SI Units Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the SI Units Ontology within the Kireth Research Semantic Library. It formalises the International System of Units as a coherent measurement system, including SI base units, derived units, prefixes, defining constants, unit expressions, conversions, dimensional consistency, metrological realisation, traceability, validation and provenance.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = SIUnits
 ENTITY_CLASS = InternationalSystemOfUnitsFramework
 PRIMARY_CONTEXT = SIBaseUnits
 DEFINITION = "SI units form the coherent measurement-unit system of the International System of Units, comprising seven base units together with coherent derived units and standard rules for prefixes, symbols, expressions and realisation."
 SYMBOLIC_FORMS = ["SI={base_units,derived_units,prefixes,defining_constants}","Q=value*SI_unit","u_derived=product(u_base^exponents)"]
 SEMANTIC_ROLE = "Machine-readable semantics for SI unit identity, base and derived units, prefixes, symbols, dimensions, definitions, conversions, realisation and traceability."
}

SCOPE {
 INCLUDE = [
 SIUnits,InternationalSystemOfUnits,SI,InternationalSystemOfQuantities,ISQ,
 SIBaseUnits,SIBaseUnit,SIBaseQuantity,SIDerivedUnit,SIDerivedQuantity,
 Unit,MeasurementUnit,BaseUnit,DerivedUnit,CoherentUnit,CanonicalUnit,
 UnitSystem,SystemOfUnits,Quantity,QuantityKind,PhysicalQuantity,
 QuantityValue,BaseQuantity,DerivedQuantity,Dimension,BaseDimension,
 DerivedDimension,DimensionalSignature,DimensionlessQuantity,
 Second,Metre,Kilogram,Ampere,Kelvin,Mole,Candela,Hertz,Newton,Pascal,
 Joule,Watt,Coulomb,Volt,Farad,Ohm,Siemens,Weber,Tesla,Henry,Lumen,Lux,
 Becquerel,Gray,Sievert,Katal,Radian,Steradian,UnitSymbol,UnitName,
 UnitIdentifier,UnitExpression,CompoundUnit,ProductUnit,QuotientUnit,
 PowerUnit,InverseUnit,UnitExponent,UnitAlgebra,QuantityCalculus,
 Prefix,SIPrefix,DecimalPrefix,PrefixSymbol,PrefixFactor,DefiningConstant,
 PhysicalConstant,DefinedConstant,Caesium133FrequencyRelationship,
 SpeedOfLight,PlanckConstant,ElementaryCharge,BoltzmannConstant,
 AvogadroConstant,LuminousEfficacyRelationship,ExactValue,UnitDefinition,
 UnitRealisation,MiseEnPratiqueRelationship,UnitConversion,ConversionRule,
 ConversionFactor,ConversionOffset,ExactConversion,MultiplicativeConversion,
 AffineConversion,UnitCompatibility,QuantityCompatibility,
 DimensionalCompatibility,UnitEquivalence,Canonicalisation,
 DimensionalAnalysis,DimensionalConsistency,DimensionalHomogeneity,
 Measurement,Measurand,MeasurementResult,MeasurementUncertainty,
 ScientificMeasurement,MeasurementSystem,Metrology,Calibration,
 ReferenceStandard,MeasurementStandard,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,CalibrationHierarchy,
 NationalMetrologyInstitute,NMI,BIPMrelationship,CGPMrelationship,
 CIPMrelationship,SIbrochureRelationship,VIMRelationship,GUMRelationship,
 Verification,Validation,UnitValidation,ConversionValidation,
 DimensionalValidation,ConsistencyCheck,ErrorAnalysis,
 ReproducibilityOntologyRelationship,Provenance,SIUnitProvenance,
 StandardProvenance,MeasurementProvenance,Metadata,UnitMetadata,
 StandardVersion,UCUMrelationship,QUDTRelationship,OMRelationship,
 SymbolicComputation,AIComputationalMathematics
 ]
 EXCLUDE_AS_PRIMARY = [
 NonSIUnitSystemsWhenSIIsNotTheReferenceSystem,
 PhysicalQuantityDefinitionsWithoutUnitSystemSemantics,
 MetrologyWhenCalibrationAndTraceabilityRatherThanSIUnitStructureArePrimary
 ]
 DISAMBIGUATION_RULE = "When the International System of Units, its base and derived units, prefixes, symbols, definitions or coherent unit algebra are primary, interpret the context as SI units."
}

CORE_CONCEPTS {
 SIUnits = "Complete coherent unit system of the International System of Units."
 SIBaseUnit = "One of the seven SI base units."
 SIDerivedUnit = "Coherent unit derived algebraically from SI base units."
 CoherentUnit = "Derived unit obtained without an additional numerical factor other than one."
 SIPrefix = "Decimal prefix used to form multiples and submultiples according to SI rules."
 DefiningConstant = "Constant assigned an exact numerical value and used in the modern SI definition framework."
 UnitExpression = "Algebraic representation of an SI unit."
 UnitRealisation = "Practical implementation of an SI unit definition in measurement."
}

