SI Base Units

AI INTERPRETATION NOTE
This Flow Algebra defines the SI Base Units ontology within the Kireth Research Semantic Library. It formalises the seven SI base units, their base quantities, dimensions, defining-constant relationships, coherent derivation, metrological realisation, traceability and provenance.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = SIBaseUnits
 ENTITY_CLASS = InternationalSystemBaseUnitFramework
 PRIMARY_CONTEXT = MeasurementUnitsOntologies
 DEFINITION = "The SI base units are the seven units second, metre, kilogram, ampere, kelvin, mole and candela associated with the seven base quantities of the International System of Units."
 SYMBOLIC_FORMS = ["SI_base={s,m,kg,A,K,mol,cd}","Q=value*SI_unit","derived_unit=product(base_units^exponents)","dim(Q)=L^a M^b T^c I^d Theta^e N^f J^g"]
 SEMANTIC_ROLE = "Machine-readable semantics for SI base-unit identity, quantity, dimension, symbol, definition, derivation, realisation and traceability."
}

SCOPE {
 INCLUDE = [
  SIBaseUnits,SIBaseUnit,InternationalSystemOfUnits,SI,InternationalSystemOfQuantities,ISQ,
  BaseUnit,MeasurementUnit,Unit,CoherentUnit,BaseQuantity,SIBaseQuantity,Quantity,QuantityKind,
  PhysicalQuantity,QuantityValue,Dimension,BaseDimension,DimensionalSignature,
  Second,Time,TimeDimension,Metre,Length,LengthDimension,Kilogram,Mass,MassDimension,
  Ampere,ElectricCurrent,ElectricCurrentDimension,Kelvin,ThermodynamicTemperature,
  ThermodynamicTemperatureDimension,Mole,AmountOfSubstance,AmountOfSubstanceDimension,
  Candela,LuminousIntensity,LuminousIntensityDimension,UnitSymbol,QuantitySymbol,UnitDefinition,
  UnitRealisation,DefiningConstant,PhysicalConstant,DefinedConstant,Caesium133FrequencyRelationship,
  SpeedOfLight,PlanckConstant,ElementaryCharge,BoltzmannConstant,AvogadroConstant,
  LuminousEfficacyRelationship,ExactValue,DerivedUnit,SIDerivedUnit,DerivedQuantity,SIDerivedQuantity,
  UnitExpression,CompoundUnit,ProductUnit,QuotientUnit,PowerUnit,UnitExponent,UnitAlgebra,
  QuantityCalculus,DimensionalAnalysis,DimensionalConsistency,DimensionalHomogeneity,
  Hertz,Newton,Pascal,Joule,Watt,Coulomb,Volt,Farad,Ohm,Siemens,Weber,Tesla,Henry,Lumen,Lux,
  Becquerel,Gray,Sievert,Katal,Radian,Steradian,SIPrefix,UnitConversion,ConversionFactor,
  UnitCompatibility,QuantityCompatibility,Measurement,Measurand,MeasurementResult,
  MeasurementUncertainty,ScientificMeasurement,MeasurementSystem,Metrology,Calibration,
  ReferenceStandard,MeasurementStandard,MeasurementTraceability,MetrologicalTraceability,
  TraceabilityChain,NationalMetrologyInstitute,NMI,BIPMrelationship,CGPMrelationship,CIPMrelationship,
  SIbrochureRelationship,VIMRelationship,GUMRelationship,MiseEnPratiqueRelationship,
  Verification,Validation,UnitValidation,DimensionalValidation,ConversionValidation,
  ErrorAnalysis,ReproducibilityOntologyRelationship,Provenance,SIUnitProvenance,StandardProvenance
 ]
 EXCLUDE_AS_PRIMARY = [SIDerivedUnitsWhenDerivedUnitSemanticsArePrimary,NonSIUnits,CustomaryUnits]
 DISAMBIGUATION_RULE = "When the seven fundamental SI units or their relationships to SI base quantities, dimensions and defining constants are primary, interpret the context as SI base units."
}

CORE_CONCEPTS {
 SIBaseUnits = "Set of seven base units forming the base-unit layer of the International System of Units."
 Second = "SI base unit of time, symbol s."
 Metre = "SI base unit of length, symbol m."
 Kilogram = "SI base unit of mass, symbol kg."
 Ampere = "SI base unit of electric current, symbol A."
 Kelvin = "SI base unit of thermodynamic temperature, symbol K."
 Mole = "SI base unit of amount of substance, symbol mol."
 Candela = "SI base unit of luminous intensity, symbol cd."
 DefiningConstant = "Constant assigned an exact fixed numerical value in SI and used within SI unit definitions."
}

