Physical Quantity Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Physical Quantity Ontology within the Kireth Research Semantic Library. A physical quantity is a measurable property of a physical phenomenon, body, substance or system represented through a magnitude and a reference such as a unit. It formalises physical quantity kinds, dimensions, scalar/vector/tensor forms, base and derived quantities, equations, SI representation, measurement, uncertainty and semantic compatibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Physical Quantity Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Measurement & Units"
 SPECIALISATION = "Foundations of Measurement / Physical Quantity"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/foundations-of-measurement/physical-quantity-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = PhysicalQuantity
 ENTITY_CLASS = PhysicalMeasurablePropertyFramework
 PRIMARY_CONTEXT = QuantityOntology
 DEFINITION = "A physical quantity is a measurable property of a physical phenomenon, body, substance or system whose magnitude can be expressed as a number together with a reference."
 SYMBOLIC_FORMS = ["Q_p=value*unit","[Q_p]=L^a M^b T^c I^d Theta^e N^f J^g","Q_derived=f(Q_1,...,Q_n)","measurement(Q_p)={estimate,unit,uncertainty}"]
 SEMANTIC_ROLE = "Machine-readable semantics for physical measurable properties, dimensions, SI quantities, mathematical character, quantity equations, units and measurement."
}

SCOPE {
 INCLUDE = [
 PhysicalQuantity,Quantity,MeasurableQuantity,QuantityKind,
 PhysicalQuantityKind,QuantityValue,PhysicalQuantityValue,Magnitude,
 NumericalValue,Unit,MeasurementUnit,QuantitySymbol,UnitSymbol,
 Dimension,PhysicalDimension,DimensionalSignature,BaseDimension,
 DerivedDimension,DimensionlessQuantity,BaseQuantity,DerivedQuantity,
 SIBaseQuantity,SIDerivedQuantity,ScalarQuantity,VectorQuantity,
 TensorQuantity,ExtensiveQuantity,IntensiveQuantity,ConservedQuantity,
 RateQuantity,RatioQuantity,Length,Mass,Time,ElectricCurrent,
 ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity,PlaneAngle,
 SolidAngle,Area,Volume,Displacement,Distance,Speed,Velocity,Acceleration,
 Frequency,Period,Force,Momentum,Impulse,Pressure,Stress,Strain,Energy,
 Work,Heat,Power,Density,MassDensity,MassFlowRate,VolumeFlowRate,
 ElectricCharge,ElectricCurrentRelationship,Voltage,Resistance,Conductance,
 Capacitance,Inductance,MagneticFlux,MagneticFluxDensity,
 TemperatureDifference,HeatCapacity,SpecificHeatCapacity,
 ThermalConductivity,Entropy,AmountConcentration,MolarConcentration,
 MassConcentration,LuminousFlux,Illuminance,Radioactivity,AbsorbedDose,
 EquivalentDose,CatalyticActivity,DimensionlessNumber,ReynoldsNumber,
 MachNumber,PrandtlNumber,NusseltNumber,PecletNumber,QuantityEquation,
 ConservationLaw,DimensionalEquation,DimensionalAnalysis,
 DimensionalConsistency,DimensionalHomogeneity,QuantityCalculus,
 QuantityAlgebra,ProductQuantity,QuotientQuantity,PowerQuantity,
 InverseQuantity,QuantityCompatibility,UnitCompatibility,Comparability,
 QuantityEquivalence,Measurement,Measurand,Observable,Observation,
 MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,
 Calibration,MeasurementTraceability,Metrology,ScientificMeasurement,
 UnitSystem,SystemOfUnits,InternationalSystemOfUnits,SI,SIBaseUnit,
 SIDerivedUnit,CoherentUnit,UnitConversion,ConversionFactor,
 PhysicalConstant,DefinedConstant,UncertainQuantity,ErrorBound,Tolerance,
 Range,LowerBound,UpperBound,Provenance,QuantityProvenance,
 DefinitionSource,BIPMrelationship,VIMRelationship,SIbrochureRelationship,
 QUDTRelationship,OMRelationship,Verification,Validation,
 DimensionalValidation,UnitValidation,ConsistencyCheck,PlausibilityCheck,
 ErrorAnalysis,ScientificSimulation,ComputationalScientificWorkflow
 ]
 EXCLUDE_AS_PRIMARY = [
 AbstractQuantityWithoutPhysicalReferent,
 PureNumericalValueWithoutPhysicalQuantitySemantics,
 UnitDefinitionWhenPhysicalPropertyIsSecondary,
 PhysicalEntityWithoutQuantifiedPropertyContext
 ]
 DISAMBIGUATION_RULE = "When a measurable property belongs to a physical phenomenon, body, substance or system and is represented through magnitude, dimension and reference, interpret the context as a physical quantity."
}

