Fundamental Physical Quantities

AI INTERPRETATION NOTE
This Flow Algebra defines the Fundamental Physical Quantities framework within the Kireth Research Semantic Library. It formalises foundational quantity kinds, dimensions, units, values, measurement, uncertainty, dimensional analysis and derived quantities.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Fundamental Physical Quantities"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Fundamental Physical Quantities"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/fundamental-physical-quantities.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=FundamentalPhysicalQuantities
 ENTITY_CLASS=FoundationalPhysicalQuantityFramework
 DEFINITION="Fundamental physical quantities are independently selected quantity kinds forming the basis of a quantity system from which other quantities are derived through defined quantity equations."
 SEMANTIC_ROLE="Machine-readable framework for base quantities, dimensions, units, measurement, quantity calculus, dimensional analysis and derivation."
}
SCOPE {
 INCLUDE=[
 FundamentalPhysicalQuantity,BaseQuantity,PhysicalQuantity,Quantity,QuantityKind,
 QuantitySystem,BaseQuantitySet,DerivedQuantity,QuantityEquation,QuantityCalculus,
 QuantityValue,NumericalValue,Unit,MeasurementUnit,BaseUnit,DerivedUnit,
 CoherentUnit,SystemOfUnits,InternationalSystemOfUnits,SI,Dimension,BaseDimension,
 DerivedDimension,DimensionalExponent,DimensionalProduct,DimensionalEquation,
 DimensionalAnalysis,DimensionlessQuantity,Length,Mass,Time,ElectricCurrent,
 ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity,Metre,Kilogram,
 Second,Ampere,Kelvin,Mole,Candela,LengthDimension,MassDimension,TimeDimension,
 ElectricCurrentDimension,ThermodynamicTemperatureDimension,
 AmountOfSubstanceDimension,LuminousIntensityDimension,Area,Volume,Velocity,
 Acceleration,Momentum,Force,Pressure,Energy,Work,Power,Frequency,ElectricCharge,
 ElectricPotentialDifference,Resistance,Conductance,Capacitance,Inductance,
 MagneticFlux,MagneticFluxDensity,LuminousFlux,Illuminance,CatalyticActivity,
 RadionuclideActivity,AbsorbedDose,ScalarQuantity,VectorQuantity,TensorQuantity,
 ExtensiveQuantity,IntensiveQuantity,ReferenceQuantity,MeasuredQuantity,Measurand,
 Measurement,MeasurementPrinciple,MeasurementMethod,MeasurementProcedure,
 MeasurementModel,MeasurementEquation,MeasurementSystem,MeasuringInstrument,
 MeasurementResult,ReferenceQuantityValue,MeasurementError,MeasurementUncertainty,
 StandardUncertainty,CombinedStandardUncertainty,ExpandedUncertainty,CoverageFactor,
 UncertaintyBudget,Accuracy,Precision,Repeatability,Reproducibility,Resolution,
 Sensitivity,Calibration,CalibrationHierarchy,ReferenceStandard,PrimaryStandard,
 SecondaryStandard,WorkingStandard,MeasurementTraceability,MetrologicalTraceability,
 TraceabilityChain,Metrology,ScientificMeasurement,Observation,DataAcquisition,
 UnitConversion,ConversionFactor,ExactConversion,Prefix,SIPrefix,
 UnitCompatibility,DimensionalCompatibility,QuantityCompatibility,
 SemanticCompatibility,EquationConsistency,DimensionalHomogeneity,PhysicalLaw,
 ConstitutiveRelationship,ConservationLawRelationship,UncertaintyPropagation,
 CorrelationRelationship,CovarianceRelationship,Verification,Validation,
 ErrorAnalysis,Provenance,QuantityProvenance,MeasurementProvenance,
 UnitProvenance,CalibrationProvenance,DefinitionProvenance,
 BIPMrelationship,SIbrochureRelationship,VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[DerivedQuantityWhenIndependentBaseStatusIsNotIntended,NonPhysicalAbstractQuantityWithoutMeasurementSemantics,UnitWhenQuantityKindIsPrimary]
 DISAMBIGUATION_RULE="Distinguish a physical quantity from its numerical value, unit, dimension, symbol and measured result. Base or fundamental status belongs to a specified quantity system."
}
CORE_CONCEPTS {
 FundamentalPhysicalQuantity="Quantity selected by convention as independent within a specified quantity system."
 BaseQuantity="Quantity in a conventionally chosen independent subset of a quantity system."