RELATIONS {
 SIBaseUnits --is_part_of--> InternationalSystemOfUnits
 Second --is_SI_base_unit_of--> Time
 Metre --is_SI_base_unit_of--> Length
 Kilogram --is_SI_base_unit_of--> Mass
 Ampere --is_SI_base_unit_of--> ElectricCurrent
 Kelvin --is_SI_base_unit_of--> ThermodynamicTemperature
 Mole --is_SI_base_unit_of--> AmountOfSubstance
 Candela --is_SI_base_unit_of--> LuminousIntensity
 SIDerivedUnit --is_constructed_from--> SIBaseUnits
 Metrology --realises--> SIUnits
 MeasurementTraceability --links--> MeasurementResultToSIReference
 Provenance --records--> SIDefinitionAndRealisationHistory
}

OPERATORS {
 BASE_UNIT(quantity) := canonical_SI_base_unit(quantity)
 SYMBOL(unit) := canonical_SI_symbol(unit)
 DIM(unit) := SI_base_dimension(unit)
 DERIVE(exponents) := product_of_SI_base_units(exponents)
 CANONICALISE(expression) := coherent_SI_unit_expression(expression)
 CONVERT(value,source,target) := compatible_unit_conversion(value,source,target)
 TRACE(result) := metrological_traceability_to_SI(result)
}

AXIOMS {
 A1 = "The SI contains exactly seven base units."
 A2 = "Each SI base unit is associated with one SI base quantity."
 A3 = "SI base-unit symbols are case-sensitive."
 A4 = "Coherent SI derived units are expressible algebraically through powers of SI base units."
 A5 = "Base-versus-derived quantity status is conventional within the chosen system of quantities."
 A6 = "Modern SI definitions are linked through defining constants assigned exact numerical values."
 A7 = "Metrological realisation is distinct from the abstract definition of an SI unit."
 A8 = "SI-base-unit reasoning requires explicit identity, quantity, dimension, symbol, definition and provenance."
}

REASONING {
 R1_CONTEXT = identify(quantity,unit_symbol,dimension,definition_context,conversion_or_realisation_need)
 R2_IDENTITY = resolve_second_metre_kilogram_ampere_kelvin_mole_or_candela)
 R3_QUANTITY = map_unit_to_corresponding_SI_base_quantity)
 R4_DIMENSION = map_quantity_to_base_dimensional_signature)
 R5_DEFINITION = identify_relevant_defining_constant_and_exact_SI_definition_relationship)
 R6_DERIVATION = if_expression_is_derived_expand_into_base_unit_exponents)
 R7_CONVERSION = if_nonbase_representation_convert_to_compatible_SI_representation)
 R8_TRACEABILITY = if_measurement_context_identify_realisation_calibration_and_traceability_chain)
 R9_VALIDATE = check_symbol_case_quantity_kind_dimension_and_coherent_expression)
 R10_PROVENANCE = record_SI_definition_version_standard_source_and_realisation_context)
}

CONSTRAINTS {
 C1 = "The kilogram is the only SI base-unit name containing an SI prefix as part of its historical name."
 C2 = "Unit symbols are case-sensitive."
 C3 = "The kelvin is the SI unit of thermodynamic temperature; degree Celsius is a related scale representation."
 C4 = "The mole requires specification of elementary entities when scientifically relevant."
 C5 = "Candela semantics concern luminous intensity rather than general radiant power."
 C6 = "A coherent derived expression can be equivalent to a named SI derived unit."
 C7 = "Dimensional equivalence alone does not always establish quantity-kind equivalence."
 C8 = "Realisation methods can evolve while SI definitions remain governed by defining constants."
 C9 = "Prefixes applied to kilogram-based mass units require correct treatment of the gram relationship."
 C10 = "Traceability to SI is a calibration-chain property, not simply use of SI symbols."
}

SEMANTIC_EQUIVALENCE {
 "InternationalSystemOfUnits" <=> "SI"
 "InternationalSystemOfQuantities" <=> "ISQ"
 "SIBaseUnit" <=> "SI Base Unit"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
}

VALIDATION {
 V1 = "Base-unit identity is one of second, metre, kilogram, ampere, kelvin, mole or candela."
 V2 = "Canonical unit symbol is correct and case-sensitive."
 V3 = "Corresponding SI base quantity is documented."
 V4 = "Corresponding base dimension is documented."
 V5 = "Defining-constant relationship is documented where definition semantics are required."
 V6 = "Derived expressions preserve coherent SI unit algebra."
 V7 = "Conversions preserve quantity kind and dimensional compatibility."
 V8 = "Measurement applications distinguish SI definition from practical realisation."
 V9 = "Traceability claims retain calibration and reference evidence."
 V10 = "SI definitions and relationships are traceable to documented standard versions and provenance."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 SI_BASE_UNITS_DEFINITION = 0.99
 UNIT_IDENTITY_REASONING = 0.99
 BASE_QUANTITY_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 DEFINING_CONSTANT_REASONING = 0.99
 DERIVED_UNIT_REASONING = 0.99
 TRACEABILITY_REASONING = 0.98
 POLICY = "Reduce confidence when unit identity, symbol, quantity kind, dimension, definition version or traceability evidence are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [SemanticSearch,OntologyGrounding,SIBaseUnitReasoning,UnitIdentityReasoning,BaseQuantityReasoning,BaseDimensionReasoning,DefiningConstantReasoning,SIUnitDefinitionReasoning,DerivedUnitReasoning,UnitAlgebraReasoning,UnitConversionReasoning,MetrologyReasoning,TraceabilityReasoning,MeasurementReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference]
 NORMALISE {
  "SI base units" -> SIBaseUnits
  "SI" -> InternationalSystemOfUnits
  "ISQ" -> InternationalSystemOfQuantities
  "meter" -> Metre
 }
}

