Candela Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Candela Ontology within the Kireth Research Semantic Library. The candela is the SI base unit of luminous intensity, symbol cd. It formalises luminous intensity, the exact K_cd definition, photometric and radiometric semantics, spectral weighting, realisation, calibration, uncertainty, traceability and provenance.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME = "Candela Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Measurement & Units"
 SPECIALISATION = "SI Base Units / Candela"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-base-units/candela-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}
IDENTITY {
 PRIMARY_ENTITY = Candela
 ENTITY_CLASS = SIBaseUnitOfLuminousIntensityFramework
 PRIMARY_CONTEXT = SIBaseUnits
 DEFINITION = "The candela, symbol cd, is the SI base unit of luminous intensity in a given direction, defined by fixing K_cd for monochromatic radiation of frequency 540×10^12 Hz at exactly 683 lm W^-1."
 SYMBOLIC_FORMS = ["K_cd=683 lm W^-1 exactly","nu=540e12 Hz","1 lm=1 cd sr","I_v=dPhi_v/dOmega","[luminous_intensity]=J"]
 SEMANTIC_ROLE = "Machine-readable semantics for candela identity, luminous intensity, spectral response, photometric relationships, realisation, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE = [
 Candela,SIBaseUnit,SIUnit,BaseUnit,MeasurementUnit,Unit,InternationalSystemOfUnits,SI,
 LuminousIntensity,PhysicalQuantity,Quantity,QuantityKind,BaseQuantity,SIBaseQuantity,
 QuantityValue,Dimension,BaseDimension,LuminousIntensityDimension,DimensionalSignature,
 UnitSymbol,UnitDefinition,CandelaDefinition,DefiningConstant,LuminousEfficacy,KcdRelationship,
 MonochromaticRadiation,Frequency,Hertz,RadiantIntensityRelationship,RadiantFluxRelationship,
 RadiometricQuantity,Photometry,Radiometry,PhotopicLuminousEfficiencyFunction,VlambdaRelationship,
 SpectralPowerDistributionRelationship,SpectralResponsivityRelationship,SpectralMismatchRelationship,
 LuminousFlux,Lumen,SolidAngle,Steradian,Illuminance,Lux,LuminanceRelationship,RadiantPower,Watt,
 UnitRealisation,CandelaRealisation,MiseEnPratiqueRelationship,DetectorBasedPhotometryRelationship,
 SourceBasedPhotometryRelationship,CryogenicRadiometerRelationship,StandardPhotometerRelationship,
 Photometer,SpectroradiometerRelationship,IntegratingSphereRelationship,GoniophotometerRelationship,
 StandardLampRelationship,StandardDetectorRelationship,PhotodiodeRelationship,GeometryRelationship,
 DistanceRelationship,InverseSquareLawRelationship,StrayLightRelationship,OpticalAlignmentRelationship,
 PhotometricMeasurement,LuminousIntensityMeasurement,LuminousFluxMeasurement,IlluminanceMeasurement,
 LuminanceMeasurement,MeasurementSystem,Measurement,Measurand,MeasurementResult,
 MeasurementUncertainty,Accuracy,Precision,Resolution,Repeatability,Reproducibility,Stability,
 Calibration,PhotometricCalibrationRelationship,ReferenceStandard,PhotometricStandardRelationship,
 MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,Metrology,
 PhotometricMetrologyRelationship,ScientificMeasurement,TemperatureInfluence,AmbientLightRelationship,
 DetectorNonlinearityRelationship,LampStabilityRelationship,SpectralCorrectionRelationship,
 SIPrefix,UnitConversion,ConversionFactor,UnitCompatibility,DimensionalCompatibility,
 SIDerivedUnit,UnitExpression,UnitAlgebra,DimensionalAnalysis,Verification,Validation,
 ErrorAnalysis,Provenance,CandelaProvenance,SIUnitProvenance,BIPMrelationship,
 SIbrochureRelationship,VIMRelationship,GUMRelationship,CIErelationship
 ]
 EXCLUDE_AS_PRIMARY = [CandleRelationship,RadiantIntensityWhenRadiometricSemanticsArePrimary,LuminousFluxWhenFluxIsPrimary,HistoricalCandleBasedDefinitions]
 DISAMBIGUATION_RULE = "When candela or cd denotes the SI base unit of luminous intensity in a given direction, interpret the context as the candela measurement unit."
