumptions.","Preserve physical-distance-versus-abstract-distance distinction.","Preserve propagation-model semantics.","Preserve measurement uncertainty and traceability.","Preserve machine-readable distance semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="Distance is a scalar physical quantity describing spatial separation under a specified metric, path or measurement model, with dimension L and coherent SI unit metre."
 GEOMETRY_SUMMARY="Distance can represent straight-line, path, surface, geodesic, network or other metric separation depending on the defined geometry."
 DISPLACEMENT_SUMMARY="Distance is scalar; displacement is vectorial, although displacement magnitude can equal straight-line distance in appropriate geometry."
 RANGING_SUMMARY="Distance can be inferred using optical, laser, radar, ultrasonic, interferometric, surveying, photogrammetric and GNSS methods."
 GEODETIC_SUMMARY="Earth-surface distance requires explicit datum, ellipsoid, projection or geodesic semantics."
 UNCERTAINTY_SUMMARY="Precision distance measurement can require geometric, alignment, timing, propagation, atmospheric, instrument, calibration and reference-frame uncertainty contributions."
}
FLOW {
 INPUT
 -> detect_distance_context
 -> identify_distance_value_unit_endpoints_path_metric_coordinate_system_reference_frame_and_method
 -> distinguish_distance_displacement_position_path_length_range_altitude_depth_or_abstract_metric
 -> verify_length_dimension_L
 -> resolve_metre_prefixed_metre_nonSI_length_unit_and_conversion
 -> identify_Euclidean_path_geodesic_network_surface_geodetic_or_propagation_model
 -> resolve_coordinate_system_reference_frame_datum_projection_and_geometry
 -> select_distance_measurement_method
 -> apply_environmental_propagation_alignment_scale_datum_and_instrument_corrections
 -> evaluate_measurement_uncertainty
 -> record_endpoints_metric_path_geometry_reference_frame_method_calibration_traceability_and_provenance
 -> route_to_related_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}
FLOW_HASH {
 METHOD="semantic-content-identity"
 ID="KIRETH-MATH-MEASUREMENT-UNITS-MECHANICAL-MEASUREMENTS-DISTANCE-ONTOLOGY-2-V1"
}
}
END_FLOW