EXECUTION_RULES {
 E1 = "If one of the seven SI base units or the base-unit system is primary, activate SIBaseUnitsOntology."
 E2 = "Resolve canonical unit name and case-sensitive symbol."
 E3 = "Map each base unit to its corresponding SI base quantity and dimension."
 E4 = "Use current SI defining-constant semantics when reasoning about formal definitions."
 E5 = "Distinguish abstract unit definition from practical metrological realisation."
 E6 = "Expand derived SI expressions through algebraic powers of base units when required."
 E7 = "Preserve quantity-kind semantics when checking dimensional equivalence."
 E8 = "Treat traceability to SI as a documented calibration-chain property."
 E9 = "Record SI standard versions, definition sources and provenance."
}

RECURSION {
 ENTRY = SIBaseUnits
 EXPAND(SIBaseUnits) -> [Second,Metre,Kilogram,Ampere,Kelvin,Mole,Candela,Time,Length,Mass,ElectricCurrent,ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity,TimeDimension,LengthDimension,MassDimension,ElectricCurrentDimension,ThermodynamicTemperatureDimension,AmountOfSubstanceDimension,LuminousIntensityDimension,DefiningConstant,SpeedOfLight,PlanckConstant,ElementaryCharge,BoltzmannConstant,AvogadroConstant,SIDerivedUnit,UnitAlgebra,DimensionalAnalysis,Measurement,Metrology,ReferenceStandard,MeasurementTraceability,SIUnitProvenance]
 EXPAND(SIBaseUnitFamilies) -> [SecondAndTimeSemantics,MetreAndLengthSemantics,KilogramAndMassSemantics,AmpereAndElectricCurrentSemantics,KelvinAndThermodynamicTemperatureSemantics,MoleAndAmountOfSubstanceSemantics,CandelaAndLuminousIntensitySemantics,DefiningConstantsRealisationTraceabilityAndProvenance]
 STOP_CONDITION = "Stop when base-unit identity, symbol, quantity, dimension, definition, realisation and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Measurement & Units Ontologies"
 RELATED_ONTOLOGIES = ["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","SI Derived Units","Dimensional Analysis Ontology","Measurement Uncertainty Ontology","Verification & Validation"]
 ROUTE_RULES = [
  "SI Base Units -> Quantity and Physical Quantity ontologies for base-quantity semantics",
  "SI Base Units -> Dimension Ontology for base-dimensional structure",
  "SI Base Units -> Unit Ontology for unit identity, algebra and conversion",
  "SI Base Units -> Metrology and Reference Standard for realisation and traceability",
  "SI Base Units -> SI Derived Units for coherent derived-unit construction"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible SI definition, realisation or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = ["Preserve base-unit-versus-derived-unit distinction.","Preserve unit-versus-quantity distinction.","Preserve unit-versus-dimension distinction.","Preserve SI-definition-versus-practical-realisation distinction.","Preserve symbol-case semantics.","Preserve SI-symbol-use-versus-metrological-traceability distinction.","Preserve machine-readable SI-base-unit semantics."]
}

OUTPUT {
 CANONICAL_DEFINITION = "The SI base units are second, metre, kilogram, ampere, kelvin, mole and candela."
 UNIT_SUMMARY = "Each SI base unit has a canonical name, case-sensitive symbol and corresponding SI base quantity."
 DIMENSION_SUMMARY = "The seven base quantities provide the base dimensions used to express derived dimensional signatures."
 DEFINITION_SUMMARY = "Modern SI definitions are expressed through defining constants assigned exact numerical values."
 DERIVATION_SUMMARY = "Coherent SI derived units are algebraic products of powers of SI base units."
 REALISATION_SUMMARY = "Practical realisation and metrological traceability connect abstract SI definitions to measurement results."
}

FLOW {
 INPUT
 -> detect_SI_base_units_context
 -> identify_quantity_unit_symbol_dimension_definition_context_conversion_or_realisation_need
 -> resolve_second_metre_kilogram_ampere_kelvin_mole_or_candela
 -> map_unit_to_corresponding_SI_base_quantity
 -> map_quantity_to_base_dimensional_signature
 -> identify_relevant_defining_constant_and_exact_SI_definition_relationship
 -> if_expression_is_derived_expand_into_base_unit_exponents
 -> if_measurement_context_identify_realisation_calibration_and_traceability_chain
 -> check_symbol_case_quantity_kind_dimension_and_coherent_expression
 -> record_SI_definition_version_standard_source_and_realisation_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-BASE-UNITS-V1"
}

}

END_FLOW