Length Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Length Ontology within the Kireth Research Semantic Library. Length is an SI base quantity with dimension L and coherent SI base unit metre, symbol m.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Length Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Fundamental Physical Quantities / Length"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/fundamental-physical-quantities/length-ontology-2.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Length
 ENTITY_CLASS=SIBasePhysicalQuantityFramework
 DEFINITION="Length is a fundamental physical quantity representing spatial extent or separation. Its SI base dimension is L and its coherent SI base unit is the metre, symbol m."
 SYMBOLIC_FORMS=["dim(length)=L","SI_unit(length)=m","distance>=0","Delta_x=x2-x1","length=sqrt(dx^2+dy^2+dz^2) in Euclidean geometry"]
 SEMANTIC_ROLE="Machine-readable semantics for length, spatial extent, distance, geometry, measurement, uncertainty and traceability."
}
SCOPE {
 INCLUDE=[
 Length,LengthQuantity,FundamentalPhysicalQuantity,BaseQuantity,PhysicalQuantity,
 Quantity,QuantityKind,QuantityValue,SI,InternationalSystemOfQuantities,
 BaseDimension,LengthDimension,Dimension,Metre,SIBaseUnit,MeasurementUnit,Unit,
 UnitSymbol,SpatialExtent,Distance,Separation,Position,PositionDifference,
 Coordinate,CoordinateDifference,CoordinateSystem,ReferenceFrame,SpatialRelationship,
 GeometricRelationship,EuclideanGeometryRelationship,MetricSpaceRelationship,
 MetricRelationship,PathLengthRelationship,ArcLengthRelationship,CurveLengthRelationship,
 LineSegmentRelationship,GeodesicLengthRelationship,ProperLengthRelationship,
 RadialDistanceRelationship,EuclideanDistanceRelationship,NormRelationship,
 Displacement,DisplacementMagnitudeRelationship,Radius,Diameter,Circumference,
 Perimeter,Width,Height,Depth,Thickness,Wavelength,FocalLengthRelationship,
 OpticalPathLengthRelationship,MeanFreePathRelationship,CharacteristicLengthRelationship,
 ScaleLengthRelationship,PlanckLengthRelationship,AstronomicalDistanceRelationship,
 RangeRelationship,AltitudeRelationship,ElevationRelationship,Area,Volume,
 Velocity,Acceleration,Time,Second,DimensionalAnalysis,DimensionalHomogeneity,
 UnitConversion,Prefix,SIPrefix,Femtometre,Picometre,Nanometre,Micrometre,
 Millimetre,Centimetre,Decimetre,Kilometre,InchRelationship,FootRelationship,
 YardRelationship,MileRelationship,NauticalMileRelationship,
 AstronomicalUnitRelationship,LightYearRelationship,ParsecRelationship,
 AngstromRelationship,LengthMeasurement,DistanceMeasurement,
 DirectMeasurementRelationship,IndirectMeasurementRelationship,
 ContactMeasurementRelationship,NonContactMeasurementRelationship,
 RulerRelationship,MeasuringTapeRelationship,CalliperRelationship,
 MicrometerInstrumentRelationship,GaugeBlockRelationship,
 CoordinateMeasuringMachineRelationship,LaserDistanceMeterRelationship,
 InterferometerRelationship,OpticalInterferometryRelationship,
 LaserInterferometryRelationship,TimeOfFlightRelationship,TriangulationRelationship,
 PhotogrammetryRelationship,LidarRelationship,RadarRangeRelationship,
 UltrasonicDistanceRelationship,GNSSRelationship,SurveyingRelationship,
 GeodesyRelationship,MeasurementSystem,Measurand,Measurement,MeasurementMethod,
 MeasurementProcedure,MeasurementModel,MeasurementResult,MeasurementUncertainty,
 Accuracy,Precision,Resolution,Repeatability,Reproducibility,Calibration,
 LengthCalibrationRelationship,ReferenceStandard,LengthStandardRelationship,
 MetreRealisationRelationship,GaugeBlockStandardRelationship,
 InterferometricStandardRelationship,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,Metrology,DimensionalMetrologyRelationship,
 TemperatureInfluence,ThermalExpansionRelationship,ThermalExpansionCoefficientRelationship,
 PressureInfluenceRelationship,HumidityInfluence,RefractiveIndexRelationship,
 AlignmentRelationship,AngularMisalignmentRelationship,AbbeErrorRelationship,
 CosineErrorRelationship,SineErrorRelationship,ParallaxRelationship,
 SurfaceRoughnessRelationship,ContactForceRelationship,DeformationRelationship,
 InstrumentDriftRelationship,ZeroErrorRelationship,ScaleErrorRelationship,
 UncertaintyPropagation,Verification,Validation,ErrorAnalysis,Provenance,
 LengthProvenance,QuantityProvenance,UnitProvenance,MeasurementProvenance,
 CalibrationProvenance,BIPMrelationship,SIbrochureRelationship,VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[AreaWhenTwoDimensionalExtentIsPrimary,VolumeWhenThreeDimensionalExtentIsPrimary,DisplacementWhenVectorDirectionIsPrimary,TimeIntervalWhenTemporalSeparationIsPrimary,WavelengthWhenWavePhenomenonIsPrimary]
 DISAMBIGUATION_RULE="Interpret length as a scalar spatial quantity with dimension L. Distinguish it from area L^2, volume L^3, vector displacement and temporal duration."