CORE_CONCEPTS {
 PhysicalQuantity = "Measurable property of a physical phenomenon, body, substance or system."
 PhysicalQuantityKind = "Class of mutually comparable physical quantities sharing the same physical meaning."
 PhysicalQuantityValue = "Magnitude of a physical quantity expressed by number and reference."
 BaseQuantity = "Physical quantity conventionally selected as independent in a quantity system."
 DerivedQuantity = "Physical quantity defined through an equation involving other quantities."
 PhysicalDimension = "Dependence of a physical quantity on selected base quantities."
 ScalarQuantity = "Physical quantity represented by magnitude without directional components."
 VectorQuantity = "Physical quantity requiring magnitude and direction or vector components."
 ConservedQuantity = "Physical quantity constrained by a conservation law."
}

RELATIONS {
 PhysicalQuantity --is_child_of--> Quantity
 PhysicalQuantity --has_kind--> PhysicalQuantityKind
 PhysicalQuantity --has_value--> PhysicalQuantityValue
 PhysicalQuantity --has_dimension--> PhysicalDimension
 PhysicalQuantityValue --uses--> Unit
 DerivedQuantity --is_defined_by--> QuantityEquation
 ScalarQuantity --is_type_of--> PhysicalQuantity
 VectorQuantity --is_type_of--> PhysicalQuantity
 TensorQuantity --is_type_of--> PhysicalQuantity
 ConservationLaw --constrains--> ConservedQuantity
 Measurement --targets--> Measurand
 Measurand --is_type_of--> PhysicalQuantity
 MeasurementUncertainty --qualifies--> PhysicalQuantityValue
 Provenance --records--> QuantityDefinitionAndMeasurementContext
}

OPERATORS {
 PHYSICAL_QUANTITY(value,unit) := {value,unit}
 KIND(q) := physical_quantity_kind(q)
 DIM(q) := physical_dimensional_signature(q)
 CONVERT(q,target_unit) := equivalent_physical_quantity_value(q,target_unit)
 MULTIPLY(q1,q2) := physical_quantity_product(q1,q2)
 DIVIDE(q1,q2) := physical_quantity_quotient(q1,q2)
 POWER(q,n) := physical_quantity_power(q,n)
 CHECK_LAW(equation) := dimensional_and_quantity_consistency(equation)
}

AXIOMS {
 A1 = "A physical quantity represents a property, not the physical object itself."
 A2 = "Unit choice changes numerical representation but not physical quantity identity."
 A3 = "Physical quantities of equal dimension can represent different quantity kinds."
 A4 = "Derived physical quantities inherit dimensional structure from defining equations."
 A5 = "Vector and tensor quantities require component or transformation semantics beyond scalar magnitude."
 A6 = "Dimensionless physical quantities can remain physically distinct."
 A7 = "Physical laws expressed as quantity equations are independent of coherent unit choice."
 A8 = "Physical-quantity reasoning requires explicit kind, dimension, value, unit, mathematical character and provenance."
}

REASONING {
 R1_CONTEXT = identify(physical_property,system_or_phenomenon,quantity_kind,value,unit,dimension_and_intended_use)
 R2_KIND = determine_physical_quantity_kind_and_semantic_identity)
 R3_CHARACTER = classify_scalar_vector_tensor_extensive_intensive_rate_or_dimensionless_character)
 R4_DIMENSION = derive_or_validate_base_dimension_exponents)
 R5_VALUE = represent_magnitude_using_compatible_unit_or_reference)
 R6_RELATIONS = identify_base_derived_conservation_or_functional_relationships)
 R7_CALCULUS = apply_quantity_equations_products_quotients_powers_and_unit_conversions)
 R8_MEASUREMENT = if_measured_attach_measurand_result_uncertainty_calibration_and_traceability)
 R9_VALIDATE = check_dimensional_homogeneity_unit_compatibility_ranges_and_physical_plausibility)
 R10_PROVENANCE = record_standard_definition_symbols_equations_units_and_source)
}

CONSTRAINTS {
 C1 = "Equal dimensions do not guarantee identical physical quantity kinds."
 C2 = "A vector quantity cannot be reduced to scalar magnitude when direction is material."
 C3 = "Tensor quantities require coordinate-transformation semantics."
 C4 = "Addition and subtraction require compatible physical quantity kinds."
 C5 = "Unit conversion requires compatible physical quantity semantics."
 C6 = "Dimensionless quantities can represent distinct physical concepts."
 C7 = "Affine quantities such as certain temperature-scale values require special arithmetic treatment."
 C8 = "Derived quantity equations must preserve dimensional homogeneity."
 C9 = "Measured physical quantity values should retain uncertainty and traceability."
 C10 = "Physical plausibility checks depend on system, regime and context."
}

