Measurement Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Measurement Ontology within the Kireth Research Semantic Library. Measurement concerns the formal assignment or estimation of quantity values through specified procedures, observations, instruments, reference standards and measurement models. It supports measurands, quantity values, units, direct and indirect measurement, calibration, corrections, influence quantities, accuracy, precision, uncertainty, traceability, validation and provenance.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = Measurement
 ENTITY_CLASS = QuantityValueDeterminationFramework
 PRIMARY_CONTEXT = FoundationsOfMeasurement
 DEFINITION = "Measurement is the process of experimentally or computationally obtaining one or more quantity values that can reasonably be attributed to a specified measurand."
 SYMBOLIC_FORMS = [
  "M: measurand -> quantity_value",
  "result = {estimate,unit,uncertainty}",
  "y = f(x_1,...,x_n)",
  "reported_measurement = corrected_value ± uncertainty"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for measurands, observations, quantity values, procedures, measurement models, corrections, uncertainty, calibration, traceability and reporting."
}

SCOPE {
 INCLUDE = [
  Measurement,MeasurementProcess,MeasurementProcedure,MeasurementMethod,
  MeasurementPrinciple,MeasurementModel,MeasurementEquation,
  Observation,Observable,Measurand,Quantity,QuantityKind,PhysicalQuantity,
  MeasurableQuantity,QuantityValue,MeasurementValue,MeasuredValue,
  NumericalValue,EstimatedValue,AssignedValue,ReferenceValue,NominalValue,
  MeasurementResult,ReportedResult,CorrectedResult,MeasurementContext,
  MeasurementCondition,ReferenceCondition,InputQuantity,OutputQuantity,
  InfluenceQuantity,InfluenceFactor,EnvironmentalInfluence,InstrumentInfluence,
  DirectMeasurement,IndirectMeasurement,DerivedMeasurement,
  ComparativeMeasurement,RatioMeasurement,RepeatedMeasurement,
  ReplicateMeasurement,MeasurementSeries,TimeSeriesMeasurement,
  SpatialMeasurement,InstrumentMeasurement,SensorMeasurement,
  ScientificMeasurement,ExperimentalMeasurement,Unit,MeasurementUnit,
  UnitSymbol,QuantitySymbol,Dimension,DimensionalSignature,MeasurementScale,
  RatioScale,IntervalScale,OrdinalScale,NominalScale,LinearScale,
  LogarithmicScale,Instrument,MeasuringInstrument,Sensor,Indication,
  RawIndication,CorrectedIndication,InstrumentResponse,ResponseFunction,
  Calibration,CalibrationFunction,CalibrationCurve,CalibrationCorrection,
  Correction,CorrectionFactor,BiasCorrection,ZeroCorrection,DriftCorrection,
  ReferenceStandard,MeasurementStandard,CalibrationStandard,PrimaryStandard,
  SecondaryStandard,MeasurementTraceability,TraceabilityChain,
  MetrologicalTraceability,Accuracy,Precision,Trueness,Bias,MeasurementError,
  SystematicError,RandomError,AbsoluteError,RelativeError,Repeatability,
  Reproducibility,Resolution,Sensitivity,DetectionLimit,Quantisation,Range,
  DynamicRange,Threshold,Noise,Signal,SignalToNoiseRatio,SNR,Drift,Stability,
  Uncertainty,MeasurementUncertainty,StandardUncertainty,CombinedUncertainty,
  ExpandedUncertainty,TypeAUncertainty,TypeBUncertainty,CoverageFactor,
  CoverageProbability,UncertaintyBudget,ErrorBudget,PropagationOfUncertainty,
  Covariance,Correlation,Sampling,Sample,SamplingInterval,SamplingFrequency,
  Averaging,DataReduction,Rounding,SignificantFigures,DecimalPlaces,
  RoundOffError,FitnessForPurpose,Tolerance,AcceptanceCriterion,RangeCheck,
  PlausibilityCheck,ConsistencyCheck,UnitCheck,DimensionalCheck,
  MeasurementValidation,InstrumentVerification,Verification,Validation,
  ErrorAnalysis,Provenance,MeasurementProvenance,CalibrationProvenance,
  StandardProvenance,DataProvenance,Metadata,MeasurementMetadata,
  InstrumentIdentifier,StandardIdentifier,ProcedureVersion,InstrumentVersion,
  CalibrationVersion,StandardVersion
 ]
 EXCLUDE_AS_PRIMARY = [
  PureObservationWithoutQuantityValueAssignment,
  UnitConversionWithoutMeasurementProcess,
  CalibrationWhenReferenceRelationshipRatherThanMeasurementIsPrimary,
  StatisticalEstimationWithoutMeasurandOrMeasurementSemantics
 ]
 DISAMBIGUATION_RULE = "When a specified quantity is observed or evaluated through a procedure to obtain a quantity value with associated context and uncertainty, interpret the context as measurement."
}

