Foundations of Measurement

AI INTERPRETATION NOTE
This Flow Algebra defines the Foundations of Measurement ontology within the Kireth Research Semantic Library. Foundations of measurement concern the mathematical and conceptual basis of assigning values to quantities, including observables, quantity kinds, measurement procedures, scales, standards, reference systems, comparability, calibration, traceability, uncertainty, error, resolution, accuracy, precision, dimensional interpretation and the relationship between measured values and the properties they represent.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Foundations of Measurement"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Measurement & Units"
 SPECIALISATION = "Foundations of Measurement"
 CANONICAL_PAGE = "https://kirethframeworkold.co.uk/books/semantic-library/ai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/foundations-of-measurement.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = FoundationsOfMeasurement
 ENTITY_CLASS = MeasurementTheoryFramework
 PRIMARY_CONTEXT = MeasurementUnitsOntologies
 DEFINITION = "Foundations of measurement provide the mathematical and conceptual framework for assigning values to quantities through defined measurement procedures, scales, units, standards and uncertainty semantics."
 SYMBOLIC_FORMS = [
  "measurement: measurand -> value_with_reference",
  "M = {estimate,unit,uncertainty}",
  "comparison(q1,q2) requires compatible quantity_kind",
  "measurement_result = model(observation,calibration,reference)"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for measurands, measurement procedures, scales, standards, value assignment, comparability, uncertainty, accuracy, precision and traceability."
}

