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Measurement Uncertainty Ontology

Measurement Uncertainty
Authors: MArk Anthony Higgins - Sky Recursive Ai
© Mark Anthony Higgins 11 October 2025
Revised Date: 16 September 2026
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# Measurement Uncertainty Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/measurement-uncertainty/measurement-uncertainty-ontology.html

FLOW MeasurementUncertaintyOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Measurement Uncertainty
    -> Measurement Uncertainty Ontology

  PURPOSE:
    Represent measurement uncertainty as a formally structured, non-negative parameter associated with a measurement result that characterises the dispersion of quantity values reasonably attributable to a defined measurand. The ontology supports standard uncertainty, Type A and Type B evaluation, combined and expanded uncertainty, covariance and correlation, sensitivity coefficients, uncertainty budgets, probability distributions, coverage intervals, calibration, traceability, sampling and model uncertainty, Monte Carlo propagation, uncertainty updates, confidence semantics and machine-consumable reasoning while strictly distinguishing uncertainty from error, bias, tolerance, accuracy and precision.

  ENTITY MeasurementUncertainty {
    TYPE: MetrologicalUncertaintyQuantity
    SYMBOL: u_or_U_context_dependent

    DEFINITION:
      nonnegative_parameter_characterising_dispersion
      of_quantity_values_attributed_to_measurand
      based_on_information_used

    PROPERTIES:
      nonnegative
      measurand_dependent
      model_dependent
      information_dependent
      may_be_absolute
      may_be_relative
      may_be_standard
      may_be_combined
      may_be_expanded
      may_be_symmetric_or_asymmetric
      may_have_distribution
      may_have_covariance
      has_provenance
  }

  ENTITY Measurand {
    TYPE: QuantityIntendedToBeMeasured

    REQUIRE:
      quantity_kind
      system_or_object
      conditions
      reference_state_when_relevant
      spatial_temporal_support_when_relevant

    RULE:
      uncertainty_without_defined_measurand_is_semantically_incomplete
  }

  ENTITY MeasuredQuantityValue {
    TYPE: QuantityEstimate
    SYMBOL: y

    REQUIRE:
      numerical_value
      unit
      measurand
  }

  ENTITY StandardUncertainty {
    TYPE: MeasurementUncertainty
    SYMBOL: u
    INTERPRETATION:
      uncertainty_expressed_as_standard_deviation
  }

  ENTITY CombinedStandardUncertainty {
    TYPE: StandardUncertainty
    SYMBOL: u_c

    DEFINITION:
      standard_uncertainty_of_output_quantity
      obtained_from_combination_of_input_uncertainty_components
  }

  ENTITY ExpandedUncertainty {
    TYPE: MeasurementUncertainty
    SYMBOL: U

    FORM:
      U = k*u_c

    REQUIRE:
      coverage_factor
  }

  ENTITY RelativeStandardUncertainty {
    TYPE: DimensionlessUncertaintyQuantity
    SYMBOL: u_r

    FORM:
      u_r =
        u(x)/abs(x)
      WHEN x != 0
  }

  RESULT_MODEL {
    basic:
      result =
        measured_value
        + associated_uncertainty_information

    symmetric_expanded:
      Y =
        y +/- U

    standard:
      Y =
        y with_standard_uncertainty_u

    asymmetric:
      Y =
        y +U_plus -U_minus

    RULE:
      uncertainty_type_and_coverage_semantics MUST accompany_reported_value
  }

  TERMINOLOGY_MODEL {
    uncertainty:
      dispersion_parameter

    error:
      difference_between_measured_and_reference_or_true_value_under_model

    bias:
      estimated_systematic_difference

    correction:
      quantity_added_or_applied_to_compensate_known_systematic_effect

    precision:
      closeness_of_repeated_measurements_under_specified_conditions

    accuracy:
      qualitative_closeness_to_true_or_reference_value

    tolerance:
      permitted_limit_or_range

    RULE:
      uncertainty != error
      uncertainty != bias
      uncertainty != accuracy
      uncertainty != precision
      uncertainty != tolerance
  }