CORE_CONCEPTS {
 Measurement = "Process of obtaining quantity values attributable to a measurand."
 Measurand = "Quantity intended to be measured."
 MeasurementProcedure = "Detailed specification of operations used to perform a measurement."
 MeasurementModel = "Mathematical relationship between output quantity and input quantities."
 MeasurementResult = "Quantity value or set of values attributed to a measurand together with relevant information."
 Indication = "Quantity value provided by a measuring instrument or system."
 InfluenceQuantity = "Quantity that affects the relation between indication and measurement result."
 MeasurementUncertainty = "Parameter characterising dispersion of quantity values attributed to the measurand."
}

RELATIONS {
 Measurement --is_child_of--> FoundationsOfMeasurement
 Measurement --targets--> Measurand
 MeasurementProcedure --implements--> MeasurementMethod
 MeasurementProcedure --produces--> MeasurementResult
 MeasurementResult --contains--> QuantityValue
 QuantityValue --uses--> Unit
 MeasurementModel --relates--> InputAndOutputQuantities
 Instrument --produces--> Indication
 Calibration --relates--> IndicationToReferenceValue
 Correction --modifies--> MeasurementEstimate
 InfluenceQuantity --affects--> MeasurementResult
 MeasurementUncertainty --qualifies--> MeasurementResult
 MeasurementTraceability --links--> ResultToReferenceStandard
 Provenance --records--> MeasurementHistory
}

OPERATORS {
 MEASURE(measurand,procedure,conditions) := obtain_quantity_value(measurand,procedure,conditions)
 MODEL(inputs,f) := f(inputs)
 CORRECT(value,c) := value + c
 CALIBRATE(indication,relation) := relation(indication)
 AVERAGE(values) := sum(values)/count(values)
 UNCERTAINTY(result) := evaluate_measurement_uncertainty(result)
 REPORT(value,unit,U) := {value,unit,U}
}

AXIOMS {
 A1 = "Measurement requires a specified measurand."
 A2 = "A measurement result is semantically richer than a bare numerical value."
 A3 = "The measurement procedure determines how observations become attributed quantity values."
 A4 = "Indirect measurements depend on a declared measurement model."
 A5 = "Influence quantities can alter the measurement result without being the measurand."
 A6 = "Calibration can correct systematic indication relationships but does not eliminate all uncertainty."
 A7 = "Measurement uncertainty is distinct from measurement error."
 A8 = "Measurement reasoning requires explicit measurand, procedure, unit, conditions, uncertainty and provenance semantics."
}

REASONING {
 R1_CONTEXT = identify(measurand,intended_use,quantity_kind,procedure,instrument,conditions,unit_and_required_uncertainty)
 R2_SPECIFY = define_measurand_and_influence_quantities)
 R3_METHOD = choose_direct_indirect_comparative_repeated_or_derived_measurement)
 R4_OBSERVE = obtain_instrument_indications_or_observations)
 R5_CALIBRATE = apply_calibration_relation_and_declared_corrections)
 R6_MODEL = if_indirect_evaluate_measurement_equation_from_input_quantities)
 R7_REDUCE = aggregate_filter_or_reduce_repeated_observations_as_declared)
 R8_UNCERTAINTY = identify_and_propagate_uncertainty_components)
 R9_VALIDATE = check_units_range_resolution_accuracy_precision_and_fitness_for_purpose)
 R10_REPORT = produce_traceable_measurement_result_with_provenance)
}

CONSTRAINTS {
 C1 = "An ambiguous measurand makes the meaning of the measurement result ambiguous."
 C2 = "Instrument resolution limits meaningful reported precision."
 C3 = "Repeated measurements do not remove common systematic bias."
 C4 = "Corrections themselves can carry uncertainty."
 C5 = "Indirect measurement uncertainty depends on input uncertainties and correlations."
 C6 = "Changing environmental conditions can invalidate calibration assumptions."
 C7 = "A precise measurement can still be inaccurate."
 C8 = "A result outside the instrument valid range requires qualification."
 C9 = "Rounding before uncertainty propagation can introduce avoidable error."
 C10 = "Measurement values must retain unit, scale and reference semantics."
}