}
CORE_CONCEPTS {
 Candela = "SI base unit of luminous intensity, symbol cd."
 LuminousIntensity = "Luminous flux per unit solid angle in a specified direction."
 LuminousIntensityDimension = "SI base dimension represented by J."
 LuminousEfficacy = "K_cd, exactly 683 lm W^-1 for monochromatic radiation of frequency 540 THz."
 LuminousFlux = "Photometric flux measured in lumens."
 SolidAngle = "Geometric quantity measured in steradians."
 CandelaRealisation = "Practical realisation of luminous intensity consistent with SI."
}

RELATIONS {
 Candela --is_type_of--> SIBaseUnit
 Candela --is_SI_base_unit_of--> LuminousIntensity
 LuminousIntensity --has_dimension--> LuminousIntensityDimension
 Candela --has_symbol--> cd
 Candela --is_defined_via--> LuminousEfficacy
 LuminousEfficacy --has_exact_value--> 683_lm_per_W
 CandelaDefinition --references--> 540_THz_MonochromaticRadiation
 Lumen --is_equivalent_to--> CandelaSteradian
 LuminousIntensity --is_luminous_flux_per--> SolidAngle
 Photometry --weights--> RadiometricQuantitiesByVisualResponse
 CandelaRealisation --implements--> CandelaDefinition
 MeasurementTraceability --links--> PhotometricMeasurementToSI
 Provenance --records--> CandelaDefinitionRealisationAndMeasurementHistory
}
OPERATORS {
 CANDELA(value) := luminous_intensity_quantity(value,Candela)
 DIM(Candela) := LuminousIntensityDimension
 LUMINOUS_INTENSITY(flux,solid_angle) := flux/solid_angle
 LUMINOUS_FLUX(intensity,solid_angle) := intensity*solid_angle
 PHOTOMETRIC_WEIGHT(spectrum,V_lambda) := integrate_visual_weighted_spectrum(spectrum,V_lambda)
 REALISE_CANDELA(method,conditions) := SI_consistent_photometric_realisation(method,conditions)
 TRACE_CANDELA(result) := traceability_chain_to_SI_candela(result)
}
AXIOMS {
 A1 = "The candela is the SI base unit of luminous intensity."
 A2 = "The canonical symbol is cd."
 A3 = "Luminous intensity has SI base dimension J."
 A4 = "K_cd is exactly 683 lm W^-1 for monochromatic radiation of frequency 540×10^12 Hz."
 A5 = "One lumen equals one candela steradian."
 A6 = "Photometric quantities incorporate spectral weighting related to human visual response."
 A7 = "Radiometric and photometric quantities are distinct."
 A8 = "Practical realisation is distinct from the abstract SI definition."
}

REASONING {
 R1_CONTEXT = identify(luminous_quantity,value,unit,spectral_distribution,geometry,measurement_method_and_intended_use)
 R2_IDENTITY = resolve_candela_or_related_photometric_unit)
 R3_DIMENSION = verify_luminous_intensity_and_dimension_J)
 R4_DEFINITION = identify_Kcd_540THz_and_radiometric_power_relationship)
 R5_PHOTOMETRY = apply_luminous_efficiency_function_and_spectral_weighting)
 R6_GEOMETRY = resolve_direction_solid_angle_distance_aperture_and_inverse_square_relationships)
 R7_REALISATION = identify_detector_source_or_radiometric_traceable_realisation)
 R8_CORRECTIONS = evaluate_spectral_mismatch_stray_light_alignment_distance_detector_nonlinearity_and_environment)
 R9_UNCERTAINTY = propagate_reference_spectral_geometry_detector_stability_and_repeatability_components)
 R10_PROVENANCE = record_definition_version_response_function_method_standards_conditions_and_traceability)
}
CONSTRAINTS {
 C1 = "Luminous intensity is directional and must not be conflated with luminous flux."