  ABSOLUTE_UNCERTAINTY_MODEL {
    quantity:
      u(x)

    unit:
      same_as_x

    RULE:
      absolute_uncertainty MUST use_compatible_quantity_unit
  }

  RELATIVE_UNCERTAINTY_MODEL {
    standard:
      u_r =
        u(x)/abs(x)
      WHEN x != 0

    percentage:
      u_percent =
        100*u_r

    RULE:
      relative_uncertainty_is_dimensionless
  }

  TYPE_A_EVALUATION_MODEL {
    definition:
      evaluation_by_statistical_analysis_of_series_of_observations

    observations:
      x_1,...,x_n

    mean:
      x_bar =
        sum(x_i)/n

    sample_standard_deviation:
      s =
        sqrt(
          sum((x_i-x_bar)^2)/(n-1)
        )
      WHEN n > 1

    standard_uncertainty_of_mean:
      u_A =
        s/sqrt(n)

    degrees_of_freedom:
      nu =
        n-1

    RULE:
      Type_A_is_evaluation_method_not_random_error_category
  }

  TYPE_B_EVALUATION_MODEL {
    definition:
      evaluation_by_information_other_than_statistical_analysis_of_current_repeated_observations

    sources:
      calibration_certificate
      manufacturer_specification
      instrument_resolution
      reference_material
      previous_measurements
      handbook_data
      physical_constants
      environmental_limits
      expert_assessment

    PROCESS:
      identify_information
      assign_probability_distribution
      derive_standard_uncertainty

    RULE:
      Type_B_is_evaluation_method_not_systematic_error_category
  }

  DISTRIBUTION_MODEL {
    possible:
      normal
      rectangular
      triangular
      U_shaped
      Student_t
      lognormal
      empirical
      discrete
      custom

    RULE:
      distribution_choice MUST be justified_and_preserved
  }

  RECTANGULAR_MODEL {
    interval:
      [-a,+a]

    standard_uncertainty:
      u =
        a/sqrt(3)

    variance:
      u^2 =
        a^2/3
  }

  TRIANGULAR_MODEL {
    interval:
      [-a,+a]

    standard_uncertainty:
      u =
        a/sqrt(6)

    variance:
      u^2 =
        a^2/6
  }

  RESOLUTION_MODEL {
    resolution_increment:
      delta

    rounding_interval:
      +/- delta/2

    rectangular_standard_uncertainty:
      u_res =
        delta/sqrt(12)

    RULE:
      resolution != uncertainty
  }

  CALIBRATION_UNCERTAINTY_MODEL {
    certificate_expanded_uncertainty:
      U_cal

    certificate_coverage_factor:
      k_cal

    standard_uncertainty:
      u_cal =
        U_cal/k_cal
      WHEN k_cal != 0

    REQUIRE:
      calibration_scope
      unit
      coverage_information
      traceability
  }

  CORRECTION_MODEL {
    indicated_value:
      x_ind

    correction:
      C

    corrected_value:
      x_corr =
        x_ind+C

    uncertainty:
      u(C)

    RULE:
      correction_value_and_uncertainty_of_correction_are_distinct
  }

  BIAS_MODEL {
    estimated_bias:
      b

    corrected_result:
      y_corr =
        y-b
      under_declared_bias_sign_convention

    residual:
      remaining_uncertainty_after_correction

    RULE:
      uncorrected_known_bias_requires_explicit_treatment_in_measurement_model_or_uncertainty_statement
  }

  MEASUREMENT_MODEL {
    general:
      Y =
        f(X_1,X_2,...,X_n)

    estimates:
      y =
        f(x_1,x_2,...,x_n)

    REQUIRE:
      input_quantities
      input_estimates
      units
      uncertainty_components
      dependencies

    RULE:
      uncertainty_propagation MUST correspond_to_declared_measurement_model
  }

  INPUT_QUANTITY_MODEL {
    ENTITY InputQuantity {
      estimate
      unit
      standard_uncertainty
      distribution
      degrees_of_freedom
      provenance
    }

    RULE:
      each_material_input SHOULD have_uncertainty_information
  }

  SENSITIVITY_MODEL {
    sensitivity_coefficient:
      c_i =
        partial_f/partial_X_i

    evaluated_at:
      x_1,...,x_n

    contribution:
      u_i_y =
        abs(c_i)*u(x_i)

