Kilogram Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Kilogram Ontology within the Kireth Research Semantic Library. The kilogram is the SI base unit of mass, symbol kg. It formalises unit identity, mass quantity, mass dimension, the Planck-constant definition, the kilogram-to-gram relationship, practical realisation, mass measurement, calibration, uncertainty, traceability and provenance.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = Kilogram
 ENTITY_CLASS = SIBaseUnitOfMassFramework
 PRIMARY_CONTEXT = SIBaseUnits
 DEFINITION = "The kilogram, symbol kg, is the SI base unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10^-34 when expressed in J s, equal to kg m^2 s^-1."
 SYMBOLIC_FORMS = ["h=6.62607015e-34 J s exactly","J s=kg m^2 s^-1","[mass]=M","Q_mass=value*kg","1 kg=1000 g"]
 SEMANTIC_ROLE = "Machine-readable semantics for the kilogram as the SI base unit of mass, including definition, dimension, scaling, realisation, measurement, calibration, uncertainty and traceability."
}

SCOPE {
 INCLUDE = [
 Kilogram,KilogramUnit,SIBaseUnit,SIUnit,BaseUnit,MeasurementUnit,Unit,
 InternationalSystemOfUnits,SI,InternationalSystemOfQuantities,ISQ,
 Mass,MassQuantity,PhysicalQuantity,Quantity,QuantityKind,BaseQuantity,
 SIBaseQuantity,QuantityValue,Dimension,BaseDimension,MassDimension,
 DimensionalSignature,UnitSymbol,UnitIdentifier,UnitDefinition,
 KilogramDefinition,DefiningConstant,PlanckConstant,ExactValue,Joule,
 Metre,Second,LengthDimension,TimeDimension,UnitRealisation,
 KilogramRealisation,MiseEnPratiqueRelationship,KibbleBalance,
 WattBalanceRelationship,XRCDRelationship,XRayCrystalDensityRelationship,
 SiliconSphereRelationship,MassMeasurement,MassMetrologyRelationship,
 Weighing,Balance,MassComparator,MeasurementSystem,Measurement,Measurand,
 MeasurementProcedure,MeasurementModel,MeasurementResult,
 MeasurementUncertainty,StandardUncertainty,CombinedUncertainty,
 ExpandedUncertainty,Accuracy,Precision,Resolution,Repeatability,
 Reproducibility,Calibration,MassCalibrationRelationship,
 CalibrationProcedure,CalibrationCorrection,ReferenceStandard,
 MassStandardRelationship,MassArtefactRelationship,MassSetRelationship,
 PrimaryStandard,SecondaryStandard,WorkingStandard,TransferStandard,
 MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,
 CalibrationHierarchy,Metrology,ScientificMeasurement,
 EnvironmentalCondition,ReferenceCondition,TemperatureInfluence,
 PressureInfluence,HumidityInfluence,AirDensityRelationship,
 AirBuoyancyRelationship,BuoyancyCorrectionRelationship,
 GravitationalAccelerationRelationship,LocalGravityRelationship,
 DensityRelationship,VolumeRelationship,SurfaceContaminationRelationship,
 HandlingInfluenceRelationship,Prefix,SIPrefix,Gram,Milligram,
 MicrogramRelationship,NanogramRelationship,TonneRelationship,
 UnitConversion,ConversionFactor,ExactConversion,UnitCompatibility,
 DimensionalCompatibility,QuantityCompatibility,PoundRelationship,
 OunceRelationship,StoneRelationship,DerivedQuantity,SIDerivedQuantity,
 DerivedUnit,SIDerivedUnit,Force,Newton,WeightRelationship,Density,
 UnitExpression,UnitAlgebra,QuantityCalculus,DimensionalAnalysis,
 DimensionalConsistency,Verification,Validation,UnitValidation,
 ConversionValidation,ErrorAnalysis,Provenance,KilogramProvenance,
 SIUnitProvenance,MeasurementProvenance,CalibrationProvenance,
 StandardProvenance,BIPMrelationship,CGPMrelationship,CIPMrelationship,
 SIbrochureRelationship,VIMRelationship,GUMRelationship,StandardVersion,
 ReproducibilityOntologyRelationship
 ]
 EXCLUDE_AS_PRIMARY = [
 WeightWhenForceRatherThanMassIsPrimary,
 GramWhenSubmultipleUnitIdentityIsPrimary,
 GeneralMassQuantityWhenUnitIdentityIsSecondary,
 HistoricalKilogramArtefactWhenHistoricalStandardRatherThanCurrentSIUnitIsPrimary
 ]
 DISAMBIGUATION_RULE = "When kilogram or symbol kg denotes the SI base unit of mass, interpret the context as the kilogram measurement unit and distinguish mass from weight as force."
}