SEMANTIC_EQUIVALENCE {
 "SignalToNoiseRatio" <=> "SNR"
 "MeasurementUnit" <=> "Unit"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
}

VALIDATION {
 V1 = "Measurand is explicitly defined."
 V2 = "Measurement procedure and method are documented."
 V3 = "Quantity kind, unit and scale are documented."
 V4 = "Instrument identity and operating range are documented where applicable."
 V5 = "Calibration status and corrections are documented."
 V6 = "Influence quantities are recorded where material."
 V7 = "Accuracy, precision, resolution, error and uncertainty are not conflated."
 V8 = "Uncertainty components and propagation method are documented."
 V9 = "Traceability and measurement provenance are retained."
 V10 = "Results are reproducible under documented procedure, instrument, calibration and standard versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 MEASUREMENT_DEFINITION = 0.99
 MEASURAND_REASONING = 0.99
 PROCEDURE_REASONING = 0.99
 CALIBRATION_REASONING = 0.99
 UNCERTAINTY_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when measurand, procedure, unit, calibration, influence quantities, uncertainty or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,MeasurementReasoning,
  MeasurandReasoning,QuantityValueReasoning,MeasurementProcedureReasoning,
  MeasurementModelReasoning,DirectMeasurementReasoning,
  IndirectMeasurementReasoning,InstrumentReasoning,CalibrationReasoning,
  InfluenceQuantityReasoning,AccuracyReasoning,PrecisionReasoning,
  UncertaintyReasoning,TraceabilityReasoning,MeasurementValidationReasoning,
  ProvenanceReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,
  RecursiveInference
 ]
 NORMALISE {
  "measurement" -> Measurement
  "measurand" -> Measurand
  "measurement unit" -> Unit
  "SNR" -> SignalToNoiseRatio
  "metrological traceability" -> MeasurementTraceability
 }
}

EXECUTION_RULES {
 E1 = "If a quantity value is obtained for a specified measurand through a declared procedure, activate MeasurementOntology."
 E2 = "Specify the measurand before collecting or interpreting observations."
 E3 = "Record quantity kind, unit, scale and measurement conditions."
 E4 = "Apply calibration and corrections before reporting the final estimate."
 E5 = "For indirect measurement, preserve the complete measurement equation and input quantities."
 E6 = "Separate accuracy, precision, error, bias, resolution and uncertainty."
 E7 = "Propagate uncertainty through the declared measurement model."
 E8 = "Validate range, units, plausibility and fitness for intended use."
 E9 = "Report measurement results with traceability and provenance."
}