SCOPE {
 INCLUDE = [
  FoundationsOfMeasurement,
  MeasurementTheory,
  Measurement,
  MeasurementProcess,
  MeasurementProcedure,
  MeasurementMethod,
  MeasurementModel,
  MeasurementPrincipleRelationship,
  Observation,
  Observable,
  Measurand,
  Quantity,
  QuantityKind,
  PhysicalQuantity,
  MeasurableQuantity,
  MeasurementValue,
  MeasuredValue,
  NumericalValue,
  QuantityValue,
  ReferenceValue,
  TrueValueRelationship,
  ConventionalTrueValueRelationship,
  NominalValue,
  EstimatedValue,
  AssignedValue,
  MeasurementResult,
  MeasurementStatement,
  MeasurementContext,
  MeasurementCondition,
  ExperimentalConditionRelationship,
  InstrumentConditionRelationship,
  QuantityComparison,
  Comparability,
  CommensurabilityRelationship,
  Ordering,
  Equality,
  Equivalence,
  GreaterThanRelationship,
  LessThanRelationship,
  Ratio,
  Difference,
  Interval,
  Scale,
  MeasurementScale,
  RatioScale,
  IntervalScale,
  OrdinalScale,
  NominalScale,
  AbsoluteScaleRelationship,
  LinearScale,
  LogarithmicScale,
  AffineScale,
  ScaleOrigin,
  ScaleUnit,
  Unit,
  MeasurementUnit,
  UnitSystem,
  StandardUnit,
  ReferenceUnit,
  CanonicalUnit,
  Dimension,
  DimensionalSignature,
  BaseDimension,
  DerivedDimension,
  DimensionlessQuantity,
  UnitConversion,
  ConversionFactor,
  ConversionOffset,
  UnitCompatibility,
  DimensionalConsistency,
  DimensionalAnalysis,
  Standard,
  MeasurementStandard,
  ReferenceStandard,
  PrimaryStandard,
  SecondaryStandard,
  WorkingStandardRelationship,
  TransferStandardRelationship,
  CalibrationStandard,
  ArtefactStandardRelationship,
  RealisationRelationship,
  UnitRealisationRelationship,
  ReferenceSystem,
  ReferenceFrameRelationship,
  ReferenceCondition,
  MeasurementTraceability,
  TraceabilityChain,
  Calibration,
  CalibrationCurveRelationship,
  CalibrationFunction,
  CalibrationCorrection,
  Correction,
  CorrectionFactor,
  BiasCorrection,
  ZeroCorrectionRelationship,
  DriftCorrectionRelationship,
  Verification,
  Validation,
  InstrumentVerificationRelationship,
  MeasurementValidationRelationship,
  Accuracy,
  Precision,
  TruenessRelationship,
  Bias,
  SystematicError,
  RandomError,
  MeasurementError,
  AbsoluteError,
  RelativeError,
  Repeatability,
  Reproducibility,
  Resolution,
  Sensitivity,
  SelectivityRelationship,
  SpecificityRelationship,
  DetectionLimit,
  QuantisationRelationship,
  DynamicRange,
  Range,
  Span,
  Threshold,
  HysteresisRelationship,
  LinearityRelationship,
  NonlinearityRelationship,
  Stability,
  Drift,
  Noise,
  Signal,
  SignalToNoiseRatioRelationship,
  SNRRelationship,
  Uncertainty,
  MeasurementUncertainty,
  StandardUncertainty,
  CombinedUncertainty,
  ExpandedUncertainty,
  TypeAUncertaintyRelationship,
  TypeBUncertaintyRelationship,
  CoverageFactor,
  CoverageProbabilityRelationship,
  ConfidenceIntervalRelationship,
  ProbabilityDistributionRelationship,
  UncertaintyBudget,
  ErrorBudget,
  PropagationOfUncertainty,
  Covariance,
  Correlation,
  IndependenceRelationship,
  SignificantFigures,
  DecimalPlaces,
  Rounding,
  RoundOffError,
  ResolutionLimitRelationship,
  Sampling,
  Sample,
  PopulationRelationship,
  SamplingIntervalRelationship,
  SamplingFrequencyRelationship,
  AliasingRelationship,
  Averaging,
  RepeatedMeasurement,
  ReplicateMeasurement,
  TimeSeriesMeasurementRelationship,
  SpatialMeasurementRelationship,
  SensorMeasurementRelationship,
  InstrumentMeasurementRelationship,
  DirectMeasurement,
  IndirectMeasurement,
  DerivedMeasurement,
  DifferentialMeasurementRelationship,
  ComparativeMeasurement,
  NullMeasurementRelationship,
  SubstitutionMeasurementRelationship,
  RatioMeasurement,
  CountingRelationship,
  Estimation,
  InferenceRelationship,
  DataReduction,
  CorrectionModel,
  MeasurementEquation,
  InputQuantity,
  OutputQuantity,
  InfluenceQuantity,
  InfluenceFactor,
  EnvironmentalInfluenceRelationship,
  TemperatureInfluenceRelationship,
  PressureInfluenceRelationship,
  HumidityInfluenceRelationship,
  InstrumentResponse,
  TransferFunctionRelationship,
  ResponseFunction,
  ObservationModel,
  InverseProblemRelationship,
  IdentifiabilityRelationship,
  UniquenessRelationship,
  Metrology,
  ScientificMeasurement,
  LegalMetrologyRelationship,
  AppliedMetrologyRelationship,
  FundamentalMetrologyRelationship,
  MeasurementScience,
  MeasurementStandardisation,
  BIPMrelationship,
  NISTrelationship,
  ISOrelationship,
  IECrelationship,
  OIMLrelationship,
  VIMRelationship,
  GUMRelationship,
  SIrelationship,
  InternationalSystemOfUnits,
  Provenance,
  MeasurementProvenance,
  CalibrationProvenance,
  StandardProvenance,
  DataProvenance,
  Traceability,
  Metadata,
  MeasurementMetadata,
  TimestampRelationship,
  LocationRelationship,
  OperatorRelationship,
  InstrumentIdentifierRelationship,
  StandardIdentifierRelationship,
  ProcedureVersion,
  CalibrationVersion,
  StandardVersion,
  InstrumentVersion,
  SoftwareVersionRelationship,
  ReproducibilityOntologyRelationship,
  VerificationValidation,
  ErrorAnalysis,
  ComputationalStatistics,
  ScientificSimulation,
  ComputationalScientificWorkflow
 ]
 EXCLUDE_AS_PRIMARY = [
  DomainSpecificPhysicalMeasurementWhenFoundationalSemanticsAreSecondary,
  PureUnitConversionWithoutMeasurementProcessContext,
  InstrumentEngineeringWithoutMeasurementTheory,
  StatisticalEstimationWithoutMeasurementSemantics
 ]
 DISAMBIGUATION_RULE = "When the core question is how values are assigned to quantities through procedures, scales, standards, calibration or uncertainty, interpret the context as foundations of measurement."
}