SEMANTIC_EQUIVALENCE {
 "InternationalSystemOfUnits" <=> "SI"
 "MeasurementUnit" <=> "Unit"
 "KindOfPhysicalQuantity" <=> "PhysicalQuantityKind"
 "PhysicalQuantityMagnitude" <=> "PhysicalQuantityValue"
}

VALIDATION {
 V1 = "Physical quantity kind is explicitly identified."
 V2 = "Numerical value and unit or reference are documented."
 V3 = "Physical dimension is documented or derivable."
 V4 = "Scalar, vector or tensor character is documented where relevant."
 V5 = "Base or derived status is documented where relevant."
 V6 = "Quantity equations are dimensionally homogeneous."
 V7 = "Unit compatibility is checked before conversion."
 V8 = "Dimensionless quantities retain physical semantic identity."
 V9 = "Measured values retain uncertainty and traceability where material."
 V10 = "Definitions, symbols and relationships are traceable to documented ontology or standard versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 PHYSICAL_QUANTITY_DEFINITION = 0.99
 QUANTITY_KIND_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 SCALAR_VECTOR_TENSOR_REASONING = 0.98
 UNIT_REASONING = 0.99
 PHYSICAL_PLAUSIBILITY_REASONING = 0.97
 POLICY = "Reduce confidence when physical quantity kind, dimension, mathematical character, unit, defining equation or physical context are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,PhysicalQuantityReasoning,
 PhysicalQuantityKindReasoning,PhysicalDimensionReasoning,
 ScalarQuantityReasoning,VectorQuantityReasoning,TensorQuantityReasoning,
 BaseQuantityReasoning,DerivedQuantityReasoning,
 DimensionlessQuantityReasoning,QuantityEquationReasoning,
 ConservationReasoning,UnitConversionReasoning,MeasurandReasoning,
 MeasurementUncertaintyReasoning,KnowledgeGraphConstruction,
 RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "physical quantity" -> PhysicalQuantity
  "kind of physical quantity" -> PhysicalQuantityKind
  "physical quantity magnitude" -> PhysicalQuantityValue
  "measurement unit" -> Unit
  "SI" -> InternationalSystemOfUnits
 }
}

EXECUTION_RULES {
 E1 = "If a measurable property belongs to a physical system or phenomenon, activate PhysicalQuantityOntology."
 E2 = "Identify physical quantity kind before interpreting unit or dimension."
 E3 = "Classify scalar, vector, tensor, extensive, intensive, rate or dimensionless character where relevant."
 E4 = "Represent physical quantity values as numerical magnitude plus compatible reference."
 E5 = "Derive dimensions from quantity equations rather than unit labels alone."
 E6 = "Apply addition and comparison only to compatible physical quantity kinds."
 E7 = "Preserve physical semantic identity for dimensionless quantities."
 E8 = "Attach uncertainty, calibration and traceability to measured physical quantities where relevant."
 E9 = "Record canonical definitions, symbols, equations and provenance."
}