CORE_CONCEPTS {
 Kilogram = "SI base unit of mass, symbol kg."
 Mass = "Physical quantity describing the mass property of a body or system."
 MassDimension = "Base physical dimension represented by M."
 PlanckConstant = "Defining constant h whose exact SI numerical value supports the kilogram definition."
 KilogramRealisation = "Practical realisation of the kilogram consistent with the SI definition."
 KibbleBalance = "Method relating mechanical power to electrical quantities for realisation or dissemination of mass."
 MassStandardRelationship = "Reference mass standard used for calibration and transfer of mass values."
 MassMeasurement = "Measurement process assigning a mass value to a specified measurand."
}

RELATIONS {
 Kilogram --is_type_of--> SIBaseUnit
 Kilogram --is_SI_base_unit_of--> Mass
 Mass --has_dimension--> MassDimension
 Kilogram --has_symbol--> kg
 Kilogram --is_defined_via--> PlanckConstant
 PlanckConstant --has_exact_value--> 6.62607015e-34_J_s
 KilogramDefinition --depends_on--> MetreAndSecond
 KilogramRealisation --implements--> KilogramDefinition
 Gram --is_decimal_submultiple_of--> Kilogram
 Milligram --is_decimal_submultiple_of--> Kilogram
 TonneRelationship --is_decimal_multiple_of--> Kilogram
 KibbleBalance --supports--> KilogramRealisation
 MassCalibrationRelationship --uses--> ReferenceStandard
 MeasurementTraceability --links--> MassMeasurementToSI
 Provenance --records--> KilogramDefinitionRealisationAndMeasurementHistory
}

OPERATORS {
 KILOGRAM(value) := mass_quantity(value,Kilogram)
 DIM(Kilogram) := MassDimension
 TO_GRAM(value_kg) := value_kg*1000
 FROM_GRAM(value_g) := value_g/1000
 CONVERT_MASS(value,source,target) := compatible_mass_conversion(value,source,target)
 REALISE_KILOGRAM(method,conditions) := SI_consistent_mass_realisation(method,conditions)
 CALIBRATE_MASS(item,reference) := mass_calibration_relation(item,reference)
 CORRECT_BUOYANCY(value,air_density,object_density) := air_buoyancy_corrected_mass(value,air_density,object_density)
 TRACE_MASS(result) := traceability_chain_to_SI_kilogram(result)
}

AXIOMS {
 A1 = "The kilogram is the SI base unit of mass."
 A2 = "The canonical symbol of the kilogram is kg."
 A3 = "The kilogram has the base dimension mass M."
 A4 = "The Planck constant has the exact SI value 6.62607015×10^-34 J s."
 A5 = "The kilogram definition is linked to the metre and second through the dimensions of the Planck constant."
 A6 = "One kilogram is exactly one thousand grams."
 A7 = "Mass and weight are distinct quantities; weight is a force dependent on gravitational field."
 A8 = "Practical realisation of the kilogram is distinct from the abstract SI definition."
 A9 = "Kilogram reasoning requires explicit mass, dimension, definition, environment, calibration and traceability semantics."
}

REASONING {
 R1_CONTEXT = identify(mass_quantity,value,unit,measurement_method,environment_and_intended_use)
 R2_IDENTITY = resolve_kilogram_gram_prefixed_mass_unit_or_nonSI_mass_unit)
 R3_DIMENSION = verify_quantity_kind_mass_and_dimension_M)
 R4_DEFINITION = identify_Planck_constant_metre_and_second_definition_relationship)
 R5_SCALE = apply_mass_prefix_rules_through_gram_where_required)
 R6_CONVERSION = if_required_convert_between_compatible_mass_units)
 R7_REALISATION = if_primary_or_high_accuracy_identify_Kibble_balance_XRCD_or_traceable_mass_standard_route)
 R8_ENVIRONMENT = evaluate_air_density_buoyancy_temperature_humidity_contamination_and_local_conditions)
 R9_UNCERTAINTY = propagate_reference_comparator_buoyancy_repeatability_drift_and_environment_components)
 R10_PROVENANCE = record_definition_version_method_reference_standards_conditions_calibration_and_traceability)
}