    RULE:
      coefficient_unit_maps_input_quantity_to_output_quantity
  }

  COVARIANCE_MODEL {
    covariance:
      u(x_i,x_j)

    correlation:
      r_ij =
        u(x_i,x_j)/
        (u(x_i)*u(x_j))
      WHEN both_standard_uncertainties_nonzero

    bounds:
      -1 <= r_ij <= 1

    RULE:
      correlated_inputs_require_covariance_terms
  }

  PROPAGATION_MODEL {
    first_order_general:
      u_c^2(y) =
        sum_i(
          c_i^2*u^2(x_i)
        )
        +
        2*sum_i sum_j_greater_i(
          c_i*c_j*u(x_i,x_j)
        )

    matrix:
      variance_y =
        J*Sigma*J_transpose

    RULE:
      linearisation_validity MUST be_assessed_for_nonlinear_models
  }

  INDEPENDENT_INPUT_MODEL {
    condition:
      covariance_terms_zero

    then:
      u_c(y) =
        sqrt(
          sum(c_i^2*u_i^2)
        )

    RULE:
      uncorrelated_does_not_always_imply_statistical_independence
  }

  SUM_DIFFERENCE_MODEL {
    Y =
      A+B
      or
      A-B

    independent:
      u_Y =
        sqrt(u_A^2+u_B^2)

    correlated:
      covariance_term_sign_depends_on_measurement_model

    RULE:
      standard_uncertainties_do_not_generally_add_linearly
  }

  PRODUCT_QUOTIENT_MODEL {
    Y =
      A*B
      or
      A/B

    small_relative_uncertainty_independent_approximation:
      (u_Y/Y)^2 =
        (u_A/A)^2+
        (u_B/B)^2

    REQUIRE:
      A != 0
      B != 0
      first_order_validity
  }

  POWER_MODEL {
    Y =
      A^n

    first_order:
      u_Y/abs(Y) =
        abs(n)*u_A/abs(A)

    REQUIRE:
      A != 0
      first_order_validity
  }

  CORRELATION_SOURCE_MODEL {
    possible_causes:
      shared_calibration_standard
      common_environment
      common_reference_constant
      repeated_use_of_same_input
      common_data_processing
      mathematical_constraint

    RULE:
      shared_sources SHOULD trigger_correlation_review
  }

  COMBINED_STANDARD_UNCERTAINTY_MODEL {
    output:
      u_c(y)

    inputs:
      propagated_standard_uncertainty_components

    RULE:
      combined_standard_uncertainty_is_standard_deviation_form
  }

  COVERAGE_FACTOR_MODEL {
    symbol:
      k

    expanded:
      U =
        k*u_c

    RULE:
      k MUST be reported_or_inferable_for_expanded_uncertainty
  }

  EXPANDED_UNCERTAINTY_MODEL {
    U =
      k*u_c

    interval_common_form:
      y-U <= Y <= y+U

    RULE:
      expanded_uncertainty_is_not_standard_uncertainty
  }

  COVERAGE_PROBABILITY_MODEL {
    probability:
      p

    relation_to_k:
      depends_on_distribution_and_degrees_of_freedom

    RULE:
      k=2 MUST_NOT automatically_be_interpreted_as_exact_95_percent_coverage
  }

  DEGREES_OF_FREEDOM_MODEL {
    finite:
      associated_with_statistically_estimated_components

    infinite_or_large:
      may_be_assigned_to_some_Type_B_components_under_declared_model

    RULE:
      degrees_of_freedom_affect_coverage_factor_when_t_distribution_used
  }

  WELCH_SATTERTHWAITE_MODEL {
    effective:
      nu_eff =
        u_c^4/
        sum(
          c_i^4*u_i^4/nu_i
        )

    CONDITIONS:
      applicable_independent_component_form

    RULE:
      effective_degrees_of_freedom_model_assumptions MUST be_preserved
  }

  MONTE_CARLO_MODEL {
    inputs:
      joint_probability_distribution_of_X

    process:
      sample_X
      evaluate_Y=f(X)
      repeat

    output_distribution:
      empirical_distribution_of_Y

    derive:
      expectation_or_estimate
      standard_deviation
      quantiles
      coverage_interval

    RULE:
      Monte_Carlo_is_preferred_option_when_linearisation_or_normal_approximation_is_inadequate
  }