CORE_CONCEPTS {
 FoundationsOfMeasurement = "Conceptual and mathematical basis of measurement."
 Measurand = "Quantity intended to be measured."
 MeasurementProcedure = "Specified sequence of operations used to obtain a measurement result."
 MeasurementResult = "Reported quantity value together with relevant uncertainty and context."
 MeasurementScale = "Rule structure relating admissible values and their meaningful transformations."
 Standard = "Realisation or reference used to define, preserve or reproduce a quantity value."
 Calibration = "Operation relating indications to reference quantity values."
 Traceability = "Documented chain linking measurement results to recognised references."
 Uncertainty = "Parameter characterising dispersion of values reasonably attributable to the measurand."
}

RELATIONS {
 FoundationsOfMeasurement --is_child_of--> MeasurementUnitsOntologies
 Measurement --targets--> Measurand
 MeasurementProcedure --produces--> MeasurementResult
 MeasurementResult --contains--> QuantityValue
 QuantityValue --uses--> Unit
 Quantity --has--> QuantityKind
 Quantity --has--> Dimension
 MeasurementScale --defines--> PermissibleValueRelations
 Calibration --links--> IndicationAndReferenceValue
 MeasurementTraceability --links--> ResultToReferenceStandard
 Uncertainty --qualifies--> MeasurementResult
 Accuracy --describes--> ClosenessToReference
 Precision --describes--> AgreementAmongRepeatedMeasurements
 Provenance --records--> MeasurementContextAndHistory
}

OPERATORS {
 MEASURE(measurand,procedure,conditions) := measurement_result(measurand,procedure,conditions)
 CALIBRATE(indication,reference) := calibration_relation(indication,reference)
 CORRECT(value,correction) := value + correction
 TRACE(result) := traceability_chain(result)
 UNCERTAINTY(result) := quantified_dispersion(result)
 COMPARE(q1,q2) := compare_if_compatible_quantity_kind(q1,q2)
 VALIDATE_SCALE(scale,transform) := admissible_transformation(scale,transform)
}

AXIOMS {
 A1 = "A measurement result is not merely a number; it refers to a quantity under declared conditions."
 A2 = "The measurand must be specified sufficiently for the intended use."
 A3 = "Different measurement scales permit different meaningful mathematical operations."
 A4 = "Calibration establishes a relation between indications and reference quantity values."
 A5 = "Traceability is a property of a measurement result through an unbroken documented chain."
 A6 = "Accuracy and precision are distinct concepts."
 A7 = "Measurement uncertainty is distinct from measurement error."
 A8 = "Foundational measurement reasoning requires explicit measurand, procedure, scale, standard, uncertainty and provenance semantics."
}

REASONING {
 R1_CONTEXT = identify(measurand,intended_use,quantity_kind,procedure,instrument,conditions,standard_and_required_uncertainty)
 R2_SPECIFY = define_measurand_and_relevant_influence_quantities)
 R3_SCALE = identify_measurement_scale_unit_dimension_and_reference_system)
 R4_PROCEDURE = identify_direct_indirect_comparative_or_derived_measurement_method)
 R5_CALIBRATION = determine_calibration_relation_corrections_and_traceability)
 R6_OBSERVE = obtain_indications_or_observations_under_declared_conditions)
 R7_MODEL = apply_measurement_equation_corrections_and_data_reduction)
 R8_UNCERTAINTY = identify_components_and_propagate_measurement_uncertainty)
 R9_VALIDATE = assess_accuracy_precision_range_resolution_and_procedure_requirements)
 R10_PROVENANCE = record_standard_versions_conditions_instrument_procedure_and_traceability)
}

CONSTRAINTS {
 C1 = "An incompletely specified measurand can make repeated measurements refer to different quantities."
 C2 = "Precision does not imply accuracy."
 C3 = "Low uncertainty does not guarantee absence of systematic bias."
 C4 = "Measurement results can depend on environmental and instrument influence quantities."
 C5 = "Ordinal and nominal scales do not support arbitrary arithmetic operations."
 C6 = "Calibration does not remove all uncertainty."
 C7 = "Traceability alone does not establish fitness for purpose."
 C8 = "Resolution limits can constrain the meaningful number of reported digits."
 C9 = "Repeated measurements can remain biased if a common systematic effect is present."
 C10 = "Measurement conclusions must remain within the conditions and scale for which the procedure is valid."
}

SEMANTIC_EQUIVALENCE {
 "InternationalSystemOfUnits" <=> "SI"
 "SignalToNoiseRatio" <=> "SNR"
 "InternationalVocabularyOfMetrology" <=> "VIM"
 "GuideToExpressionOfUncertaintyInMeasurement" <=> "GUM"
}