RELATIONS {
 SIUnits --contains--> SIBaseUnits
 SIUnits --contains--> SIDerivedUnits
 SIBaseUnit --corresponds_to--> SIBaseQuantity
 SIDerivedUnit --is_derived_from--> SIBaseUnits
 Unit --has_dimension--> Dimension
 SIPrefix --scales--> Unit
 UnitSymbol --denotes--> Unit
 UnitExpression --combines--> Units
 DefiningConstant --supports_definition_of--> SIUnits
 UnitRealisation --implements--> SIUnitDefinition
 UnitConversion --maps--> CompatibleUnits
 Metrology --realises--> SIUnits
 MeasurementTraceability --links--> MeasurementResultToSIReference
 Provenance --records--> SIUnitDefinitionAndUse
}

OPERATORS {
 SI_UNIT(name,symbol,kind,dimension) := canonical_SI_unit(name,symbol,kind,dimension)
 DERIVE_UNIT(exponents) := coherent_product_of_SI_base_units(exponents)
 DIM(unit) := dimensional_signature(unit)
 PREFIX(unit,prefix) := decimal_scaled_SI_unit(unit,prefix)
 COMPATIBLE(u1,u2) := compatible_quantity_kind_and_dimension(u1,u2)
 CONVERT(value,u1,u2) := valid_conversion_rule(u1,u2)(value)
 CANONICALISE(expression) := canonical_SI_unit_expression(expression)
 TRACE(result) := metrological_traceability_to_SI(result)
}

AXIOMS {
 A1 = "The SI is a coherent system built from seven base units and derived units."
 A2 = "Coherent SI derived units are products of powers of SI base units with numerical factor one."
 A3 = "Unit symbols and prefix symbols are case-sensitive."
 A4 = "SI prefixes represent powers of ten and modify unit magnitude without changing quantity kind."
 A5 = "Unit conversion preserves the represented quantity when units are compatible."
 A6 = "Modern SI definitions are founded on exact numerical values assigned to defining constants."
 A7 = "Abstract SI definitions and practical metrological realisations are distinct."
 A8 = "SI-unit reasoning requires explicit unit identity, quantity kind, dimension, symbol, definition and provenance."
}

REASONING {
 R1_CONTEXT = identify(quantity_kind,unit_name,symbol,dimension,prefix,conversion_definition_or_realisation_need)
 R2_IDENTITY = resolve_base_derived_named_or_compound_SI_unit)
 R3_QUANTITY = identify_corresponding_quantity_kind_and_quantity_equation)
 R4_DIMENSION = derive_or_validate_dimensional_signature)
 R5_EXPRESSION = parse_prefix_products_quotients_powers_and_named_derived_units)
 R6_DEFINITION = identify_defining_constant_or_coherent_derivation_relationship)
 R7_CONVERSION = if_required_apply_exact_multiplicative_affine_or_declared_conversion)
 R8_REALISATION = if_measurement_context_identify_realisation_calibration_and_traceability)
 R9_VALIDATE = check_symbol_case_prefix_rules_dimension_quantity_kind_and_coherence)
 R10_PROVENANCE = record_SI_standard_version_definition_source_conversion_rule_and_context)
}

CONSTRAINTS {
 C1 = "SI symbols are case-sensitive."
 C2 = "The kilogram requires special prefix handling because prefixes for mass are applied through the gram."
 C3 = "Degree Celsius and kelvin share interval magnitude but differ in scale-origin semantics."
 C4 = "Equal dimensions do not necessarily imply identical quantity kinds."
 C5 = "Dimensionless SI expressions can retain distinct quantity meanings."
 C6 = "Prefixes must follow SI syntax rules."
 C7 = "Non-SI units accepted for use with SI remain distinct from SI units."
 C8 = "Traceability to SI requires documented calibration relationships, not merely SI notation."
 C9 = "Unit conversion must preserve uncertainty where relevant."
 C10 = "Historical SI definitions must not silently replace the applicable definition version."
}

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

VALIDATION {
 V1 = "Unit identity and canonical symbol are documented."
 V2 = "Base or derived status is documented."
 V3 = "Corresponding quantity kind and dimension are documented."
 V4 = "Compound-unit algebra is dimensionally consistent."
 V5 = "Prefixes follow SI decimal-prefix rules."
 V6 = "Conversions preserve quantity kind and unit compatibility."
 V7 = "Named derived units map correctly to coherent base-unit expressions."
 V8 = "Definition and practical realisation are distinguished."
 V9 = "Traceability claims retain calibration and reference evidence."
 V10 = "SI unit definitions are traceable to documented standard versions and provenance."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 SI_UNITS_DEFINITION = 0.99
 UNIT_IDENTITY_REASONING = 0.99
 DERIVED_UNIT_REASONING = 0.99
 PREFIX_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 CONVERSION_REASONING = 0.99
 TRACEABILITY_REASONING = 0.98
 POLICY = "Reduce confidence when unit identity, symbol, quantity kind, dimension, prefix syntax, definition version or traceability evidence are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,SIUnitReasoning,SIBaseUnitReasoning,
 SIDerivedUnitReasoning,UnitIdentityReasoning,PrefixReasoning,
 UnitAlgebraReasoning,DimensionReasoning,DefiningConstantReasoning,
 UnitConversionReasoning,MetrologyReasoning,TraceabilityReasoning,
 MeasurementReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,
 RecursiveInference
 ]
 NORMALISE {
  "SI units" -> SIUnits
  "SI" -> InternationalSystemOfUnits
  "ISQ" -> InternationalSystemOfQuantities
  "meter" -> Metre
 }
}