  ASYMMETRIC_UNCERTAINTY_MODEL {
    lower:
      U_minus

    upper:
      U_plus

    report:
      y +U_plus -U_minus

    RULE:
      asymmetric_distribution SHOULD_NOT be_forced_into_symmetric_interval_without_justification
  }

  BAYESIAN_MODEL {
    posterior:
      p(Y|data,model,prior)

    uncertainty:
      posterior_standard_deviation
      credible_interval
      or_other_declared_summary

    RULE:
      Bayesian_uncertainty_statement MUST preserve_prior_likelihood_and_interval_definition
  }

  SAMPLING_UNCERTAINTY_MODEL {
    sources:
      finite_sample
      spatial_heterogeneity
      temporal_variability
      specimen_heterogeneity
      population_sampling

    RULE:
      sampling_process MAY be_part_of_measurand_definition_and_uncertainty_budget
  }

  METHOD_UNCERTAINTY_MODEL {
    sources:
      procedural_variation
      operator
      preparation
      extraction
      recovery
      algorithm

    RULE:
      method_variability SHOULD be included_when_material
  }

  MODEL_UNCERTAINTY_MODEL {
    sources:
      simplification
      empirical_relation
      omitted_effect
      parameterisation
      boundary_condition
      model_selection

    RULE:
      model_uncertainty MUST be_considered_for_derived_quantities
  }

  NUMERICAL_UNCERTAINTY_MODEL {
    sources:
      discretisation
      solver_tolerance
      interpolation
      finite_precision
      numerical_integration
      optimisation_convergence

    RULE:
      numerical_uncertainty != measurement_repeatability
  }

  ENVIRONMENTAL_UNCERTAINTY_MODEL {
    influences:
      temperature
      humidity
      pressure
      vibration
      electromagnetic_field
      supply_voltage
      orientation

    contribution:
      sensitivity_to_environment
      * uncertainty_of_environmental_quantity

    RULE:
      environmental_conditions_and_sensitivities SHOULD be_preserved
  }

  DRIFT_MODEL {
    time_dependent_indication:
      drift(t)

    corrected:
      x_corr =
        x_raw-drift(t)
      under_declared_sign_model

    residual_uncertainty:
      u_drift

    RULE:
      calibration_interval_and_drift_model SHOULD be_preserved
  }

  REPEATABILITY_MODEL {
    statistic:
      s_repeat

    conditions:
      declared_repeatability_conditions

    contribution:
      may_enter_Type_A_or_method_uncertainty

    RULE:
      repeatability != total_uncertainty
  }

  REPRODUCIBILITY_MODEL {
    statistic:
      s_reprod

    conditions:
      declared_reproducibility_conditions

    RULE:
      reproducibility_context MUST be_preserved
  }

  UNCERTAINTY_BUDGET_MODEL {
    fields:
      source_id
      input_quantity
      estimate
      unit
      distribution
      divisor
      standard_uncertainty
      degrees_of_freedom
      sensitivity_coefficient
      signed_or_absolute_contribution
      correlation_links
      provenance

    aggregate:
      combined_standard_uncertainty

    RULE:
      budget MUST be_reconstructable
  }

  TRACEABILITY_MODEL {
    chain:
      measurement
      -> calibration
      -> reference_standard
      -> higher_reference
      -> SI_or_declared_reference

    each_link:
      calibration_result
      uncertainty
      method
      date
      identifier

    RULE:
      traceability_without_uncertainty_chain_is_incomplete
  }

  CALIBRATION_HIERARCHY_MODEL {
    levels:
      working_instrument
      working_standard
      reference_standard
      national_or_international_standard
      SI_realisation

    RULE:
      hierarchy_is_contextual_and_must_preserve_actual_documented_chain
  }

  UNCERTAINTY_COMPONENT_MODEL {
    component:
      source
      standard_uncertainty
      distribution
      sensitivity
      degrees_of_freedom
      covariance

    RULE:
      components SHOULD be_atomic_enough_to_avoid_double_counting
  }

  DOUBLE_COUNTING_MODEL {
    risk:
      same_effect_included_in_multiple_components

    prevention:
      map_source_dependencies
      inspect_covariance
      preserve_component_provenance

