Lumen Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Lumen Ontology within the Kireth Research Semantic Library. The lumen, symbol lm, is the coherent SI derived unit of luminous flux: 1 lm = 1 cd sr.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Lumen Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="SI Derived Units / Lumen"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-derived-units/lumen-ontology.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Lumen
 ENTITY_CLASS=SIDerivedUnitOfLuminousFluxFramework
 DEFINITION="The lumen, symbol lm, is the coherent SI derived unit of luminous flux. One lumen equals one candela steradian."
 SYMBOLIC_FORMS=["1 lm=1 cd sr","Phi_v=integral(I_v dOmega)","E_v=Phi_v/A under stated geometry"]
 SEMANTIC_ROLE="Machine-readable semantics for luminous flux, luminous intensity, solid angle, photometric weighting, illuminance, measurement, uncertainty and traceability."
}
SCOPE {
 INCLUDE=[
 Lumen,LumenUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,SI,Candela,Steradian,
 LuminousFlux,PhotometricQuantity,Quantity,QuantityKind,LuminousFluxDimension,
 UnitSymbol,LumenDefinition,UnitExpression,UnitAlgebra,LuminousIntensity,SolidAngle,
 AngularDistributionRelationship,Photometry,VisibleRadiationRelationship,RadiantFlux,
 SpectralRadiantFluxRelationship,SpectralPowerDistributionRelationship,
 PhotopicVisionRelationship,SpectralLuminousEfficiencyRelationship,
 PhotopicLuminousEfficiencyFunction,VLambdaRelationship,LuminousEfficacyRelationship,
 WavelengthRelationship,HumanVisualResponseRelationship,Illuminance,Lux,
 LuminousExitanceRelationship,LuminanceRelationship,InverseSquareLawRelationship,
 CosineLawRelationship,LambertianEmitterRelationship,AreaRelationship,
 LightSourceRelationship,LampRelationship,LuminaireRelationship,LEDrelationship,
 TotalLuminousFluxRelationship,UsefulLuminousFluxRelationship,BeamFluxRelationship,
 OpticalEfficiencyRelationship,ElectricalPowerRelationship,WattRelationship,
 IntegratingSphereRelationship,GoniophotometerRelationship,PhotometerRelationship,
 SpectroradiometerRelationship,PhotodiodeRelationship,DetectorRelationship,
 SpectralResponsivityRelationship,CosineResponseRelationship,StrayLightRelationship,
 Measurement,Measurand,MeasurementResult,MeasurementUncertainty,Accuracy,Precision,
 Resolution,Repeatability,Reproducibility,Calibration,PhotometricCalibrationRelationship,
 LuminousFluxCalibrationRelationship,ReferenceStandard,LuminousFluxStandardRelationship,
 StandardLampRelationship,ReferenceLampRelationship,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,Metrology,PhotometricMetrologyRelationship,
 RadiometricMetrologyRelationship,TemperatureInfluence,AmbientLightRelationship,
 SpectralMismatchRelationship,SpatialNonuniformityRelationship,
 IntegratingSphereSubstitutionErrorRelationship,SelfAbsorptionRelationship,
 GeometryCorrectionRelationship,SIPrefix,MillilumenRelationship,MicrolumenRelationship,
 Kilolumen,MegalumenRelationship,UnitConversion,Verification,Validation,
 ErrorAnalysis,Provenance,LumenProvenance,SIDerivedUnitProvenance,
 SIUnitProvenance,MeasurementProvenance,CalibrationProvenance,
 BIPMrelationship,SIbrochureRelationship,CIErelationship,VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[LumenAsAnatomicalCavityRelationship,LuxWhenIlluminanceIsPrimary,CandelaWhenLuminousIntensityIsPrimary,WattWhenRadiantPowerIsPrimary]
 DISAMBIGUATION_RULE="When lumen or lm denotes the coherent SI derived unit of luminous flux, interpret it as the photometric unit. Distinguish it from anatomical lumen, lux, candela and watt."
}
CORE_CONCEPTS {
 Lumen="Coherent SI derived unit of luminous flux, symbol lm, equal to cd sr."
 LuminousFlux="Photometric quantity representing visible radiant power weighted according to human visual sensitivity."
 LuminousIntensity="Luminous flux per unit solid angle in a specified direction."
 SolidAngle="Three-dimensional angular measure used to integrate luminous intensity."
 Candela="SI base unit of luminous intensity."
 Illuminance="Luminous flux incident per unit area, measured in lux."
 Photometry="Measurement of light weighted according to specified human visual response."
