Lux Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Lux Ontology within the Kireth Research Semantic Library. The lux, symbol lx, is the coherent SI derived unit of illuminance. One lux equals one lumen per square metre: 1 lx = 1 lm m^-2.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME="Lux Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="SI Derived Units / Lux"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-derived-units/lux-ontology.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}

IDENTITY {
 PRIMARY_ENTITY=Lux
 ENTITY_CLASS=SIDerivedUnitOfIlluminanceFramework
 PRIMARY_CONTEXT=SIDerivedUnits
 DEFINITION="The lux, symbol lx, is the coherent SI derived unit of illuminance. One lux equals one lumen per square metre."
 SYMBOLIC_FORMS=["1 lx=1 lm m^-2","1 lx=1 cd sr m^-2","E_v=Phi_v/A","E_v=I_v cos(theta)/r^2 under stated assumptions"]
 SEMANTIC_ROLE="Machine-readable semantics for lux identity, illuminance, luminous flux per area, photometric geometry, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE=[
 Lux,LuxUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,SI,Lumen,Metre,
 Candela,Steradian,Illuminance,PhotometricQuantity,Quantity,QuantityKind,
 IlluminanceDimension,UnitSymbol,LuxDefinition,UnitExpression,UnitAlgebra,
 LuminousFlux,LuminousIntensity,SolidAngle,Area,SurfaceAreaRelationship,
 IncidentLuminousFluxRelationship,FluxPerAreaRelationship,AverageIlluminanceRelationship,
 PointIlluminanceRelationship,HorizontalIlluminanceRelationship,
 VerticalIlluminanceRelationship,CylindricalIlluminanceRelationship,
 Photometry,RadiantFluxRelationship,IrradianceRelationship,RadiometryRelationship,
 SpectralDistributionRelationship,PhotopicVisionRelationship,
 PhotopicLuminousEfficiencyFunction,VLambdaRelationship,HumanVisualResponseRelationship,
 InverseSquareLawRelationship,CosineLawRelationship,IncidenceAngleRelationship,
 DistanceRelationship,SourceGeometryRelationship,PointSourceRelationship,
 ExtendedSourceRelationship,NearFieldRelationship,FarFieldRelationship,
 SurfaceNormalRelationship,OrientationRelationship,LightSourceRelationship,
 LampRelationship,LuminaireRelationship,LEDrelationship,DaylightRelationship,
 SunlightRelationship,SkyLightRelationship,ArtificialLightingRelationship,
 InteriorLightingRelationship,ExteriorLightingRelationship,TaskLightingRelationship,
 EmergencyLightingRelationship,RoadLightingRelationship,LightingDesignRelationship,
 LightingCalculationRelationship,UtilisationFactorRelationship,
 MaintenanceFactorRelationship,ReflectanceRelationship,InterreflectionRelationship,
 UniformityRelationship,MinimumIlluminanceRelationship,AverageIlluminanceRelationship,
 GlareRelationship,DaylightFactorRelationship,LuminousExposureRelationship,
 LuxHourRelationship,IlluminanceMeasurement,LuxMeterRelationship,
 IlluminanceMeterRelationship,PhotometerRelationship,PhotodiodeRelationship,
 DetectorRelationship,PhotopicFilterRelationship,CosineCorrectorRelationship,
 CosineResponseRelationship,SpectralResponsivityRelationship,
 SpectralMismatchRelationship,CosineErrorRelationship,LinearityRelationship,
 DarkSignalRelationship,StrayLightRelationship,Measurement,Measurand,
 MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,
 Repeatability,Reproducibility,Calibration,IlluminanceCalibrationRelationship,
 PhotometricCalibrationRelationship,ReferenceStandard,IlluminanceStandardRelationship,
 StandardLampRelationship,ReferenceLampRelationship,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,Metrology,PhotometricMetrologyRelationship,
 RadiometricMetrologyRelationship,TemperatureInfluence,AmbientLightRelationship,
 BackgroundCorrectionRelationship,StabilisationTimeRelationship,AgeingRelationship,
 SpatialNonuniformityRelationship,AlignmentRelationship,DistanceUncertaintyRelationship,
 SourceStabilityRelationship,SpectralMismatchCorrectionRelationship,
 CosineCorrectionRelationship,SIPrefix,Millilux,MicroluxRelationship,Kilolux,
 MegaluxRelationship,UnitConversion,FootCandleRelationship,Verification,Validation,
 ErrorAnalysis,Provenance,LuxProvenance,SIDerivedUnitProvenance,
 SIUnitProvenance,MeasurementProvenance,CalibrationProvenance,
 BIPMrelationship,SIbrochureRelationship,CIErelationship,VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[
 LumenWhenLuminousFluxIsPrimary,
 CandelaWhenLuminousIntensityIsPrimary,
 IrradianceWhenRadiometricPowerPerAreaIsPrimary,
 LuxAsBrandOrNameRelationship
 ]
 DISAMBIGUATION_RULE="When lux or symbol lx denotes the coherent SI derived unit of illuminance, interpret it as the photometric unit. Distinguish illuminance in lux from luminous flux in lumens, luminous intensity in candelas and irradiance in watts per square metre."
}