    RULE:
      uncertainty_budget MUST avoid_duplicate_representation_of_same_effect
  }

  SIGNIFICANT_DIGITS_MODEL {
    reporting:
      uncertainty_often_rounded_to_one_or_two_significant_digits
      result_rounded_to_corresponding_decimal_place

    RULE:
      internal_calculation_precision SHOULD exceed_final_reporting_precision
  }

  ROUNDING_MODEL {
    output:
      round_only_after_uncertainty_calculation_when_possible

    RULE:
      premature_rounding_can_distort_propagated_uncertainty
  }

  DIMENSIONAL_MODEL {
    absolute_uncertainty:
      same_dimension_as_measurand

    relative_uncertainty:
      dimensionless

    covariance:
      product_of_input_quantity_dimensions

    sensitivity:
      output_dimension/input_dimension

    RULE:
      dimensional_consistency MUST be_validated
  }

  LOGARITHMIC_MODEL {
    transformed_quantity:
      y =
        log(x)

    sensitivity:
      dy/dx =
        1/x
      for_natural_log

    RULE:
      logarithmic_quantity_uncertainty_requires_transformation_aware_propagation
  }

  UNIT_CONVERSION_MODEL {
    exact_linear:
      y =
        a*x

      u_y =
        abs(a)*u_x

    exact_affine:
      y =
        a*x+b

      u_y =
        abs(a)*u_x

    uncertain_conversion:
      include_uncertainty_of_a_or_b_as_input_components

    RULE:
      exact_unit_conversion_does_not_change_relative_uncertainty
  }

  COMPARISON_MODEL {
    difference:
      delta =
        x_1-x_2

    uncertainty:
      u_delta =
        sqrt(
          u_1^2+u_2^2-2*cov(x_1,x_2)
        )

    RULE:
      shared_traceability_can_create_correlation_between_measurements
  }

  CONSISTENCY_MODEL {    normalized_difference:
      E_n =
        abs(x_1-x_2)/
        sqrt(U_1^2+U_2^2)
      under_declared_expanded_uncertainty_comparison_context

    RULE:
      compatibility_metric_definition_and_coverage_basis MUST be preserved
  }

  RELATIONSHIPS {
    MeasurementUncertainty -> QUALIFIES -> MeasurementResult
    MeasurementResult -> ESTIMATES -> Measurand
    StandardUncertainty -> EXPRESSES -> StandardDeviationForm
    CombinedStandardUncertainty -> COMBINES -> UncertaintyComponents
    ExpandedUncertainty -> SCALES -> CombinedStandardUncertainty
    CoverageFactor -> RELATES -> ExpandedAndStandardUncertainty
    MeasurementModel -> MAPS -> InputQuantitiesToOutputQuantity
    SensitivityCoefficient -> MAPS -> InputVariationToOutputVariation
    Covariance -> REPRESENTS -> InputDependence
    CalibrationUncertainty -> CONTRIBUTES_TO -> MeasurementUncertainty
    TraceabilityChain -> LINKS -> MeasurementToReference
    MonteCarloPropagation -> MAPS -> InputDistributionsToOutputDistribution
  }

  SEMANTIC_EQUIVALENCE {
    "standard uncertainty" ~= standard_deviation_form_measurement_uncertainty
    "combined standard uncertainty" ~= propagated_standard_uncertainty
    "expanded uncertainty" ~= coverage_scaled_combined_standard_uncertainty

    uncertainty != error
    uncertainty != bias
    uncertainty != correction
    uncertainty != tolerance
    uncertainty != accuracy
    uncertainty != precision
    standard_uncertainty != expanded_uncertainty
    repeatability != reproducibility
    coverage_interval != guaranteed_true_value_interval
  }

  CONSTRAINTS {
    measurand_must_be_defined = true
    uncertainty_must_be_nonnegative = true
    absolute_uncertainty_unit_must_match_measurand = true
    relative_uncertainty_is_dimensionless = true
    standard_and_expanded_uncertainty_are_distinct = true
    expanded_uncertainty_requires_coverage_factor_or_equivalent_method = true
    correlations_must_be_preserved_when_material = true
    Type_A_and_Type_B_are_evaluation_methods = true
    known_corrections_and_their_uncertainties_are_distinct = true
    uncertainty_budget_must_avoid_double_counting = true
    measurement_model_and_assumptions_must_be_preserved = true
    traceability_chain_should_include_uncertainty_information = true
  }