VALIDATION {
 V1 = "Measurand is explicitly specified."
 V2 = "Quantity kind, unit and measurement scale are documented."
 V3 = "Measurement procedure and conditions are documented."
 V4 = "Instrument or observation system is identified."
 V5 = "Calibration status and reference standards are documented where relevant."
 V6 = "Accuracy, precision and resolution are distinguished."
 V7 = "Uncertainty components and propagation method are documented."
 V8 = "Influence quantities and corrections are recorded where material."
 V9 = "Traceability chain and provenance are retained."
 V10 = "Results are reproducible under documented procedure, standard and environment versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 FOUNDATIONS_OF_MEASUREMENT_DEFINITION = 0.99
 MEASURAND_REASONING = 0.99
 SCALE_REASONING = 0.99
 CALIBRATION_REASONING = 0.99
 TRACEABILITY_REASONING = 0.99
 UNCERTAINTY_REASONING = 0.98
 POLICY = "Reduce confidence when measurand definition, scale, reference standard, calibration status, influence quantities or uncertainty components are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,MeasurementTheoryReasoning,
  MeasurandReasoning,MeasurementProcedureReasoning,
  MeasurementScaleReasoning,QuantityReasoning,
  CalibrationReasoning,TraceabilityReasoning,
  AccuracyReasoning,PrecisionReasoning,
  MeasurementErrorReasoning,UncertaintyReasoning,
  MeasurementEquationReasoning,InfluenceQuantityReasoning,
  MetrologyReasoning,VerificationReasoning,
  KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "foundations of measurement" -> FoundationsOfMeasurement
  "measurand" -> Measurand
  "SI" -> InternationalSystemOfUnits
  "SNR" -> SignalToNoiseRatio
  "VIM" -> InternationalVocabularyOfMetrology
  "GUM" -> GuideToExpressionOfUncertaintyInMeasurement
 }
}

EXECUTION_RULES {
 E1 = "If the interpretation or design of a measurement process is primary, activate FoundationsOfMeasurement."
 E2 = "Specify the measurand before interpreting observed values."
 E3 = "Identify scale type, quantity kind, unit and reference system before performing mathematical operations."
 E4 = "Use calibration and corrections according to documented reference standards."
 E5 = "Separate accuracy, precision, bias, error and uncertainty."
 E6 = "Identify influence quantities that can materially affect the measurement result."
 E7 = "Propagate uncertainty through the declared measurement model."
 E8 = "Retain traceability and provenance from observation to reported result."
 E9 = "Report only precision and digits justified by resolution and uncertainty."
}