}
RELATIONS {
 Lumen--is_type_of-->SIDerivedUnit
 Lumen--is_coherent_derived_unit_of-->LuminousFlux
 Lumen--has_symbol-->lm
 Lumen--has_expression-->candela_steradian
 LuminousFlux--is_integral_of-->LuminousIntensityOverSolidAngle
 LuminousFlux--is_photometrically_weighted_from-->RadiantFlux
 LuminousIntensity--is_measured_in-->Candela
 SolidAngle--is_measured_in-->Steradian
 Illuminance--relates_to-->LuminousFluxPerArea
 Lux--is_equivalent_to-->LumenPerSquareMetre
 MeasurementTraceability--links-->LuminousFluxMeasurementToSI
}
OPERATORS {
 LUMEN(value):=luminous_flux_quantity(value,Lumen)
 LUMINOUS_FLUX_FROM_INTENSITY(intensity_distribution,solid_angle_domain):=integral(intensity_distribution,dOmega)
 UNIFORM_INTENSITY_FLUX(intensity,solid_angle):=intensity*solid_angle
 ISOTROPIC_FLUX(intensity):=4*pi*intensity
 ILLUMINANCE_FROM_FLUX(flux,area):=flux/area
 LUMINOUS_EFFICACY(flux,power):=flux/power
 PREFIX_LUMEN(prefix):=decimal_scaled_unit(Lumen,prefix)
 TRACE_LUMINOUS_FLUX(result):=traceability_chain_to_SI_lumen(result)
}
AXIOMS {
 A1="The lumen is the coherent SI derived unit of luminous flux."
 A2="One lumen equals one candela steradian."
 A3="The canonical symbol is lm."
 A4="Luminous flux is a photometric quantity distinct from radiant flux."
 A5="Luminous flux is obtained by integrating luminous intensity over solid angle."
 A6="Radiometric-to-photometric conversion requires specified spectral luminous-efficiency weighting."
 A7="Illuminance and luminous flux are distinct quantities."
 A8="Total source luminous flux can require integration over the complete angular emission distribution."
 A9="Luminous-flux measurement traceability requires documented photometric or radiometric standards."
}
REASONING {
 R1=identify(luminous_flux_quantity,value,unit,source,spectrum,angular_distribution,measurement_method)
 R2=resolve_lumen_lm_anatomical_lumen_lux_candela_watt_ambiguity)
 R3=distinguish_luminous_flux_luminous_intensity_illuminance_luminance_radiant_flux)
 R4=verify_cd_sr_unit_expression)
 R5=expand_lumen_to_candela_steradian)
 R6=choose_intensity_solid_angle_spectral_weighting_illuminance_or_efficacy_relationship)
 R7=if_radiometric_input_apply_specified_visual_weighting)
 R8=identify_integrating_sphere_goniophotometer_photometer_or_spectroradiometric_method)
 R9=evaluate_spectral_angular_geometry_detector_environment_and_repeatability_uncertainty)
 R10=record_quantity_weighting_geometry_method_standard_calibration_traceability_and_provenance)
}
CONSTRAINTS {
 C1="The symbol lm denotes lumen only in photometric unit context."
 C2="Luminous flux must not be conflated with radiant flux measured in watts."
 C3="Luminous flux must not be conflated with luminous intensity measured in candelas."
 C4="Luminous flux must not be conflated with illuminance measured in lux."
 C5="Phi_v=I_v*Omega requires uniform luminous intensity over the stated solid angle."
 C6="Radiometric-to-photometric conversion requires spectral information and a specified luminous-efficiency function."
 C7="Arbitrary spectra require spectral integration rather than a single luminous-efficacy constant."
 C8="Integrating-sphere measurements can require self-absorption and geometry corrections."
 C9="Instrument resolution alone does not determine total luminous-flux uncertainty."
 C10="Traceability requires a documented photometric or radiometric calibration chain."
}
SEMANTIC_EQUIVALENCE {
 "LumenUnit"<=>"Lumen"
 "LuminousFluxQuantity"<=>"LuminousFlux"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
 "Vlambda"<=>"PhotopicLuminousEfficiencyFunction"
}
VALIDATION {
 V1="Unit identity is lumen and canonical symbol is lm."
 V2="Quantity kind is luminous flux."
 V3="Coherent SI expression is cd sr."
 V4="Luminous flux, intensity, illuminance, luminance and radiant flux remain distinct."
 V5="Solid-angle integration is represented where angular emission is non-uniform."
 V6="Spectral luminous-efficiency weighting is applied correctly when required."
 V7="Source and measurement geometry are represented where material."
 V8="Prefixed lumen units use correct decimal scaling."
 V9="Measurement uncertainty includes relevant spectral, angular, detector and environmental effects."
 V10="Luminous-flux calibration and traceability evidence are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 LUMEN_DEFINITION=0.99
 LUMINOUS_FLUX_REASONING=0.99
 PHOTOMETRIC_REASONING=0.99
 SOLID_ANGLE_REASONING=0.99
 SPECTRAL_WEIGHTING_REASONING=0.98
 MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when spectrum, angular distribution, visual weighting, geometry, method, calibration or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,LumenReasoning,SIDerivedUnitReasoning,LuminousFluxReasoning,LuminousIntensityReasoning,SolidAngleReasoning,PhotometryReasoning,SpectralWeightingReasoning,IlluminanceReasoning,LuminousEfficacyReasoning,LightingReasoning,MeasurementReasoning,PhotometricMetrologyReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "lumen"->Lumen
  "lumens"->Lumen
  "lm"->Lumen
  "klm"->Kilolumen
  "cd"->Candela
  "sr"->Steradian
 }
}
EXECUTION_RULES {
 E1="Activate LumenOntology when lumen or lm denotes the SI unit of luminous flux."
