Quantity Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Quantity Ontology within the Kireth Research Semantic Library. A quantity is a measurable or quantifiable property expressed through a magnitude together with a reference such as a unit or scale. This ontology formalises quantity kinds, values, dimensions, base and derived quantities, quantity equations, comparability, unit compatibility, measurement, uncertainty and semantic identity.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = Quantity
 ENTITY_CLASS = MeasurablePropertySemanticFramework
 PRIMARY_CONTEXT = FoundationsOfMeasurement
 DEFINITION = "A quantity is a property of a phenomenon, body, substance, system or abstract object whose magnitude can be expressed as a number together with a reference."
 SYMBOLIC_FORMS = ["Q={numerical_value,reference}","Q=value*unit","[Q]=dimensional_signature","Q_derived=f(Q_1,...,Q_n)"]
 SEMANTIC_ROLE = "Machine-readable semantics for measurable properties, quantity kinds, values, dimensions, units, equations, comparability and measurement relationships."
}

SCOPE {
 INCLUDE = [
 Quantity,MeasurableQuantity,PhysicalQuantity,QuantityKind,KindOfQuantity,
 QuantityClass,QuantityInstance,QuantityValue,MeasurementValue,MeasuredValue,
 NumericalValue,Magnitude,Reference,MeasurementUnit,Unit,ReferenceValue,
 NominalValue,EstimatedValue,ExactValue,QuantitySymbol,QuantityName,
 QuantityIdentifier,CanonicalQuantity,QuantityAlias,BaseQuantity,
 DerivedQuantity,DependentQuantity,IndependentQuantity,InputQuantity,
 OutputQuantity,InfluenceQuantity,ExtensiveQuantity,IntensiveQuantity,
 ScalarQuantity,VectorQuantity,TensorQuantity,DiscreteQuantity,
 ContinuousQuantity,Dimension,PhysicalDimension,DimensionalSignature,
 BaseDimension,DerivedDimension,DimensionlessQuantity,QuantityDimension,
 DimensionalExponent,DimensionalEquation,DimensionalAnalysis,
 DimensionalConsistency,DimensionalHomogeneity,UnitCompatibility,
 QuantityCompatibility,Comparability,QuantityEquivalence,QuantityEquality,
 QuantityOrdering,QuantityDifference,QuantityRatio,QuantityInterval,
 QuantityRange,LowerBound,UpperBound,Minimum,Maximum,Threshold,Tolerance,
 QuantityEquation,QuantityCalculus,QuantityAlgebra,ProductQuantity,
 QuotientQuantity,PowerQuantity,InverseQuantity,Proportionality,
 DirectProportionality,InverseProportionality,FunctionalRelationship,
 Measurement,Measurand,Observable,Observation,MeasurementProcedure,
 MeasurementResult,MeasurementUncertainty,Uncertainty,Accuracy,Precision,
 Resolution,Calibration,MeasurementTraceability,UnitSystem,SystemOfUnits,
 InternationalSystemOfUnits,SI,SIBaseQuantity,SIBaseUnit,
 SIDerivedQuantity,SIDerivedUnit,Length,Mass,Time,ElectricCurrent,
 ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity,Area,Volume,
 Velocity,Speed,Acceleration,Frequency,Force,Pressure,Energy,Power,Density,
 ElectricCharge,Voltage,Resistance,Conductance,Capacitance,Inductance,
 DimensionlessNumber,RatioQuantity,TimeDependentQuantity,
 SpatiallyDependentQuantity,UncertainQuantity,QuantityTransformation,
 UnitConversion,Normalisation,NonDimensionalisation,QuantityMapping,
 OntologyMapping,SemanticMapping,QuantityRegistry,QuantityDictionary,
 Metadata,QuantityMetadata,Provenance,QuantityProvenance,
 BIPMrelationship,VIMRelationship,SIbrochureRelationship,QUDTRelationship,
 OMRelationship,UCUMrelationship,Verification,Validation,UnitValidation,
 DimensionalValidation,ConsistencyCheck,PlausibilityCheck,ErrorAnalysis,
 ScientificMeasurement,Metrology,ComputationalScientificWorkflow
 ]
 EXCLUDE_AS_PRIMARY = [
 PureNumericalValueWithoutQuantityReference,
 UnitDefinitionWhenQuantityKindIsSecondary,
 MeasurementProcedureWhenValueAcquisitionIsPrimary,
 PhysicalEntityWithoutQuantifiablePropertyContext
 ]
 DISAMBIGUATION_RULE = "When a property is represented through a magnitude and a reference, or classified by measurable kind and dimension, interpret the context as a quantity."
}