CONSTRAINTS {
 C1 = "The kilogram is the only SI base unit whose name contains an SI prefix historically."
 C2 = "SI prefixes for mass are applied to gram rather than directly concatenated with kilogram."
 C3 = "Mass must not be conflated with weight or gravitational force."
 C4 = "High-accuracy comparison of mass artefacts can require air-buoyancy correction."
 C5 = "Surface contamination, adsorption and handling can change realised artefact mass."
 C6 = "Instrument resolution alone does not determine total mass-measurement uncertainty."
 C7 = "Local gravitational acceleration can affect weighing-system indications even though mass itself is location-independent."
 C8 = "Conversion to non-SI mass units must use declared conversion definitions."
 C9 = "Traceability to the kilogram requires a documented realisation or calibration chain."
 C10 = "The historical International Prototype of the Kilogram must not be treated as the current defining basis of the SI kilogram."
}

SEMANTIC_EQUIVALENCE {
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
 "WattBalance" <=> "KibbleBalance"
 "XRayCrystalDensity" <=> "XRCD"
}

VALIDATION {
 V1 = "Unit identity is kilogram and canonical symbol is kg."
 V2 = "Quantity kind is mass."
 V3 = "Base dimension is M."
 V4 = "Modern definition uses the exact SI numerical value of the Planck constant."
 V5 = "Mass prefixes are handled correctly through the gram relationship."
 V6 = "Conversions occur only between compatible mass units."
 V7 = "Mass is distinguished from weight."
 V8 = "Environmental and buoyancy corrections are documented where material."
 V9 = "Measurement uncertainty and traceability evidence are retained."
 V10 = "Definition, realisation and calibration relationships are traceable to documented standards and versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 KILOGRAM_DEFINITION = 0.99
 MASS_QUANTITY_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 PREFIX_REASONING = 0.99
 CONVERSION_REASONING = 0.99
 REALISATION_REASONING = 0.98
 BUOYANCY_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when unit identity, mass quantity, environmental conditions, realisation method, calibration status or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,KilogramReasoning,SIBaseUnitReasoning,
 MassReasoning,MassDimensionReasoning,DefiningConstantReasoning,
 PlanckConstantReasoning,MassPrefixReasoning,MassConversionReasoning,
 MassMeasurementReasoning,MassMetrologyReasoning,KibbleBalanceReasoning,
 CalibrationReasoning,BuoyancyCorrectionReasoning,UncertaintyReasoning,
 TraceabilityReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,
 RecursiveInference
 ]
 NORMALISE {
  "kilogram" -> Kilogram
  "kg" -> Kilogram
  "SI" -> InternationalSystemOfUnits
  "watt balance" -> KibbleBalance
  "XRCD" -> XRayCrystalDensity
 }
}

EXECUTION_RULES {
 E1 = "If kilogram or symbol kg denotes the SI base unit of mass, activate KilogramOntology."
 E2 = "Confirm quantity kind mass and base dimension M."
 E3 = "Use the modern Planck-constant defining relationship when formal definition semantics are required."
 E4 = "Apply mass prefixes through the gram according to SI rules."
 E5 = "Convert only between compatible mass units."
 E6 = "Distinguish mass from weight and gravitational-force semantics."
 E7 = "For high-accuracy mass comparison, evaluate air buoyancy, contamination and environmental effects."
 E8 = "Distinguish kilogram definition from practical realisation and calibration."
 E9 = "Preserve uncertainty and record definition versions, reference standards, conditions and provenance."
}