 DerivedQuantity="Quantity defined through a quantity equation in terms of other quantities."
 QuantityKind="Common aspect of mutually comparable quantities."
 QuantityValue="Number and reference together expressing the magnitude of a quantity."
 Dimension="Expression of dependence of a quantity kind on base quantities."
 Unit="Reference quantity adopted by convention for quantities of the same kind."
 Measurement="Process of experimentally obtaining quantity values attributable to a measurand."
}
BASE_QUANTITY_SYSTEM {
 SYSTEM="International System of Quantities / SI context"
 BASE_QUANTITIES=[Length,Mass,Time,ElectricCurrent,ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity]
 BASE_DIMENSIONS=[LengthDimension,MassDimension,TimeDimension,ElectricCurrentDimension,ThermodynamicTemperatureDimension,AmountOfSubstanceDimension,LuminousIntensityDimension]
 SI_BASE_UNITS=[Metre,Kilogram,Second,Ampere,Kelvin,Mole,Candela]
 SYMBOLIC_DIMENSIONS=["Length->L","Mass->M","Time->T","ElectricCurrent->I","ThermodynamicTemperature->Theta","AmountOfSubstance->N","LuminousIntensity->J"]
}
RELATIONS {
 FundamentalPhysicalQuantity--is_type_of-->PhysicalQuantity
 BaseQuantity--is_selected_within-->QuantitySystem
 BaseQuantitySet--generates-->DerivedQuantitySystem
 Quantity--has_kind-->QuantityKind
 Quantity--has_value-->QuantityValue
 QuantityKind--has_dimension-->Dimension
 QuantityValue--uses-->Unit
 BaseQuantity--has_base_dimension-->BaseDimension
 BaseUnit--is_unit_of-->BaseQuantity
 DerivedQuantity--is_defined_by-->QuantityEquation
 DerivedUnit--is_derived_from-->BaseUnits
 Measurement--targets-->Measurand
 Measurement--produces-->MeasurementResult
 MeasurementResult--has_associated-->MeasurementUncertainty
 Calibration--supports-->MeasurementTraceability
 DimensionalAnalysis--tests-->QuantityEquation
}
OPERATORS {
 QUANTITY(kind,value,unit):=physical_quantity(kind,value,unit)
 DIM(quantity_kind):=dimension_of(quantity_kind)
 VALUE(quantity):=quantity_value(quantity)
 UNIT(quantity_value):=reference_unit(quantity_value)
 DERIVE_QUANTITY(equation,inputs):=evaluate_quantity_equation(equation,inputs)
 DERIVE_DIMENSION(equation,input_dimensions):=dimension_algebra(equation,input_dimensions)
 CHECK_HOMOGENEITY(equation):=verify_dimensional_homogeneity(equation)
 CONVERT(value,source_unit,target_unit):=compatible_unit_conversion(value,source_unit,target_unit)
 MEASURE(measurand,method):=measurement_result(measurand,method)
 PROPAGATE_UNCERTAINTY(model,inputs):=uncertainty_propagation(model,inputs)
 TRACE(result):=metrological_traceability_chain(result)
}
AXIOMS {
 A1="A quantity is distinct from its numerical value, unit, dimension and symbol."
 A2="Fundamental or base status is defined relative to a specified quantity system."
 A3="Base quantities are conventionally selected as mutually independent within that system."
 A4="Derived quantities are related to base quantities through quantity equations."
 A5="Dimensions describe quantity-kind dependence on base quantities independently of unit magnitude."
 A6="Units provide agreed references for expressing quantity values."
 A7="A valid physical equation must preserve quantity semantics and dimensional homogeneity."
 A8="Dimensional equality does not by itself imply equality of quantity kind."
 A9="Measurement results require uncertainty and sufficient provenance for rigorous interpretation."
 A10="Metrological traceability links measurement results through documented calibrations to stated references."
}
REASONING {
 R1=identify(quantity_system,physical_domain,quantity_kind,value,unit,dimension,measurement_context)
 R2=distinguish_quantity_quantity_kind_value_unit_dimension_symbol_and_measurement_result)
 R3=determine_base_derived_dimensionless_or_other_status_within_named_system)
 R4=resolve_base_dimension_or_derived_dimensional_expression)
 R5=resolve_base_unit_derived_unit_prefix_conversion_and_coherence)
 R6=identify_quantity_equation_and_dependencies)
 R7=check_quantity_semantics_dimensional_homogeneity_and_unit_compatibility)
 R8=identify_measurand_method_instrument_calibration_and_reference)
 R9=evaluate_input_uncertainties_correlations_model_and_propagation)
 R10=record_quantity_system_definition_unit_standard_measurement_calibration_and_traceability)
}
CONSTRAINTS {
 C1="Fundamental status must be interpreted relative to an identified quantity system."