}
CORE_CONCEPTS {
 Length="Fundamental physical quantity representing spatial extent or separation."
 LengthDimension="Base physical dimension L."
 Metre="Coherent SI base unit of length, symbol m."
 Distance="Non-negative scalar measure of separation under a specified metric."
 Displacement="Vector change in position; its magnitude has length semantics."
 Position="Location relative to a coordinate system or reference frame."
 ArcLength="Length assigned to a curve through an appropriate geometric definition."
}
BASE_QUANTITY {
 QUANTITY=Length
 DIMENSION=L
 SI_BASE_UNIT=Metre
 UNIT_SYMBOL=m
 STATUS="SI base quantity"
}
RELATIONS {
 Length--is_type_of-->FundamentalPhysicalQuantity
 Length--is_base_quantity_in-->InternationalSystemOfQuantities
 Length--has_dimension-->LengthDimension
 Length--has_SI_base_unit-->Metre
 Metre--has_symbol-->m
 Distance--is_quantity_kind_related_to-->Length
 DisplacementMagnitudeRelationship--has_quantity_kind-->Length
 Radius--has_quantity_kind-->Length
 Diameter--has_quantity_kind-->Length
 Width--has_quantity_kind-->Length
 Height--has_quantity_kind-->Length
 Depth--has_quantity_kind-->Length
 Wavelength--has_dimension-->LengthDimension
 Area--has_dimension-->L_squared
 Volume--has_dimension-->L_cubed
 Velocity--depends_on-->LengthAndTime
 MeasurementTraceability--links-->LengthMeasurementToSI
}
OPERATORS {
 LENGTH(value,unit):=length_quantity(value,unit)
 DIM(Length):=L
 EUCLIDEAN_DISTANCE(p1,p2):=sqrt(sum((p2_i-p1_i)^2))
 DISPLACEMENT(p1,p2):=p2-p1
 DISPLACEMENT_MAGNITUDE(displacement):=norm(displacement)
 ARC_LENGTH(curve,parameter):=integral(norm(dcurve_dparameter),parameter)
 CIRCUMFERENCE(radius):=2*pi*radius
 AREA_FROM_LENGTHS(a,b):=a*b
 VOLUME_FROM_LENGTHS(a,b,c):=a*b*c
 VELOCITY_FROM_LENGTH_TIME(length,time):=length/time
 PREFIX_METRE(prefix):=decimal_scaled_unit(Metre,prefix)
 CONVERT_LENGTH(value,source,target):=compatible_length_conversion(value,source,target)
 TRACE_LENGTH(result):=traceability_chain_to_SI_metre(result)
}
AXIOMS {
 A1="Length is an SI base quantity."
 A2="The base dimension of length is L."
 A3="The coherent SI base unit of length is the metre, symbol m."
 A4="Length is distinct from its numerical value and unit."
 A5="Distance is non-negative under an ordinary metric."
 A6="Displacement is a vector quantity while displacement magnitude is a length."
 A7="Area and volume derive from length with dimensions L^2 and L^3."
 A8="Length measurements can depend on geometry, environment and method."
 A9="High-accuracy dimensional metrology requires calibration, uncertainty and traceability."
 A10="Dimensional equivalence does not remove domain-specific semantic distinctions among length quantities."