CORE_CONCEPTS {
 Quantity = "Property whose magnitude can be expressed as a number and a reference."
 QuantityKind = "Common aspect shared by mutually comparable quantities."
 QuantityValue = "Number and reference together expressing the magnitude of a quantity."
 BaseQuantity = "Quantity conventionally chosen as independent within a system of quantities."
 DerivedQuantity = "Quantity defined through a quantity equation involving other quantities."
 Dimension = "Expression of dependence of a quantity on base quantities independent of unit choice."
 DimensionlessQuantity = "Quantity whose dimensional exponents are all zero."
 QuantityEquation = "Mathematical relation between quantities independent of particular unit choices."
 Measurand = "Quantity intended to be measured."
}

RELATIONS {
 Quantity --is_child_of--> FoundationsOfMeasurement
 Quantity --has_kind--> QuantityKind
 Quantity --has_value--> QuantityValue
 QuantityValue --uses_reference--> UnitOrScale
 Quantity --has_dimension--> Dimension
 DerivedQuantity --is_defined_by--> QuantityEquation
 QuantityEquation --relates--> Quantities
 Measurement --targets--> Measurand
 Measurand --is_type_of--> Quantity
 Unit --realises--> QuantityKind
 QuantityCompatibility --depends_on--> QuantityKindAndDimension
 MeasurementUncertainty --qualifies--> QuantityValue
 Provenance --records--> QuantityDefinitionAndSource
}

OPERATORS {
 QUANTITY(value,reference) := {value,reference}
 KIND(q) := quantity_kind(q)
 DIM(q) := dimensional_signature(q)
 VALUE(q) := numerical_value_and_reference(q)
 COMPATIBLE(q1,q2) := same_quantity_kind_or_declared_compatible_kind(q1,q2)
 MULTIPLY(q1,q2) := quantity_product(q1,q2)
 DIVIDE(q1,q2) := quantity_quotient(q1,q2)
 POWER(q,n) := quantity_power(q,n)
 CONVERT(q,target_unit) := equivalent_quantity_value(q,target_unit)
}

AXIOMS {
 A1 = "A bare number is not a quantity value unless a reference or defined dimensionless semantics is supplied."
 A2 = "Quantities of the same kind are mutually comparable under compatible references."
 A3 = "Quantities can share dimensions without being quantities of the same kind."
 A4 = "Unit choice changes numerical representation but not represented quantity."
 A5 = "Derived quantities inherit dimensions through defining quantity equations."
 A6 = "Dimensionless quantities can remain semantically distinct despite identical dimension."
 A7 = "A measurand is a quantity specified for measurement, not the measurement result itself."
 A8 = "Quantity reasoning requires explicit kind, value, dimension, reference and provenance semantics."
}

REASONING {
 R1_CONTEXT = identify(property,phenomenon_or_object,quantity_kind,value,reference,dimension_and_intended_use)
 R2_KIND = determine_quantity_kind_and_semantic_identity)
 R3_DIMENSION = derive_or_validate_dimensional_signature)
 R4_VALUE = represent_magnitude_as_numerical_value_plus_unit_scale_or_reference)
 R5_RELATIONS = identify_base_derived_dependency_ratio_or_conservation_relationships)
 R6_COMPATIBILITY = assess_quantity_kind_dimension_and_unit_compatibility)
 R7_CALCULUS = apply_quantity_equations_products_quotients_powers_or_conversions)
 R8_MEASUREMENT = if_measured_attach_measurand_result_uncertainty_and_traceability)
 R9_VALIDATE = check_dimensional_consistency_ranges_units_and_semantic_equivalence)
 R10_PROVENANCE = record_definition_standard_aliases_equations_and_source)
}