EXECUTION_RULES {
 E1 = "If SI unit structure, identity, derivation or notation is primary, activate SIUnitsOntology."
 E2 = "Resolve canonical unit name and case-sensitive symbol before interpretation."
 E3 = "Identify quantity kind and dimensional signature before conversion."
 E4 = "Expand derived units into coherent base-unit expressions when needed."
 E5 = "Apply SI prefixes according to decimal-prefix syntax and mass-specific rules."
 E6 = "Use defining-constant semantics when formal SI definition reasoning is required."
 E7 = "Distinguish abstract unit definition from practical metrological realisation."
 E8 = "Preserve uncertainty and quantity meaning through conversions."
 E9 = "Record standard versions, definition sources and provenance."
}

RECURSION {
 ENTRY = SIUnits
 EXPAND(SIUnits) -> [
 InternationalSystemOfUnits,SI,SIBaseUnits,SIBaseUnit,SIDerivedUnit,
 SIPrefix,Second,Metre,Kilogram,Ampere,Kelvin,Mole,Candela,Hertz,
 Newton,Pascal,Joule,Watt,Coulomb,Volt,Farad,Ohm,Siemens,Weber,Tesla,
 Henry,Lumen,Lux,Becquerel,Gray,Sievert,Katal,Radian,Steradian,
 UnitExpression,UnitAlgebra,DimensionalAnalysis,DefiningConstant,
 UnitConversion,UnitRealisation,Metrology,ReferenceStandard,
 MeasurementTraceability,SIUnitProvenance
 ]
 EXPAND(SIUnitFamilies) -> [
 BaseUnitsAndBaseQuantities,NamedDerivedUnits,CoherentCompoundUnits,
 SIPrefixesAndDecimalScaling,DefiningConstantsAndDefinitions,
 UnitConversionAndCanonicalisation,MetrologicalRealisationAndTraceability,
 ValidationStandardsAndProvenance
 ]
 STOP_CONDITION = "Stop when unit identity, symbol, quantity kind, dimension, derivation, prefix, definition, conversion and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Base Units"
 RELATED_ONTOLOGIES = [
 "SI Base Units","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 Units -> SI Base Units for base-unit semantics",
 "SI Units -> Unit Ontology for general unit identity and conversion semantics",
 "SI Units -> Quantity and Physical Quantity ontologies for quantity-kind semantics",
 "SI Units -> Dimension Ontology for dimensional structure",
 "SI Units -> SI Derived Units for named and coherent derived-unit semantics",
 "SI Units -> Metrology and Reference Standard for realisation and traceability",
 "SI Units -> Verification & Validation for symbol, dimension and conversion checks"
 ]
}

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

OUTPUT {
 CANONICAL_DEFINITION = "SI units form the coherent measurement-unit system of the International System of Units, including seven base units and coherent derived units."
 BASE_SUMMARY = "The seven SI base units provide the foundational unit references for the system."
 DERIVED_SUMMARY = "SI derived units are algebraic products of powers of base units, with named units for selected derived quantities."
 PREFIX_SUMMARY = "SI prefixes form decimal multiples and submultiples according to standard symbol and syntax rules."
 DEFINITION_SUMMARY = "Modern SI definitions are founded on defining constants assigned exact numerical values."
 TRACEABILITY_SUMMARY = "Metrological realisation and calibration chains connect SI definitions to measurement results."
}

FLOW {
 INPUT
 -> detect_SI_units_context
 -> identify_quantity_kind_unit_name_symbol_dimension_prefix_conversion_definition_or_realisation_need
 -> resolve_base_derived_named_or_compound_SI_unit
 -> identify_corresponding_quantity_kind_and_quantity_equation
 -> derive_or_validate_dimensional_signature
 -> parse_prefix_products_quotients_powers_and_named_derived_units
 -> identify_defining_constant_or_coherent_derivation_relationship
 -> if_required_apply_exact_multiplicative_affine_or_declared_conversion
 -> if_measurement_context_identify_realisation_calibration_and_traceability
 -> check_symbol_case_prefix_rules_dimension_quantity_kind_and_coherence
 -> record_SI_standard_version_definition_source_conversion_rule_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-BASE-UNITS-SI-UNITS-ONTOLOGY-V1"
}

}

END_FLOW