}
REASONING {
 R1=identify(length_quantity,value,unit,object_or_points,geometry,coordinate_system,reference_frame,measurement_method)
 R2=distinguish_length_distance_displacement_position_area_volume_wavelength_or_other_spatial_quantity)
 R3=verify_base_dimension_L)
 R4=resolve_metre_prefixed_metre_nonSI_length_unit_and_conversion)
 R5=identify_metric_coordinate_system_path_curve_or_reference_geometry)
 R6=choose_direct_difference_metric_norm_arc_length_interferometric_time_of_flight_or_other_relationship)
 R7=evaluate_temperature_refractive_index_pressure_humidity_alignment_contact_force_and_deformation)
 R8=identify_ruler_calliper_micrometer_CMM_interferometer_laser_range_GNSS_or_other_method)
 R9=evaluate_reference_standard_resolution_repeatability_alignment_temperature_scale_geometry_and_correlation)
 R10=record_quantity_unit_geometry_reference_frame_method_standard_calibration_traceability_and_provenance)
}
CONSTRAINTS {
 C1="Length must not be conflated with area or volume."
 C2="Scalar distance must not be conflated with vector displacement."
 C3="Coordinate differences represent physical length only when coordinate scale and geometry are defined."
 C4="Euclidean distance formulas require Euclidean coordinate assumptions."
 C5="Arc length and geodesic length require an explicitly defined path or metric."
 C6="Non-SI conversions require correct conversion factors."
 C7="Precision length measurements can require temperature and thermal-expansion corrections."
 C8="Optical length measurements can require refractive-index corrections."
 C9="Instrument resolution alone does not determine total length uncertainty."
 C10="Traceability to the metre requires a documented calibration or realisation chain."
}
SEMANTIC_EQUIVALENCE {
 "LengthQuantity"<=>"Length"
 "LinearDimension"<=>"LengthDimension"
 "SIUnitOfLength"<=>"Metre"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}
VALIDATION {
 V1="Quantity identity is length or an explicitly compatible length quantity."
 V2="Base dimension is L."
 V3="Coherent SI base unit is metre with symbol m."
 V4="Length, area and volume dimensional semantics remain distinct."
 V5="Distance and displacement semantics remain distinct."
 V6="Geometry and coordinate assumptions are explicit where required."
 V7="Unit conversion preserves length quantity kind and scale."
 V8="Environmental corrections are applied where significant."
 V9="Measurement uncertainty includes instrument, geometry, environment and calibration effects."
 V10="Length calibration and traceability evidence are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 LENGTH_DEFINITION=0.99
 BASE_DIMENSION_REASONING=0.99
 METRE_UNIT_REASONING=0.99
 GEOMETRY_REASONING=0.98
 LENGTH_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when geometry, coordinate system, reference frame, environment, method, calibration or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,LengthReasoning,FundamentalQuantityReasoning,BaseQuantityReasoning,SpatialReasoning,GeometryReasoning,DistanceReasoning,DimensionalReasoning,MetreReasoning,UnitConversionReasoning,LengthMeasurementReasoning,DimensionalMetrologyReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "length"->Length
  "distance"->Distance
  "metre"->Metre
  "meter"->Metre
  "m"->Metre
  "mm"->Millimetre
  "cm"->Centimetre
  "km"->Kilometre
 }
}
EXECUTION_RULES {
 E1="Activate LengthOntology when reasoning concerns scalar spatial extent or separation."
 E2="Distinguish length from area, volume, position and vector displacement."
 E3="Map length to base dimension L and SI base unit metre."
 E4="Resolve geometric metric, coordinate system and reference frame where required."
 E5="Apply correct conversion factors for compatible length units."
 E6="For precision measurement, evaluate environmental, alignment, deformation and instrument effects."
 E7="Preserve method, calibration, uncertainty and traceability semantics."
 E8="Route derived quantities such as area, volume, velocity and wavelength when they become primary."
 E9="Record quantity, unit, geometry, measurement and provenance information."