CORE_CONCEPTS {
 Lux="Coherent SI derived unit of illuminance, symbol lx, equal to lm m^-2."
 Illuminance="Luminous flux incident on a surface per unit area."
 LuminousFlux="Photometric flux measured in lumens."
 LuminousIntensity="Directional photometric quantity measured in candelas."
 Area="Surface extent over which incident luminous flux is distributed."
 PointIlluminanceRelationship="Illuminance from a point source determined by luminous intensity, distance and incidence angle under appropriate assumptions."
 IlluminanceMeasurement="Measurement process assigning an illuminance value."
}

RELATIONS {
 Lux--is_type_of-->SIDerivedUnit
 Lux--is_coherent_derived_unit_of-->Illuminance
 Lux--has_symbol-->lx
 Lux--has_expression-->lumen_per_square_metre
 Lux--has_equivalent_expression-->candela_steradian_per_square_metre
 Illuminance--relates_to-->IncidentLuminousFluxPerArea
 Illuminance--is_photometric_counterpart_of-->IrradianceRelationship
 Lumen--is_unit_component_of-->Lux
 InverseSquareLawRelationship--relates-->PointSourceIlluminanceAndDistance
 CosineLawRelationship--relates-->IlluminanceAndIncidenceAngle
 LuxMeterRelationship--measures-->Illuminance
 MeasurementTraceability--links-->IlluminanceMeasurementToSI
}

OPERATORS {
 LUX(value):=illuminance_quantity(value,Lux)
 ILLUMINANCE(flux,area):=flux/area
 AVERAGE_ILLUMINANCE(total_incident_flux,area):=total_incident_flux/area
 POINT_SOURCE_ILLUMINANCE(intensity,distance,angle):=intensity*cos(angle)/(distance^2)
 LUMINOUS_FLUX_FROM_ILLUMINANCE(illuminance,area):=illuminance*area
 LUX_HOURS(illuminance,time_hours):=illuminance*time_hours
 PREFIX_LUX(prefix):=decimal_scaled_unit(Lux,prefix)
 CONVERT_ILLUMINANCE(value,source,target):=compatible_illuminance_conversion(value,source,target)
 TRACE_ILLUMINANCE(result):=traceability_chain_to_SI_lux(result)
}

AXIOMS {
 A1="The lux is the coherent SI derived unit of illuminance."
 A2="One lux equals one lumen per square metre."
 A3="One lux equals one candela steradian per square metre."
 A4="The canonical symbol is lx."
 A5="Illuminance is luminous flux incident per unit area."
 A6="Illuminance and luminous flux are distinct quantities."
 A7="Illuminance and irradiance are photometric and radiometric counterparts, not interchangeable quantities."
 A8="Point-source illuminance can follow inverse-square and cosine relationships under appropriate geometric assumptions."
 A9="Illuminance measurement traceability requires documented photometric or radiometric reference standards."
}

REASONING {
 R1_CONTEXT=identify(illuminance_quantity,value,unit,source_geometry,surface_area,distance,orientation,spectrum,measurement_method)
 R2_IDENTITY=resolve_lux_lx_lumen_candela_irradiance_foot_candle_or_name_ambiguity)
 R3_QUANTITY=distinguish_illuminance_luminous_flux_luminous_intensity_luminance_irradiance_or_related_quantity)
 R4_UNIT=verify_lumen_per_square_metre_and_cd_sr_per_square_metre_expression)
 R5_GEOMETRY=identify_point_source_extended_source_distance_incidence_angle_and_surface_orientation)
 R6_MODEL=choose_flux_area_inverse_square_cosine_interreflection_or_lighting_calculation_relationship)
 R7_SPECTRAL=preserve_photometric_visual_weighting_and_spectral_mismatch_semantics)
 R8_MEASUREMENT=identify_lux_meter_photometer_detector_or_calibrated_photometric_method)
 R9_UNCERTAINTY=evaluate_reference_spectral_mismatch_cosine_error_distance_alignment_source_stability_temperature_resolution_and_repeatability)
 R10_PROVENANCE=record_unit_quantity_geometry_weighting_method_reference_standard_calibration_and_traceability)
}