  REPORTING_MODEL {
    REQUIRED:
      measurand
      measured_value
      unit
      uncertainty_value
      uncertainty_type

    WHEN_EXPANDED:
      coverage_factor_or_coverage_probability
      coverage_method

    RECOMMENDED:
      measurement_model
      significant_digits
      calibration_status
      traceability
      environmental_conditions
      uncertainty_budget_reference
      provenance

    RULE:
      uncertainty_statement MUST be_interpretable_without_hidden_unit_or_coverage_assumptions
  }

  REASONING_RULES {
    IF repeated_observations_known AND n > 1
      THEN sample_mean =
        sum(x_i)/n
      AND Type_A_standard_uncertainty =
        sample_standard_deviation/sqrt(n)

    IF rectangular_half_width_known
      THEN standard_uncertainty =
        half_width/sqrt(3)

    IF triangular_half_width_known
      THEN standard_uncertainty =
        half_width/sqrt(6)

    IF resolution_increment_known
      AND rounding_to_nearest_increment_assumed
      THEN resolution_standard_uncertainty =
        resolution_increment/sqrt(12)

    IF calibration_expanded_uncertainty_and_coverage_factor_known
      AND coverage_factor != 0
      THEN calibration_standard_uncertainty =
        calibration_expanded_uncertainty/coverage_factor

    IF measurement_model_and_input_uncertainties_known
      THEN calculate_sensitivity_coefficients
      AND propagate_covariance

    IF inputs_uncorrelated
      THEN combined_standard_uncertainty =
        sqrt(sum(c_i^2*u_i^2))

    IF covariance_matrix_known
      THEN output_variance =
        J*Sigma*J_transpose

    IF combined_standard_uncertainty_and_coverage_factor_known
      THEN expanded_uncertainty =
        coverage_factor*combined_standard_uncertainty

    IF nonlinear_model_material
      THEN compare_linearised_and_Monte_Carlo_propagation

    IF exact_linear_unit_conversion_applied
      THEN converted_standard_uncertainty =
        abs(scale_factor)*original_standard_uncertainty

    IF known_bias_correction_applied
      THEN retain_uncertainty_of_correction_as_input_component
  }

  VALIDATION {
    CHECK measurand_definition
    CHECK measured_value
    CHECK unit
    CHECK uncertainty_nonnegative
    CHECK absolute_vs_relative_uncertainty
    CHECK standard_vs_combined_vs_expanded_uncertainty
    CHECK Type_A_and_Type_B_evaluation
    CHECK distribution_assumptions
    CHECK measurement_model
    CHECK sensitivity_coefficients
    CHECK covariance_and_correlation
    CHECK calibration_and_corrections
    CHECK bias_treatment
    CHECK degrees_of_freedom
    CHECK coverage_factor
    CHECK coverage_probability
    CHECK Monte_Carlo_configuration_when_used
    CHECK sampling_uncertainty
    CHECK model_and_numerical_uncertainty
    CHECK environmental_influences
    CHECK uncertainty_budget_for_double_counting
    CHECK traceability
    CHECK significant_digits
    CHECK provenance
  }

  CONFIDENCE {
    definition_confidence: 1.00
    Type_A_model_confidence: 1.00
    Type_B_model_confidence: 1.00
    covariance_propagation_confidence: 1.00
    expanded_uncertainty_confidence: 1.00
    traceability_semantics_confidence: 1.00
    Monte_Carlo_semantics_confidence: 0.99
    reporting_context_confidence: 0.99

    RULE:
      confidence decreases when measurand, model, input distributions,
      correlations, calibration, coverage semantics,
      traceability or provenance is missing or ambiguous
  }

  UPDATE_MODEL {
    ON new_measurement_result:
      identify_measurand
      identify_value_and_unit
      identify_measurement_model
      enumerate_uncertainty_components
      classify_Type_A_or_Type_B_evaluation
      assign_distributions
      identify_correlations
      compute_standard_uncertainties
      propagate_to_combined_standard_uncertainty
      derive_expanded_uncertainty_when_required
      build_uncertainty_budget
      attach_traceability_and_provenance