 C2 = "Photometric and radiometric quantities require spectral-response semantics for conversion."
 C3 = "Spectral mismatch can introduce bias."
 C4 = "Inverse-square relationships require valid geometry assumptions."
 C5 = "Stray light, alignment and aperture geometry can affect measurements."
 C6 = "Detector nonlinearity and temperature dependence can affect results."
 C7 = "Resolution alone does not determine total uncertainty."
 C8 = "Traceability requires a documented photometric or radiometric calibration chain."
 C9 = "Historical candle-based definitions are not the current defining basis."
}
SEMANTIC_EQUIVALENCE {
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
 "PhotopicLuminousEfficiencyFunction" <=> "Vlambda"
 "LuminousEfficacyOfMonochromaticRadiation" <=> "Kcd"
}

VALIDATION {
 V1 = "Unit identity is candela and canonical symbol is cd."
 V2 = "Quantity kind is luminous intensity."
 V3 = "Base dimension is J."
 V4 = "Modern definition uses K_cd = 683 lm W^-1 at 540×10^12 Hz."
 V5 = "Luminous intensity is distinguished from luminous flux and radiometric intensity."
 V6 = "Solid-angle and directional semantics are documented."
 V7 = "Spectral weighting and detector response are documented where material."
 V8 = "Geometry, alignment and spectral corrections are documented where material."
 V9 = "Measurement uncertainty and traceability evidence are retained."
 V10 = "Definition, realisation and calibration relationships are traceable."
}
CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 CANDELA_DEFINITION = 0.99
 LUMINOUS_INTENSITY_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 PHOTOMETRIC_RADIOMETRIC_REASONING = 0.98
 SPECTRAL_WEIGHTING_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when spectrum, visual-response function, geometry, detector response, calibration or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES = [SemanticSearch,OntologyGrounding,CandelaReasoning,SIBaseUnitReasoning,LuminousIntensityReasoning,LuminousEfficacyReasoning,PhotometryReasoning,RadiometryReasoning,SpectralWeightingReasoning,LuminousFluxReasoning,SolidAngleReasoning,OpticalMeasurementReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "candela" -> Candela
  "cd" -> Candela
  "SI" -> InternationalSystemOfUnits
  "K_cd" -> LuminousEfficacyOfMonochromaticRadiation
 }
}

EXECUTION_RULES {
 E1 = "If candela or cd denotes the SI base unit of luminous intensity, activate CandelaOntology."
 E2 = "Confirm luminous intensity and base dimension J."
 E3 = "Use the K_cd defining relationship at 540×10^12 Hz."
 E4 = "Distinguish luminous intensity, luminous flux, illuminance, luminance and radiometric quantities."
 E5 = "Apply appropriate spectral luminous-efficiency weighting."
 E6 = "Resolve direction, solid angle, distance and geometry."
 E7 = "Evaluate spectral mismatch, stray light, detector nonlinearity and alignment where material."
 E8 = "Distinguish definition from practical realisation and calibration."
 E9 = "Preserve uncertainty and provenance."