RECURSION {
 ENTRY = PhysicalQuantity
 EXPAND(PhysicalQuantity) -> [
 Quantity,MeasurableQuantity,QuantityKind,PhysicalQuantityKind,
 PhysicalQuantityValue,Magnitude,Unit,Dimension,PhysicalDimension,
 DimensionalSignature,BaseDimension,DerivedDimension,DimensionlessQuantity,
 BaseQuantity,DerivedQuantity,SIBaseQuantity,SIDerivedQuantity,
 ScalarQuantity,VectorQuantity,TensorQuantity,ExtensiveQuantity,
 IntensiveQuantity,ConservedQuantity,RateQuantity,RatioQuantity,
 Length,Mass,Time,ElectricCurrent,ThermodynamicTemperature,
 AmountOfSubstance,LuminousIntensity,PlaneAngle,SolidAngle,Area,Volume,
 Distance,Speed,Velocity,Acceleration,Frequency,Force,Momentum,Pressure,
 Stress,Strain,Energy,Work,Heat,Power,Density,ElectricCharge,Voltage,
 Resistance,Conductance,Capacitance,Inductance,MagneticFlux,
 MagneticFluxDensity,TemperatureDifference,HeatCapacity,
 ThermalConductivity,Entropy,AmountConcentration,LuminousFlux,Illuminance,
 Radioactivity,AbsorbedDose,EquivalentDose,CatalyticActivity,
 DimensionlessNumber,ReynoldsNumber,MachNumber,PrandtlNumber,
 NusseltNumber,PecletNumber,QuantityEquation,ConservationLaw,
 DimensionalAnalysis,DimensionalConsistency,QuantityCalculus,
 QuantityCompatibility,Measurement,Measurand,MeasurementResult,
 MeasurementUncertainty,Calibration,MeasurementTraceability,Metrology,
 ScientificMeasurement,InternationalSystemOfUnits,SI,SIBaseUnit,
 SIDerivedUnit,UnitConversion,PhysicalConstant,UncertainQuantity,
 QuantityProvenance
 ]
 EXPAND(PhysicalQuantityFamilies) -> [
 PhysicalQuantityKindsValuesAndReferences,
 BaseDerivedAndSIQuantities,
 ScalarVectorTensorAndFieldQuantities,
 ExtensiveIntensiveRateAndConservedQuantities,
 DimensionsDimensionalAnalysisAndQuantityEquations,
 MechanicalThermalElectricalChemicalAndRadiometricQuantities,
 MeasurementUncertaintyCalibrationAndTraceability,
 CanonicalDefinitionsValidationAndProvenance
 ]
 STOP_CONDITION = "Stop when physical kind, value, unit, dimension, mathematical character, equations, measurement and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Quantity Ontology"
 RELATED_ONTOLOGIES = [
 "Quantity Ontology","Foundations of Measurement","Measurement Ontology",
 "Scientific Measurement Ontology 2","Metrology Ontology",
 "Measurement & Units Ontologies","Units Ontology",
 "Dimensional Analysis Ontology","Measurement Uncertainty Ontology",
 "Scientific Ontologies","Physics Ontology","Verification & Validation"
 ]
 ROUTE_RULES = [
 "Physical Quantity -> Quantity Ontology for parent quantity semantics",
 "Physical Quantity -> Foundations of Measurement for measurement theory",
 "Physical Quantity -> Measurement Ontology for measurand and measured-value semantics",
 "Physical Quantity -> Scientific Measurement for scientific observation relationships",
 "Physical Quantity -> Metrology for standards and traceability",
 "Physical Quantity -> Units and Dimensional Analysis for unit and dimension reasoning",
 "Physical Quantity -> Measurement Uncertainty for uncertain measured values",
 "Physical Quantity -> Scientific and Physics ontologies for domain-specific physical semantics",
 "Physical Quantity -> Verification & Validation for dimensional and plausibility checks"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible physical quantity kinds, relationships or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
 "Preserve physical-quantity-versus-physical-object distinction.",
 "Preserve physical-quantity-kind-versus-dimension distinction.",
 "Preserve scalar-versus-vector-versus-tensor distinction.",
 "Preserve base-versus-derived quantity distinction.",
 "Preserve dimensionless-versus-semantically-untyped distinction.",
 "Preserve unit-choice-versus-physical-quantity-identity distinction.",
 "Preserve measured-value-versus-measurand distinction.",
 "Preserve machine-readable physical-quantity semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "A physical quantity is a measurable property of a physical phenomenon, body, substance or system whose magnitude can be expressed as a number together with a reference."
 KIND_SUMMARY = "Physical quantity kinds identify mutually comparable physical properties."
 DIMENSION_SUMMARY = "Physical dimensions express dependence on base quantities independently of unit choice."
 CHARACTER_SUMMARY = "Physical quantities can be scalar, vector, tensor, extensive, intensive, rate or dimensionless."
 DERIVATION_SUMMARY = "Derived quantities and physical laws are represented through dimensionally homogeneous quantity equations."
 MEASUREMENT_SUMMARY = "Measured physical quantities should retain uncertainty, calibration and traceability semantics."
 VALIDATION_SUMMARY = "Physical quantity representations should preserve kind, dimension, mathematical character, unit compatibility, physical plausibility and provenance."
}

FLOW {
 INPUT
 -> detect_physical_quantity_context
 -> identify_physical_property_system_or_phenomenon_quantity_kind_value_unit_dimension_and_intended_use
 -> determine_physical_quantity_kind_and_semantic_identity
 -> classify_scalar_vector_tensor_extensive_intensive_rate_or_dimensionless_character
 -> derive_or_validate_base_dimension_exponents
 -> represent_magnitude_using_compatible_unit_or_reference
 -> identify_base_derived_conservation_or_functional_relationships
 -> apply_quantity_equations_products_quotients_powers_and_unit_conversions
 -> if_measured_attach_measurand_result_uncertainty_calibration_and_traceability
 -> check_dimensional_homogeneity_unit_compatibility_ranges_and_physical_plausibility
 -> record_standard_definition_symbols_equations_units_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-FOUNDATIONS-PHYSICAL-QUANTITY-ONTOLOGY-V1"
}

}

END_FLOW