RECURSION {
 ENTRY = FoundationsOfMeasurement
 EXPAND(FoundationsOfMeasurement) -> [
  MeasurementTheory,Measurement,MeasurementProcess,
  MeasurementProcedure,MeasurementMethod,MeasurementModel,
  Observation,Observable,Measurand,Quantity,QuantityKind,
  MeasurementValue,MeasuredValue,ReferenceValue,MeasurementResult,
  QuantityComparison,Comparability,Scale,MeasurementScale,
  RatioScale,IntervalScale,OrdinalScale,NominalScale,
  Unit,MeasurementUnit,Dimension,DimensionalSignature,
  UnitConversion,MeasurementStandard,ReferenceStandard,
  PrimaryStandard,SecondaryStandard,CalibrationStandard,
  Calibration,CalibrationFunction,Correction,BiasCorrection,
  MeasurementTraceability,TraceabilityChain,Accuracy,Precision,
  Bias,SystematicError,RandomError,MeasurementError,
  Repeatability,Reproducibility,Resolution,Sensitivity,
  DetectionLimit,Range,DynamicRange,Noise,Signal,
  SignalToNoiseRatioRelationship,Uncertainty,MeasurementUncertainty,
  StandardUncertainty,CombinedUncertainty,ExpandedUncertainty,
  CoverageFactor,UncertaintyBudget,PropagationOfUncertainty,
  SignificantFigures,Rounding,Sampling,RepeatedMeasurement,
  DirectMeasurement,IndirectMeasurement,ComparativeMeasurement,
  MeasurementEquation,InputQuantity,OutputQuantity,
  InfluenceQuantity,InstrumentResponse,Metrology,
  ScientificMeasurement,MeasurementStandardisation,
  BIPMrelationship,NISTrelationship,VIMRelationship,GUMRelationship,
  Provenance,MeasurementProvenance,CalibrationProvenance
 ]
 EXPAND(FoundationsOfMeasurementFamilies) -> [
  MeasurandsQuantitiesAndMeasurementResults,
  MeasurementProceduresModelsAndObservations,
  MeasurementScalesUnitsAndComparability,
  StandardsCalibrationAndTraceability,
  AccuracyPrecisionResolutionAndError,
  UncertaintyBudgetsAndPropagation,
  InfluenceQuantitiesSamplingAndInstrumentResponse,
  MetrologyValidationAndProvenance
 ]
 STOP_CONDITION = "Stop when measurand, quantity, scale, procedure, calibration, uncertainty, traceability and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Measurement & Units Ontologies"
 RELATED_ONTOLOGIES = [
  "Measurement & Units Ontologies",
  "Scientific Measurement Ontology",
  "Units Ontology",
  "Quantity Ontology",
  "Dimensional Analysis Ontology",
  "Measurement Uncertainty Ontology",
  "Calibration Ontology",
  "Metrology Ontology",
  "Error Analysis Ontology",
  "Verification & Validation",
  "Probability & Statistics Ontologies",
  "Computational Scientific Workflows"
 ]
 ROUTE_RULES = [
  "Foundations of Measurement -> Measurement & Units Ontologies for parent semantics",
  "Foundations of Measurement -> Scientific Measurement for applied observation semantics",
  "Foundations of Measurement -> Units and Quantity ontologies for value representation",
  "Foundations of Measurement -> Dimensional Analysis for quantity compatibility",
  "Foundations of Measurement -> Measurement Uncertainty for uncertainty semantics",
  "Foundations of Measurement -> Calibration and Metrology for reference and traceability semantics",
  "Foundations of Measurement -> Error Analysis for error and bias semantics",
  "Foundations of Measurement -> Verification & Validation for measurement-system checking",
  "Foundations of Measurement -> Probability & Statistics for repeated measurements and uncertainty analysis",
  "Foundations of Measurement -> Computational Scientific Workflows for traceable computational measurement processes"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible measurement concepts, scale classes or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve measurand-versus-measurement-result distinction.",
  "Preserve quantity-versus-unit distinction.",
  "Preserve scale-type distinctions.",
  "Preserve calibration-versus-traceability distinction.",
  "Preserve accuracy-versus-precision distinction.",
  "Preserve error-versus-uncertainty distinction.",
  "Preserve observation-versus-inference distinction.",
  "Preserve machine-readable foundations-of-measurement semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Foundations of measurement define how values are assigned to quantities through specified procedures, scales, standards, calibration, uncertainty and traceability."
 MEASURAND_SUMMARY = "The measurand identifies exactly what quantity is intended to be measured."
 SCALE_SUMMARY = "Measurement scales determine which comparisons and mathematical operations are meaningful."
 CALIBRATION_SUMMARY = "Calibration relates indications to reference quantity values under declared conditions."
 UNCERTAINTY_SUMMARY = "Measurement uncertainty quantifies dispersion attributable to the measurand and must be distinguished from error."
 TRACEABILITY_SUMMARY = "Traceability links a measurement result through documented calibrations to recognised reference standards."
 VALIDATION_SUMMARY = "Measurement results should be scale-aware, uncertainty-aware, traceable, provenance-linked and reported with only justified precision."
}

FLOW {
 INPUT
 -> detect_foundations_of_measurement_context
 -> identify_measurand_intended_use_quantity_kind_procedure_instrument_conditions_standard_and_required_uncertainty
 -> define_measurand_and_influence_quantities
 -> identify_measurement_scale_unit_dimension_and_reference_system
 -> select_direct_indirect_comparative_or_derived_measurement_method
 -> determine_calibration_relation_corrections_and_traceability_chain
 -> obtain_observations_or_indications
 -> apply_measurement_equation_corrections_and_data_reduction
 -> identify_uncertainty_components_and_propagate_combined_uncertainty
 -> assess_accuracy_precision_range_resolution_and_fitness_for_purpose
 -> record_standard_versions_conditions_instrument_procedure_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-OF-MEASUREMENT-V1"
}

}

END_FLOW