}
RECURSION {
 ENTRY = Candela
 EXPAND(Candela) -> [SIBaseUnits,SIUnits,LuminousIntensity,LuminousIntensityDimension,CandelaDefinition,DefiningConstant,LuminousEfficacy,KcdRelationship,MonochromaticRadiation,Frequency,Hertz,LuminousFlux,Lumen,SolidAngle,Steradian,Illuminance,Lux,LuminanceRelationship,RadiantPower,Watt,Photometry,Radiometry,PhotopicLuminousEfficiencyFunction,SpectralPowerDistributionRelationship,CandelaRealisation,CryogenicRadiometerRelationship,Photometer,SpectroradiometerRelationship,IntegratingSphereRelationship,GoniophotometerRelationship,PhotometricMeasurement,MeasurementSystem,MeasurementUncertainty,Calibration,ReferenceStandard,MeasurementTraceability,Metrology,SpectralMismatchRelationship,InverseSquareLawRelationship,StrayLightRelationship,UnitConversion,SIDerivedUnit,DimensionalAnalysis,Verification,Validation,CandelaProvenance]
 EXPAND(CandelaFamilies) -> [CandelaIdentitySymbolQuantityAndDimension,KcdDefinitionFrequencyAndRadiometricPowerSemantics,LuminousIntensityFluxSolidAngleIlluminanceAndLuminance,SpectralVisualResponseAndPhotometricWeighting,DetectorSourceAndRadiometricRealisationMethods,PhotometricInstrumentsGeometryAndCorrections,UncertaintyCalibrationAndTraceability,ValidationStandardsVersionsAndProvenance]
 STOP_CONDITION = "Stop when identity, quantity, dimension, definition, spectral weighting, geometry, realisation, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Base Units"
 RELATED_ONTOLOGIES = ["SI Base Units","SI Units Ontology","Measurement & Units Ontologies","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Scientific Measurement Ontology 2","Metrology Ontology","Reference Standard Ontology","Measurement System Ontology","Measurement Uncertainty Ontology","Physics Ontology","Optics Ontology","Verification & Validation"]
 ROUTE_RULES = [
 "Candela -> SI Base Units for parent base-unit semantics",
 "Candela -> SI Units Ontology for system-wide SI semantics",
 "Candela -> Quantity and Physical Quantity ontologies for luminous-intensity semantics",
 "Candela -> Dimension Ontology for base dimension J",
 "Candela -> Unit Ontology for unit identity and conversion",
 "Candela -> Measurement and Scientific Measurement for photometric measurement",
 "Candela -> Metrology and Reference Standard for realisation and traceability",
 "Candela -> Physics and Optics ontologies for radiation and detector semantics",
 "Candela -> Measurement Uncertainty for uncertainty evaluation"
 ]
}
UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible candela realisation or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = ["Preserve candela-versus-luminous-intensity distinction.","Preserve luminous-intensity-versus-luminous-flux distinction.","Preserve photometric-versus-radiometric distinction.","Preserve unit-versus-quantity distinction.","Preserve definition-versus-realisation distinction.","Preserve current-definition-versus-historical-definition distinction.","Preserve machine-readable candela semantics."]
}

OUTPUT {
 CANONICAL_DEFINITION = "The candela, symbol cd, is the SI base unit of luminous intensity in a given direction and is defined through the exact luminous efficacy K_cd."
 QUANTITY_SUMMARY = "The candela expresses luminous intensity, whose SI base dimension is J."
 DEFINITION_SUMMARY = "K_cd is exactly 683 lm W^-1 for monochromatic radiation of frequency 540×10^12 Hz."
 PHOTOMETRY_SUMMARY = "Photometric quantities weight radiometric power according to specified human visual-response functions."
 GEOMETRY_SUMMARY = "Luminous intensity is directional and relates luminous flux to solid angle."
 REALISATION_SUMMARY = "Practical realisation can use detector-based or source-based photometry linked to radiometric standards."
 UNCERTAINTY_SUMMARY = "Precision photometry can require uncertainty contributions from spectral mismatch, geometry, detector response, alignment, stability, stray light and calibration."
}
FLOW {
 INPUT
 -> detect_candela_context
 -> identify_luminous_quantity_value_unit_spectrum_geometry_method_and_intended_use
 -> resolve_candela_or_related_photometric_unit
 -> verify_luminous_intensity_and_dimension_J
 -> identify_Kcd_540THz_and_radiometric_power_relationship
 -> apply_luminous_efficiency_function_and_spectral_weighting
 -> resolve_direction_solid_angle_distance_and_geometry
 -> identify_traceable_photometric_realisation
 -> evaluate_spectral_geometry_detector_and_environmental_effects
 -> propagate_measurement_uncertainty
 -> record_definition_method_standards_conditions_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-BASE-UNITS-CANDELA-ONTOLOGY-V1"
}
}
END_FLOW