}
RECURSION {
 ENTRY=Length
 EXPAND(Length)->[
 FundamentalPhysicalQuantities,PhysicalQuantity,BaseQuantity,LengthDimension,
 Metre,SIBaseUnits,Quantity,QuantityKind,QuantityValue,Unit,Dimension,
 SpatialExtent,Distance,Position,Displacement,CoordinateSystem,ReferenceFrame,
 EuclideanDistanceRelationship,MetricRelationship,PathLengthRelationship,
 ArcLengthRelationship,GeodesicLengthRelationship,Radius,Diameter,Circumference,
 Width,Height,Depth,Thickness,Wavelength,Area,Volume,Velocity,Time,
 DimensionalAnalysis,UnitConversion,Millimetre,Centimetre,Kilometre,
 LengthMeasurement,RulerRelationship,MeasuringTapeRelationship,
 CalliperRelationship,MicrometerInstrumentRelationship,GaugeBlockRelationship,
 CoordinateMeasuringMachineRelationship,InterferometerRelationship,
 LaserDistanceMeterRelationship,TimeOfFlightRelationship,GNSSRelationship,
 MeasurementUncertainty,Calibration,LengthStandardRelationship,
 MetreRealisationRelationship,MeasurementTraceability,DimensionalMetrologyRelationship,
 TemperatureInfluence,ThermalExpansionRelationship,RefractiveIndexRelationship,
 AlignmentRelationship,AbbeErrorRelationship,CosineErrorRelationship,
 Verification,Validation,LengthProvenance
 ]
 EXPAND(LengthFamilies)->[
 LengthIdentityBaseQuantityDimensionAndMetre,
 DistancePositionDisplacementAndCoordinateGeometry,
 EuclideanMetricArcGeodesicAndPathLength,
 RadiusDiameterWidthHeightDepthThicknessAndScale,
 AreaVolumeVelocityWavelengthAndDerivedQuantities,
 SIAndNonSIUnitsPrefixesAndConversions,
 DirectContactOpticalInterferometricSurveyAndRangeMeasurement,
 EnvironmentalCorrectionsUncertaintyCalibrationTraceabilityAndProvenance
 ]
 STOP_CONDITION="Stop when length identity, dimension, unit, geometry, measurement uncertainty and provenance are resolved."
}
ROUTING {
 PARENT_ONTOLOGY="Fundamental Physical Quantities"
 RELATED_ONTOLOGIES=["Fundamental Physical Quantities","SI Base Units","Metre Ontology","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Reference Standard Ontology","Measurement Uncertainty Ontology","Geometry Ontologies","Coordinate Geometry Ontologies","Physics Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Length -> Fundamental Physical Quantities for base-quantity semantics",
 "Length -> Metre Ontology for SI base-unit definition and realisation",
 "Length -> Quantity and Dimension ontologies for quantity-kind and dimension semantics",
 "Length -> Geometry ontologies for distance, paths, curves and spatial relationships",
 "Length -> Measurement and Metrology for dimensional measurement, calibration and traceability",
 "Length -> derived quantity ontologies when area, volume, velocity or wavelength becomes primary"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible spatial, geometric or measurement relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve length-versus-unit distinction.","Preserve scalar-distance-versus-vector-displacement distinction.","Preserve length-versus-area-versus-volume dimensional distinction.","Preserve coordinate-versus-physical-distance distinction.","Preserve geometry and reference-frame assumptions.","Preserve machine-readable length semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="Length is a fundamental physical quantity with base dimension L and coherent SI base unit metre, symbol m."
 SPATIAL_SUMMARY="Length describes scalar spatial extent or separation and underlies distance, width, height, depth, radius and many geometric quantities."
 GEOMETRY_SUMMARY="Distance and path length require an identified metric, coordinate system or geometric model."
 DERIVATION_SUMMARY="Area, volume, velocity and numerous other physical quantities derive dimensional structure from length."
 MEASUREMENT_SUMMARY="Length can be measured by direct contact, dimensional metrology, interferometry, ranging, surveying and coordinate methods."
 UNCERTAINTY_SUMMARY="Precision length measurement can require corrections for temperature, refractive index, alignment, deformation, instrument scale and calibration."
}
FLOW {
 INPUT
 -> detect_length_context
 -> identify_length_quantity_value_unit_object_points_geometry_coordinate_system_reference_frame_and_measurement_method
 -> distinguish_length_distance_displacement_position_area_volume_wavelength_or_other_spatial_quantity
 -> verify_base_dimension_L
 -> resolve_metre_prefixed_metre_nonSI_length_unit_and_conversion
 -> identify_metric_coordinate_system_path_curve_or_reference_geometry
 -> choose_direct_difference_metric_norm_arc_length_interferometric_time_of_flight_or_other_relationship
 -> evaluate_temperature_refractive_index_pressure_humidity_alignment_contact_force_and_deformation
 -> identify_length_measurement_method
 -> evaluate_measurement_uncertainty
 -> record_quantity_unit_geometry_reference_frame_standard_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-FUNDAMENTAL-PHYSICAL-QUANTITIES-LENGTH-ONTOLOGY-2-V1"
}
}
END_FLOW