RECURSION {
 ENTRY = Kilogram
 EXPAND(Kilogram) -> [
 SIBaseUnits,SIBaseUnit,SIUnits,InternationalSystemOfUnits,SI,Mass,
 PhysicalQuantity,Quantity,QuantityKind,QuantityValue,MassDimension,
 Dimension,BaseDimension,DimensionalSignature,Unit,MeasurementUnit,
 UnitSymbol,KilogramDefinition,DefiningConstant,PlanckConstant,Joule,
 Metre,Second,LengthDimension,TimeDimension,UnitRealisation,
 KilogramRealisation,KibbleBalance,XRCDRelationship,SiliconSphereRelationship,
 MassMeasurement,MassComparator,MeasurementSystem,Measurement,Measurand,
 MeasurementResult,MeasurementUncertainty,Calibration,ReferenceStandard,
 MassStandardRelationship,MeasurementTraceability,Metrology,
 ScientificMeasurement,EnvironmentalCondition,AirDensityRelationship,
 AirBuoyancyRelationship,BuoyancyCorrectionRelationship,
 GravitationalAccelerationRelationship,Gram,Milligram,TonneRelationship,
 UnitConversion,Force,Newton,WeightRelationship,Density,SIDerivedUnit,
 DimensionalAnalysis,Verification,Validation,KilogramProvenance
 ]
 EXPAND(KilogramFamilies) -> [
 KilogramIdentitySymbolQuantityAndDimension,
 PlanckConstantDefinitionAndMetreSecondDependencies,
 KibbleBalanceXRCDAndSIRealisation,
 GramPrefixesMultiplesAndMassConversions,
 MassMeasurementComparatorsAndStandards,
 AirBuoyancyEnvironmentContaminationAndGravity,
 UncertaintyCalibrationAndTraceability,
 ValidationStandardsVersionsAndProvenance
 ]
 STOP_CONDITION = "Stop when kilogram identity, mass quantity, dimension, definition, scaling, realisation, measurement, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Base Units"
 RELATED_ONTOLOGIES = [
 "SI Base Units","SI Units Ontology","Measurement & Units Ontologies",
 "Foundations of Measurement","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","Dimensional Analysis Ontology",
 "Verification & Validation"
 ]
 ROUTE_RULES = [
 "Kilogram -> SI Base Units for parent base-unit semantics",
 "Kilogram -> SI Units Ontology for system-wide SI semantics",
 "Kilogram -> Quantity and Physical Quantity ontologies for mass semantics",
 "Kilogram -> Dimension Ontology for base dimension M",
 "Kilogram -> Unit Ontology for unit identity, prefixes and conversion",
 "Kilogram -> Measurement and Scientific Measurement for mass measurement",
 "Kilogram -> Metrology and Reference Standard for realisation, calibration and traceability",
 "Kilogram -> Measurement System for comparator and weighing-system semantics",
 "Kilogram -> Measurement Uncertainty for uncertainty evaluation",
 "Kilogram -> Verification & Validation for dimensional, conversion and measurement checks"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible kilogram realisation, calibration or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
 "Preserve kilogram-versus-mass distinction.",
 "Preserve mass-versus-weight distinction.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve kilogram-definition-versus-realisation distinction.",
 "Preserve exact-definition-versus-measurement-uncertainty distinction.",
 "Preserve mass-dimension-versus-unit distinction.",
 "Preserve historical-prototype-versus-current-definition distinction.",
 "Preserve machine-readable kilogram semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "The kilogram, symbol kg, is the SI base unit of mass and is defined through the exact SI numerical value of the Planck constant."
 QUANTITY_SUMMARY = "The kilogram expresses values of mass, whose base dimension is M."
 DEFINITION_SUMMARY = "The exact value h = 6.62607015×10^-34 J s links the kilogram definition to the metre and second."
 SCALE_SUMMARY = "One kilogram equals exactly 1000 grams; SI mass prefixes are formed through the gram."
 REALISATION_SUMMARY = "Practical realisation and dissemination can use Kibble balances, XRCD methods and traceable mass-standard hierarchies."
 UNCERTAINTY_SUMMARY = "High-accuracy mass measurements can require uncertainty contributions from reference standards, comparators, air buoyancy, environment, drift and contamination."
 VALIDATION_SUMMARY = "Kilogram semantics should preserve unit identity, mass quantity, dimension, definition, realisation, uncertainty, mass-versus-weight distinction and provenance."
}

FLOW {
 INPUT
 -> detect_kilogram_context
 -> identify_mass_quantity_value_unit_measurement_method_environment_and_intended_use
 -> resolve_kilogram_gram_prefixed_mass_unit_or_nonSI_mass_unit
 -> verify_quantity_kind_mass_and_dimension_M
 -> identify_Planck_constant_metre_and_second_definition_relationship
 -> apply_mass_prefix_rules_through_gram_where_required
 -> if_required_convert_between_compatible_mass_units
 -> if_high_accuracy_identify_Kibble_balance_XRCD_or_traceable_mass_standard_realisation
 -> evaluate_air_density_buoyancy_temperature_humidity_contamination_and_local_conditions
 -> propagate_reference_comparator_buoyancy_repeatability_drift_and_environment_uncertainty
 -> record_definition_version_method_reference_standards_conditions_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-BASE-UNITS-KILOGRAM-ONTOLOGY-V1"
}

}

END_FLOW