 E2="Confirm luminous-flux quantity semantics."
 E3="Map lumen coherently to candela steradian."
 E4="Distinguish luminous flux from intensity, illuminance, luminance and radiant flux."
 E5="Integrate luminous intensity over solid angle when angular distribution is non-uniform."
 E6="Apply specified spectral weighting when deriving photometric flux from radiometric data."
 E7="Apply SI prefixes as exact decimal transformations."
 E8="Evaluate spectral mismatch, angular response, geometry, detector behaviour, calibration and uncertainty."
 E9="Record photometric reference, calibration and traceability provenance."
}
RECURSION {
 ENTRY=Lumen
 EXPAND(Lumen)->[
 SIDerivedUnits,Candela,Steradian,LuminousFlux,LuminousIntensity,SolidAngle,
 Photometry,RadiantFlux,PhotopicLuminousEfficiencyFunction,LuminousEfficacyRelationship,
 Illuminance,Lux,LuminanceRelationship,LightSourceRelationship,LuminaireRelationship,
 LEDrelationship,IntegratingSphereRelationship,GoniophotometerRelationship,
 PhotometerRelationship,SpectroradiometerRelationship,PhotodiodeRelationship,
 MeasurementUncertainty,Calibration,LuminousFluxStandardRelationship,
 MeasurementTraceability,Metrology,PhotometricMetrologyRelationship,
 SpectralMismatchRelationship,SelfAbsorptionRelationship,SIPrefix,
 Kilolumen,UnitConversion,Verification,Validation,LumenProvenance
 ]
 EXPAND(LumenFamilies)->[
 LumenIdentitySymbolQuantityAndUnitExpression,
 CandelaSteradianLuminousIntensityAndSolidAngle,
 LuminousFluxAngularDistributionAndSourceGeometry,
 RadiometryPhotometrySpectralWeightingAndVisualResponse,
 IlluminanceLuxLuminanceAndLuminousEfficacy,
 LightSourcesLuminairesAndLightingSystems,
 IntegratingSphereGoniophotometryDetectorMethodsAndCalibration,
 SpectralAngularEnvironmentalUncertaintyTraceabilityAndProvenance
 ]
 STOP_CONDITION="Stop when lumen identity, luminous-flux quantity, angular and spectral semantics, measurement uncertainty and provenance are resolved."
}
ROUTING {
 PARENT_ONTOLOGY="SI Derived Units"
 RELATED_ONTOLOGIES=["SI Derived Units","Candela Ontology","Steradian Ontology","Lux Ontology","Watt Ontology","Quantity Ontology","Unit Ontology","Measurement Ontology","Metrology Ontology","Measurement Uncertainty Ontology","Physics Ontology","Optics Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Lumen -> Candela and Steradian for cd sr semantics",
 "Lumen -> Lux for luminous-flux-per-area relationships",
 "Lumen -> Watt and radiometry for radiant-power relationships",
 "Lumen -> Physics and Optics for light and source semantics",
 "Lumen -> Measurement and Metrology for calibration and traceability"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible photometric or measurement relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve lumen-versus-luminous-flux distinction.","Preserve flux-versus-intensity distinction.","Preserve flux-versus-illuminance distinction.","Preserve photometric-versus-radiometric distinction.","Preserve angular and spectral weighting semantics.","Preserve machine-readable lumen semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="The lumen, symbol lm, is the coherent SI derived unit of luminous flux and equals cd sr."
 QUANTITY_SUMMARY="Luminous flux represents visible radiant output weighted according to specified human visual response."
 INTENSITY_SUMMARY="Luminous flux is obtained by integrating luminous intensity over solid angle."
 ILLUMINANCE_SUMMARY="Illuminance is luminous flux incident per unit area and is measured in lux."
 MEASUREMENT_SUMMARY="Luminous flux can be measured using integrating spheres, goniophotometers, photometers and spectroradiometric methods."
 UNCERTAINTY_SUMMARY="Precision luminous-flux measurement can require spectral, angular, detector, geometry, environmental and calibration corrections."
}
FLOW {
 INPUT
 -> detect_lumen_context
 -> identify_luminous_flux_quantity_value_unit_source_spectrum_angular_distribution_and_method
 -> resolve_lumen_lm_anatomical_lumen_lux_candela_watt_ambiguity
 -> distinguish_luminous_flux_luminous_intensity_illuminance_luminance_radiant_flux
 -> verify_cd_sr_unit_expression
 -> expand_lumen_to_candela_steradian
 -> choose_intensity_solid_angle_spectral_weighting_illuminance_or_efficacy_relationship
 -> apply_visual_weighting_if_required
 -> identify_luminous_flux_measurement_method
 -> evaluate_measurement_uncertainty
 -> record_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-SI-DERIVED-UNITS-LUMEN-ONTOLOGY-V1"
}
}
END_FLOW