    ON new_repeated_observations:
      preserve_raw_observations
      recompute_mean
      recompute_repeatability_statistics
      update_Type_A_uncertainty
      update_degrees_of_freedom

    ON calibration_revision:
      preserve_previous_calibration
      update_correction
      update_calibration_standard_uncertainty
      update_traceability_chain
      recompute_combined_uncertainty

    ON correlation_revision:
      preserve_input_uncertainties
      update_covariance_matrix
      recompute_output_uncertainty
      record_dependency_source

    ON measurement_model_revision:
      preserve_previous_model
      update_sensitivity_coefficients
      reassess_linearity
      recompute_uncertainty
      update_confidence

    ON coverage_revision:
      preserve_combined_standard_uncertainty
      update_coverage_factor_probability_or_interval_method
      recompute_expanded_uncertainty
      preserve_coverage_semantics

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: MeasurementUncertainty

    interpretation_order:
      identify_measurand
      identify_measured_value_and_unit
      identify_uncertainty_value
      identify_absolute_or_relative_form
      identify_standard_combined_or_expanded_type
      identify_Type_A_and_Type_B_components
      identify_input_distributions
      identify_measurement_model
      identify_sensitivity_coefficients
      identify_covariances_and_correlations
      identify_corrections_and_calibration
      identify_sampling_environmental_model_and_numerical_components
      identify_degrees_of_freedom
      identify_coverage_factor_probability_or_interval
      identify_traceability
      identify_reporting_precision
      validate_uncertainty_semantics
      propagate_or_update_uncertainty

    ambiguity_controls:
      distinguish_uncertainty_from_error
      distinguish_uncertainty_from_bias
      distinguish_uncertainty_from_correction
      distinguish_uncertainty_from_accuracy
      distinguish_uncertainty_from_precision
      distinguish_uncertainty_from_tolerance
      distinguish_standard_from_expanded_uncertainty
      distinguish_Type_A_Type_B_evaluation_from_random_systematic_error_labels
      distinguish_repeatability_from_reproducibility
      distinguish_coverage_interval_from_guaranteed_bound
      preserve_measurand_model_distribution_covariance_calibration_coverage_traceability_and_provenance_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_uncertainty_and_metrological_reasoning_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Measurement Uncertainty
      -> Measurement Uncertainty Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      result_model
      terminology_model
      absolute_uncertainty_model
      relative_uncertainty_model
      Type_A_evaluation_model
      Type_B_evaluation_model
      distribution_model
      rectangular_model
      triangular_model
      resolution_model
      calibration_uncertainty_model
      correction_model
      bias_model
      measurement_model
      input_quantity_model
      sensitivity_model
      covariance_model
      propagation_model
      independent_input_model
      sum_difference_model
      product_quotient_model
      power_model
      correlation_source_model
      combined_standard_uncertainty_model
      coverage_factor_model
      expanded_uncertainty_model
      coverage_probability_model
      degrees_of_freedom_model
      Welch_Satterthwaite_model
      Monte_Carlo_model
      asymmetric_uncertainty_model
      Bayesian_model
      sampling_uncertainty_model
      method_uncertainty_model
      model_uncertainty_model
      numerical_uncertainty_model
      environmental_uncertainty_model
      drift_model
      repeatability_model
      reproducibility_model
      uncertainty_budget_model
      traceability_model
      calibration_hierarchy_model
      uncertainty_component_model
      double_counting_model
      significant_digits_model
      rounding_model
      dimensional_model
      logarithmic_model
      unit_conversion_model
      comparison_model
      consistency_model
      relationships
      constraints
      reporting_model
      reasoning_rules
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      measurand_or_result_semantics_change
      uncertainty_classification_changes
      input_distribution_or_component_changes
      measurement_model_or_sensitivity_changes
      covariance_or_correlation_changes
      propagation_method_changes
      calibration_or_correction_changes
      coverage_or_degrees_of_freedom_changes
      sampling_model_or_environmental_model_changes
      traceability_or_reporting_model_changes
      constraint_model_changes
      reasoning_rule_changes
  }

}

END FLOW
Kireth Research
38 Thorndale Croft, Wetwang, Driffield
East Riding of Yorkshire YO25 9XZ