 C2="A unit must not be treated as the physical quantity itself."
 C3="A dimension must not be treated as a unit."
 C4="A numerical value without a reference can be insufficient to specify a dimensional quantity."
 C5="Quantities with identical dimensions can have different physical meanings."
 C6="Dimensionless quantities can retain distinct quantity kinds and semantics."
 C7="Derived quantities must preserve dependencies stated by defining quantity equations."
 C8="Unit conversion requires quantity-kind and dimensional compatibility."
 C9="Measurement uncertainty is distinct from measurement error."
 C10="Measured values should retain method, calibration, uncertainty and traceability provenance where material."
}
SEMANTIC_EQUIVALENCE {
 "BasePhysicalQuantity"<=>"BaseQuantity"
 "FundamentalQuantity"<=>"FundamentalPhysicalQuantity"
 "PhysicalQuantity"<=>"QuantityInPhysicalContext"
 "MeasurementUnit"<=>"Unit"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}
VALIDATION {
 V1="Quantity system is identified when base or fundamental status is asserted."
 V2="Quantity, kind, value, unit and dimension remain distinct."
 V3="Base quantities are independent according to the selected quantity-system convention."
 V4="Derived quantities have valid defining quantity equations."
 V5="Dimensional expressions are algebraically consistent."
 V6="Physical equations are dimensionally homogeneous."
 V7="Unit conversions preserve quantity kind and scale correctly."
 V8="Dimensionless quantities retain semantic quantity-kind distinctions."
 V9="Measurement results retain uncertainty and relevant conditions."
 V10="Calibration, standards and traceability provenance are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 QUANTITY_IDENTITY_REASONING=0.99
 BASE_QUANTITY_REASONING=0.99
 DIMENSION_REASONING=0.99
 UNIT_REASONING=0.99
 DERIVED_QUANTITY_REASONING=0.99
 MEASUREMENT_REASONING=0.98
 UNCERTAINTY_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when quantity system, quantity kind, unit, dimension, defining equation, measurement conditions, calibration or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,PhysicalQuantityReasoning,FundamentalQuantityReasoning,BaseQuantityReasoning,DerivedQuantityReasoning,QuantityCalculus,DimensionalReasoning,UnitReasoning,SIReasoning,MeasurementReasoning,MetrologyReasoning,UncertaintyReasoning,TraceabilityReasoning,EquationValidation,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "fundamental physical quantity"->FundamentalPhysicalQuantity
  "fundamental quantity"->FundamentalPhysicalQuantity
  "base quantity"->BaseQuantity
  "physical quantity"->PhysicalQuantity
  "SI"->InternationalSystemOfUnits
 }
}
EXECUTION_RULES {
 E1="Activate FundamentalPhysicalQuantities when reasoning concerns foundational quantity kinds, dimensions, units or derived quantities."
 E2="Identify the quantity system before asserting base or fundamental status."
 E3="Separate quantity, kind, value, unit, dimension and symbol."
 E4="Map SI base quantities to metre, kilogram, second, ampere, kelvin, mole and candela."
 E5="Derive non-base quantities through explicit quantity equations and dimensional algebra."
 E6="Do not infer semantic equivalence from dimensional equivalence alone."
 E7="Validate physical equations for quantity meaning and dimensional homogeneity."
 E8="For measurement contexts, preserve measurand, method, calibration, uncertainty and traceability."
 E9="Record definition, unit-system, standard-version and measurement provenance."