CONSTRAINTS {
 C1 = "Equal dimensions do not necessarily imply equal quantity kinds."
 C2 = "Dimensionless does not mean semantically unspecified."
 C3 = "Addition and subtraction require compatible quantity semantics."
 C4 = "Unit conversion cannot convert between incompatible quantity kinds."
 C5 = "Affine scale values require care in multiplication and ratio operations."
 C6 = "Nominal or ordinal properties should not be treated as ratio-scale physical quantities without justification."
 C7 = "Quantity aliases can create ambiguity unless mapped to canonical kinds."
 C8 = "Derived quantity definitions must preserve dimensional consistency."
 C9 = "A measured quantity value should retain uncertainty and traceability when relevant."
 C10 = "Normalisation can remove units without removing semantic identity."
}

SEMANTIC_EQUIVALENCE {
 "KindOfQuantity" <=> "QuantityKind"
 "InternationalSystemOfUnits" <=> "SI"
 "MeasurementUnit" <=> "Unit"
 "QuantityMagnitude" <=> "QuantityValue"
}

VALIDATION {
 V1 = "Quantity kind is explicitly identified."
 V2 = "Quantity value includes an appropriate reference."
 V3 = "Dimension is documented or derivable."
 V4 = "Base or derived status is documented where relevant."
 V5 = "Quantity equations are dimensionally consistent."
 V6 = "Unit compatibility is checked before conversion."
 V7 = "Dimensionless quantities retain quantity-kind semantics."
 V8 = "Measured quantity values retain uncertainty where material."
 V9 = "Aliases map to canonical quantity definitions."
 V10 = "Quantity definitions and relationships are traceable to documented ontology or standard versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 QUANTITY_DEFINITION = 0.99
 QUANTITY_KIND_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 QUANTITY_VALUE_REASONING = 0.99
 COMPATIBILITY_REASONING = 0.99
 DIMENSIONLESS_REASONING = 0.98
 POLICY = "Reduce confidence when quantity kind, reference, dimension, scale, defining equation or semantic identity are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,QuantityReasoning,QuantityKindReasoning,
 QuantityValueReasoning,DimensionReasoning,BaseQuantityReasoning,
 DerivedQuantityReasoning,DimensionlessQuantityReasoning,
 QuantityEquationReasoning,QuantityCompatibilityReasoning,
 UnitConversionReasoning,MeasurandReasoning,UncertaintyReasoning,
 SemanticMappingReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,
 RecursiveInference
 ]
 NORMALISE {
  "quantity" -> Quantity
  "kind of quantity" -> QuantityKind
  "quantity kind" -> QuantityKind
  "quantity magnitude" -> QuantityValue
  "measurement unit" -> Unit
  "SI" -> InternationalSystemOfUnits
 }
}

EXECUTION_RULES {
 E1 = "If a property is represented by magnitude plus reference or classified by measurable kind, activate QuantityOntology."
 E2 = "Identify quantity kind before interpreting unit, dimension or conversion."
 E3 = "Represent quantity values as numerical value plus reference."
 E4 = "Distinguish quantity kind from dimension."
 E5 = "Apply addition and comparison only to semantically compatible quantities."
 E6 = "Derive dimensions of product, quotient and power quantities algebraically."
 E7 = "Preserve semantic identity for dimensionless quantities."
 E8 = "Attach uncertainty and traceability to measured quantity values where relevant."
 E9 = "Record canonical definition, aliases, equations and provenance."
}