CONSTRAINTS {
 C1="The symbol lx denotes lux only in illuminance unit context."
 C2="Illuminance must not be conflated with luminous flux measured in lumens."
 C3="Illuminance must not be conflated with luminous intensity measured in candelas."
 C4="Illuminance must not be conflated with irradiance measured in watts per square metre."
 C5="E=Phi/A requires the relevant incident flux and area semantics."
 C6="E=I cos(theta)/r^2 requires point-source or equivalent far-field assumptions."
 C7="Extended sources, reflections and near-field geometry can require spatial integration rather than inverse-square simplification."
 C8="Lux-meter measurements can be affected by spectral mismatch and imperfect cosine response."
 C9="Instrument resolution alone does not determine total illuminance uncertainty."
 C10="Traceability to the lux requires a documented photometric or radiometric calibration chain."
}

SEMANTIC_EQUIVALENCE {
 "LuxUnit"<=>"Lux"
 "IlluminanceQuantity"<=>"Illuminance"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
 "IlluminanceMeter"<=>"LuxMeter"
}

VALIDATION {
 V1="Unit identity is lux and canonical symbol is lx."
 V2="Quantity kind is illuminance."
 V3="Coherent SI expression is lm m^-2."
 V4="Equivalent expression cd sr m^-2 is semantically consistent."
 V5="Illuminance, luminous flux, luminous intensity, luminance and irradiance remain distinct."
 V6="Distance and incidence-angle relationships are applied only under appropriate geometry assumptions."
 V7="Spectral and angular detector response are represented where material."
 V8="Prefixed lux units use correct decimal scaling."
 V9="Measurement uncertainty includes spectral, cosine, distance, alignment, source and environmental effects."
 V10="Illuminance calibration and traceability evidence are retained."
}

CONFIDENCE {
 BASE_CONFIDENCE=0.99
 LUX_DEFINITION=0.99
 ILLUMINANCE_REASONING=0.99
 PHOTOMETRIC_REASONING=0.99
 GEOMETRY_REASONING=0.98
 SPECTRAL_REASONING=0.98
 ILLUMINANCE_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when source geometry, distance, orientation, spectral distribution, detector response, measurement method, calibration status or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES=[
 SemanticSearch,OntologyGrounding,LuxReasoning,SIDerivedUnitReasoning,
 IlluminanceReasoning,LuminousFluxReasoning,LuminousIntensityReasoning,
 PhotometryReasoning,LightingGeometryReasoning,InverseSquareReasoning,
 CosineLawReasoning,DaylightingReasoning,LightingDesignReasoning,
 IlluminanceMeasurementReasoning,PhotometricMetrologyReasoning,
 CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,
 KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "lux"->Lux
  "lx"->Lux
  "mlx"->Millilux
  "klx"->Kilolux
  "lm/m2"->Lux
  "lm m^-2"->Lux
 }
}

EXECUTION_RULES {
 E1="If lux or lx denotes the SI derived unit of illuminance, activate LuxOntology."
 E2="Confirm quantity kind illuminance rather than relying only on lighting terminology."
 E3="Map lux coherently to lm m^-2 and cd sr m^-2."
 E4="Distinguish illuminance from luminous flux, luminous intensity, luminance and irradiance."
 E5="Apply inverse-square and cosine relationships only under appropriate source and geometry assumptions."
 E6="Preserve photometric spectral weighting and detector spectral-response semantics."
 E7="Apply SI prefixes as exact decimal scale transformations."
 E8="For measurement contexts, evaluate spectral mismatch, cosine response, distance, alignment, source stability, environment, calibration and uncertainty."
 E9="Record photometric reference, calibration and traceability provenance."
}