RECURSION {
 ENTRY = Measurement
 EXPAND(Measurement) -> [
  MeasurementProcess,MeasurementProcedure,MeasurementMethod,
  MeasurementPrinciple,MeasurementModel,MeasurementEquation,
  Observation,Observable,Measurand,Quantity,QuantityKind,QuantityValue,
  MeasurementValue,MeasuredValue,ReferenceValue,MeasurementResult,
  MeasurementContext,MeasurementCondition,InputQuantity,OutputQuantity,
  InfluenceQuantity,DirectMeasurement,IndirectMeasurement,
  DerivedMeasurement,ComparativeMeasurement,RepeatedMeasurement,
  MeasurementSeries,InstrumentMeasurement,SensorMeasurement,
  ScientificMeasurement,Unit,MeasurementUnit,Dimension,MeasurementScale,
  Instrument,MeasuringInstrument,Sensor,Indication,InstrumentResponse,
  Calibration,CalibrationFunction,CalibrationCurve,Correction,
  BiasCorrection,ReferenceStandard,MeasurementTraceability,
  TraceabilityChain,Accuracy,Precision,Trueness,Bias,MeasurementError,
  SystematicError,RandomError,Repeatability,Reproducibility,Resolution,
  Sensitivity,DetectionLimit,Range,DynamicRange,Noise,Signal,
  SignalToNoiseRatio,SNR,Drift,Stability,Uncertainty,
  MeasurementUncertainty,StandardUncertainty,CombinedUncertainty,
  ExpandedUncertainty,TypeAUncertainty,TypeBUncertainty,CoverageFactor,
  UncertaintyBudget,PropagationOfUncertainty,Sampling,Averaging,
  DataReduction,SignificantFigures,MeasurementValidation,Verification,
  Provenance,MeasurementProvenance,CalibrationProvenance
 ]
 EXPAND(MeasurementFamilies) -> [
  MeasurandQuantityAndValueSemantics,
  ProceduresMethodsAndMeasurementModels,
  DirectIndirectAndComparativeMeasurement,
  InstrumentsIndicationsAndCalibration,
  AccuracyPrecisionResolutionAndError,
  UncertaintyComponentsAndPropagation,
  StandardsTraceabilityAndValidation,
  ReportingMetadataAndProvenance
 ]
 STOP_CONDITION = "Stop when measurand, procedure, observation, calibration, result, uncertainty, traceability and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Foundations of Measurement"
 RELATED_ONTOLOGIES = [
  "Foundations of Measurement",
  "Measurement & Units Ontologies",
  "Quantity Ontology",
  "Units Ontology",
  "Measurement Scale Ontology",
  "Measurement Uncertainty Ontology",
  "Calibration Ontology",
  "Metrology Ontology",
  "Scientific Measurement Ontology",
  "Error Analysis Ontology",
  "Verification & Validation",
  "Probability & Statistics Ontologies"
 ]
 ROUTE_RULES = [
  "Measurement -> Foundations of Measurement for parent theory semantics",
  "Measurement -> Measurement & Units Ontologies for quantity and unit semantics",
  "Measurement -> Quantity Ontology for measurand and quantity-kind semantics",
  "Measurement -> Units Ontology for unit representation and conversion",
  "Measurement -> Measurement Scale Ontology for scale semantics",
  "Measurement -> Measurement Uncertainty for uncertainty evaluation",
  "Measurement -> Calibration and Metrology for standards and traceability",
  "Measurement -> Scientific Measurement for applied measurement processes",
  "Measurement -> Error Analysis for error and bias semantics",
  "Measurement -> Verification & Validation for procedure and result checks",
  "Measurement -> Probability & Statistics for repeated observations and uncertainty analysis"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible measurement methods, result classes or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve measurand-versus-measured-value distinction.",
  "Preserve observation-versus-measurement-result distinction.",
  "Preserve direct-versus-indirect measurement distinction.",
  "Preserve indication-versus-corrected-result distinction.",
  "Preserve accuracy-versus-precision distinction.",
  "Preserve error-versus-uncertainty distinction.",
  "Preserve calibration-versus-measurement distinction.",
  "Preserve machine-readable measurement semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Measurement is the process of obtaining one or more quantity values that can reasonably be attributed to a specified measurand."
 MEASURAND_SUMMARY = "The measurand defines the quantity intended to be measured and must be specified before interpreting results."
 PROCEDURE_SUMMARY = "Measurement procedures define how observations, indications and input quantities become a reported quantity value."
 CALIBRATION_SUMMARY = "Calibration relates instrument indications to reference values and supplies corrections with associated uncertainty."
 UNCERTAINTY_SUMMARY = "A complete measurement result includes uncertainty appropriate to the measurement model and intended use."
 TRACEABILITY_SUMMARY = "Traceability links the reported result through documented calibrations to recognised reference standards."
 VALIDATION_SUMMARY = "Measurement results should preserve unit, scale, conditions, calibration, uncertainty, traceability and provenance semantics."
}

FLOW {
 INPUT
 -> detect_measurement_context
 -> identify_measurand_intended_use_quantity_kind_procedure_instrument_conditions_unit_and_required_uncertainty
 -> specify_measurand_and_material_influence_quantities
 -> choose_direct_indirect_comparative_repeated_or_derived_measurement_method
 -> obtain_instrument_indications_observations_or_input_quantity_values
 -> apply_calibration_relation_and_declared_corrections
 -> if_indirect_evaluate_measurement_equation
 -> aggregate_filter_or_reduce_repeated_observations_as_declared
 -> identify_and_propagate_measurement_uncertainty_components
 -> check_units_scale_range_resolution_accuracy_precision_and_fitness_for_purpose
 -> construct_reported_measurement_result
 -> record_traceability_standard_versions_instrument_procedure_conditions_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-MEASUREMENT-ONTOLOGY-V1"
}

}

END_FLOW