RECURSION {
 ENTRY = Quantity
 EXPAND(Quantity) -> [
 MeasurableQuantity,PhysicalQuantity,QuantityKind,KindOfQuantity,
 QuantityValue,MeasurementValue,MeasuredValue,NumericalValue,Magnitude,
 Reference,Unit,MeasurementUnit,QuantitySymbol,QuantityIdentifier,
 BaseQuantity,DerivedQuantity,DependentQuantity,IndependentQuantity,
 InputQuantity,OutputQuantity,InfluenceQuantity,ExtensiveQuantity,
 IntensiveQuantity,ScalarQuantity,VectorQuantity,TensorQuantity,
 DiscreteQuantity,ContinuousQuantity,Dimension,PhysicalDimension,
 DimensionalSignature,BaseDimension,DerivedDimension,DimensionlessQuantity,
 QuantityDimension,DimensionalEquation,DimensionalAnalysis,
 DimensionalConsistency,UnitCompatibility,QuantityCompatibility,
 Comparability,QuantityEquivalence,QuantityDifference,QuantityRatio,
 QuantityInterval,QuantityRange,QuantityEquation,QuantityCalculus,
 QuantityAlgebra,ProductQuantity,QuotientQuantity,PowerQuantity,
 InverseQuantity,Proportionality,Measurement,Measurand,MeasurementResult,
 MeasurementUncertainty,Calibration,MeasurementTraceability,UnitSystem,
 InternationalSystemOfUnits,SI,Length,Mass,Time,ElectricCurrent,
 ThermodynamicTemperature,AmountOfSubstance,LuminousIntensity,Area,Volume,
 Velocity,Acceleration,Frequency,Force,Pressure,Energy,Power,Density,
 ElectricCharge,Voltage,Resistance,DimensionlessNumber,RatioQuantity,
 UncertainQuantity,QuantityTransformation,UnitConversion,Normalisation,
 NonDimensionalisation,QuantityMapping,QuantityRegistry,QuantityMetadata,
 QuantityProvenance
 ]
 EXPAND(QuantityFamilies) -> [
 QuantityKindsValuesAndReferences,
 BaseDerivedAndDependentQuantities,
 ScalarVectorTensorAndStructuredQuantities,
 DimensionsAndDimensionalAnalysis,
 QuantityEquationsAndQuantityCalculus,
 ComparabilityCompatibilityAndConversion,
 MeasurandsUncertaintyAndMeasurement,
 CanonicalDefinitionsMappingsAndProvenance
 ]
 STOP_CONDITION = "Stop when quantity kind, value, reference, dimension, equations, compatibility, measurement and provenance are sufficiently resolved."
}

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

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

OUTPUT {
 CANONICAL_DEFINITION = "A quantity is a property whose magnitude can be expressed as a number together with a reference such as a measurement unit or scale."
 KIND_SUMMARY = "Quantity kinds identify mutually comparable classes of measurable properties."
 VALUE_SUMMARY = "A quantity value combines numerical magnitude with a unit, scale or other reference."
 DIMENSION_SUMMARY = "Dimensions express dependence on base quantities independently of unit choice."
 DERIVATION_SUMMARY = "Derived quantities are defined through quantity equations and inherit dimensional structure from inputs."
 DIMENSIONLESS_SUMMARY = "Dimensionless quantities can remain semantically distinct even when dimensional signatures are identical."
 VALIDATION_SUMMARY = "Quantity representations should preserve kind, value, reference, dimension, compatibility, uncertainty and provenance."
}

FLOW {
 INPUT
 -> detect_quantity_context
 -> identify_property_phenomenon_or_object_quantity_kind_value_reference_dimension_and_intended_use
 -> determine_quantity_kind_and_semantic_identity
 -> derive_or_validate_dimensional_signature
 -> represent_magnitude_as_numerical_value_plus_unit_scale_or_reference
 -> identify_base_derived_dependency_ratio_or_conservation_relationships
 -> assess_quantity_kind_dimension_and_unit_compatibility
 -> apply_quantity_equations_products_quotients_powers_or_conversions
 -> if_measured_attach_measurand_result_uncertainty_and_traceability
 -> check_dimensional_consistency_ranges_units_and_semantic_equivalence
 -> record_definition_standard_aliases_equations_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-QUANTITY-ONTOLOGY-V1"
}

}

END_FLOW