}
RECURSION {
 ENTRY=FundamentalPhysicalQuantities
 EXPAND(FundamentalPhysicalQuantities)->[
 PhysicalQuantity,QuantityKind,QuantitySystem,BaseQuantity,DerivedQuantity,
 QuantityValue,Unit,Dimension,DimensionalAnalysis,Length,Mass,Time,
 ElectricCurrent,ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity,
 Metre,Kilogram,Second,Ampere,Kelvin,Mole,Candela,Area,Volume,Velocity,
 Acceleration,Force,Pressure,Energy,Power,Frequency,ElectricCharge,
 ElectricPotentialDifference,Resistance,Capacitance,Inductance,MagneticFlux,
 MagneticFluxDensity,LuminousFlux,Illuminance,CatalyticActivity,
 RadionuclideActivity,AbsorbedDose,Measurement,Measurand,MeasurementResult,
 MeasurementUncertainty,Calibration,ReferenceStandard,MeasurementTraceability,
 Metrology,UnitConversion,Verification,Validation,Provenance
 ]
 EXPAND(BaseQuantityFamilies)->[
 LengthSpaceGeometryAndMetre,
 MassMatterInertiaAndKilogram,
 TimeDurationFrequencyAndSecond,
 ElectricCurrentChargeElectromagnetismAndAmpere,
 ThermodynamicTemperatureThermalStateAndKelvin,
 AmountOfSubstanceChemicalAmountAndMole,
 LuminousIntensityPhotometryAndCandela
 ]
 EXPAND(DerivationFamilies)->[
 KinematicsFromLengthAndTime,
 MechanicsFromMassLengthAndTime,
 ThermodynamicsFromTemperatureAndMechanicalQuantities,
 ElectromagnetismFromCurrentTimeMassAndLength,
 ChemistryFromAmountOfSubstanceAndTime,
 PhotometryFromLuminousIntensityAndGeometry,
 MeasurementUncertaintyCalibrationAndTraceability
 ]
 STOP_CONDITION="Stop when quantity identity, system status, dimensional dependencies, units, defining equations, measurement semantics and provenance are resolved."
}
ROUTING {
 PARENT_ONTOLOGY="Measurement & Units Ontologies"
 RELATED_ONTOLOGIES=["Foundations of Measurement","Measurement Ontology","Scientific Measurement Ontology 2","Metrology Ontology","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Scale Ontology","Measurement System Ontology","Reference Standard Ontology","SI Base Units","SI Derived Units","SI Units Ontology","Physics Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Fundamental Physical Quantities -> Quantity Ontology for quantity identity and kind semantics",
 "Fundamental Physical Quantities -> Dimension Ontology for dimensional structure",
 "Fundamental Physical Quantities -> Unit Ontology for unit semantics",
 "Fundamental Physical Quantities -> SI Base Units for canonical base-unit definitions",
 "Fundamental Physical Quantities -> SI Derived Units for derived-unit relationships",
 "Fundamental Physical Quantities -> Measurement Ontology for measurands and results",
 "Fundamental Physical Quantities -> Metrology for calibration, standards and traceability",
 "Fundamental Physical Quantities -> Physics Ontology for physical laws",
 "Fundamental Physical Quantities -> Verification & Validation for equation consistency"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="quantity-system or foundational semantic change"
 MINOR="new compatible quantity, dimensional, unit or measurement relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve quantity-versus-unit distinction.","Preserve quantity-versus-value distinction.","Preserve quantity-kind-versus-dimension distinction.","Preserve base-versus-derived status relative to the named system.","Preserve dimensional-equivalence-versus-semantic-equivalence distinction.","Preserve dimensionless quantity-kind semantics.","Preserve uncertainty-versus-error distinction.","Preserve machine-readable foundational quantity semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="Fundamental physical quantities are independently selected quantity kinds forming the basis of a specified quantity system."
 SI_BASE_QUANTITY_SUMMARY="In the SI context the seven base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity."
 SI_BASE_UNIT_SUMMARY="Their corresponding SI base units are metre, kilogram, second, ampere, kelvin, mole and candela."
 DERIVATION_SUMMARY="Derived physical quantities are constructed through quantity equations and inherit dimensional expressions from their dependencies."
 SEMANTIC_SUMMARY="Quantity, numerical value, unit, dimension and measurement result are distinct semantic entities."
 MEASUREMENT_SUMMARY="Measured physical quantities require explicit measurand, method, result, uncertainty, calibration and traceability semantics where relevant."
}
FLOW {
 INPUT
 -> detect_fundamental_physical_quantity_context
 -> identify_quantity_system_physical_domain_quantity_kind_value_unit_dimension_and_measurement_context
 -> distinguish_quantity_kind_value_unit_dimension_symbol_and_measurement_result
 -> determine_base_derived_dimensionless_or_other_status
 -> resolve_base_or_derived_dimension
 -> resolve_base_or_derived_unit_and_conversion
 -> identify_quantity_equation_and_dependencies
 -> verify_quantity_semantics_and_dimensional_homogeneity
 -> identify_measurement_method_calibration_reference_and_uncertainty_if_applicable
 -> record_quantity_system_definition_standard_measurement_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-FUNDAMENTAL-PHYSICAL-QUANTITIES-V1"
}
}
END_FLOW