RECURSION {
 ENTRY=Lux
 EXPAND(Lux)->[
 SIDerivedUnits,Lumen,Metre,Candela,Steradian,Illuminance,LuminousFlux,
 LuminousIntensity,SolidAngle,Area,Photometry,IrradianceRelationship,
 PhotopicLuminousEfficiencyFunction,InverseSquareLawRelationship,
 CosineLawRelationship,PointSourceRelationship,ExtendedSourceRelationship,
 LightSourceRelationship,LuminaireRelationship,DaylightRelationship,
 LightingDesignRelationship,ReflectanceRelationship,UniformityRelationship,
 LuminousExposureRelationship,LuxMeterRelationship,PhotometerRelationship,
 PhotodiodeRelationship,CosineResponseRelationship,SpectralMismatchRelationship,
 IlluminanceMeasurement,MeasurementUncertainty,Calibration,
 IlluminanceStandardRelationship,MeasurementTraceability,Metrology,
 PhotometricMetrologyRelationship,TemperatureInfluence,AlignmentRelationship,
 DistanceUncertaintyRelationship,SIPrefix,Millilux,Kilolux,
 FootCandleRelationship,UnitConversion,Verification,Validation,LuxProvenance
 ]
 EXPAND(LuxFamilies)->[
 LuxIdentitySymbolQuantityAndUnitExpression,
 LumenAreaCandelaSteradianAndPhotometricFoundations,
 IlluminanceFluxPerAreaAndSurfaceGeometry,
 PointSourceInverseSquareCosineAndOrientationRelationships,
 ExtendedSourcesReflectionsDaylightAndLightingDesign,
 LuxMetersPhotometersDetectorSpectralAndCosineResponse,
 CalibrationStandardsUncertaintyTraceabilityAndProvenance
 ]
 STOP_CONDITION="Stop when lux identity, illuminance quantity, geometry, photometric weighting, measurement uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY="SI Derived Units"
 RELATED_ONTOLOGIES=[
 "SI Derived Units","Lumen Ontology","Candela Ontology","Steradian Ontology",
 "Metre Ontology","Watt Ontology","Quantity Ontology","Unit Ontology",
 "Measurement Ontology","Scientific Measurement Ontology 2","Metrology Ontology",
 "Reference Standard Ontology","Measurement Uncertainty Ontology",
 "Physics Ontology","Optics Ontology","Verification & Validation"
 ]
 ROUTE_RULES=[
 "Lux -> SI Derived Units for parent derived-unit semantics",
 "Lux -> Lumen and Metre ontologies for lm m^-2 semantics",
 "Lux -> Candela and Steradian ontologies for photometric angular semantics",
 "Lux -> Watt and radiometry for illuminance-versus-irradiance distinction",
 "Lux -> Physics and Optics for propagation, geometry and reflection semantics",
 "Lux -> Measurement and Metrology for illuminance measurement, calibration and traceability",
 "Lux -> Verification & Validation for photometric, unit and semantic checks"
 ]
}

UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible illuminance, lighting, measurement or reasoning relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=[
 "Preserve lux-versus-illuminance distinction.",
 "Preserve illuminance-versus-luminous-flux distinction.",
 "Preserve illuminance-versus-luminous-intensity distinction.",
 "Preserve illuminance-versus-irradiance distinction.",
 "Preserve source-geometry and incidence-angle semantics.",
 "Preserve photometric-versus-radiometric distinction.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve machine-readable lux semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION="The lux, symbol lx, is the coherent SI derived unit of illuminance and equals lm m^-2."
 QUANTITY_SUMMARY="Illuminance represents luminous flux incident on a surface per unit area."
 GEOMETRY_SUMMARY="Point-source illuminance can depend on luminous intensity, inverse-square distance and cosine of incidence angle under appropriate assumptions."
 PHOTOMETRY_SUMMARY="Illuminance is a photometric quantity and is distinct from radiometric irradiance."
 LIGHTING_SUMMARY="Illuminance is used in interior, exterior, task, road, daylight and architectural lighting analysis."
 MEASUREMENT_SUMMARY="Illuminance can be measured with calibrated lux meters or photometers with appropriate spectral and cosine response."
 UNCERTAINTY_SUMMARY="Precision illuminance measurement can require uncertainty contributions from spectral mismatch, cosine response, distance, alignment, source stability, temperature and calibration."
}

FLOW {
 INPUT
 -> detect_lux_context
 -> identify_illuminance_quantity_value_unit_source_geometry_surface_area_distance_orientation_spectrum_and_measurement_method
 -> resolve_lux_lx_lumen_candela_irradiance_foot_candle_or_name_ambiguity
 -> distinguish_illuminance_luminous_flux_luminous_intensity_luminance_irradiance_or_related_quantity
 -> verify_lumen_per_square_metre_and_cd_sr_per_square_metre_expression
 -> identify_point_source_extended_source_distance_incidence_angle_and_surface_orientation
 -> choose_flux_area_inverse_square_cosine_interreflection_or_lighting_calculation_relationship
 -> preserve_photometric_visual_weighting_and_spectral_mismatch_semantics
 -> identify_illuminance_measurement_method
 -> evaluate_reference_spectral_mismatch_cosine_error_distance_alignment_source_stability_temperature_resolution_and_repeatability
 -> record_unit_quantity_geometry_weighting_method_reference_standard_calibration_and_traceability
 -> 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-SI-DERIVED-UNITS-LUX-ONTOLOGY-V1"
}

}

END_FLOW