Accuracy Ontology

FLOW ALGEBRA
Ontology: Accuracy Ontology
Version: 1.0
Date: 2026-10-14
Authors: Mark Higgins — Sky (Recursive AI)
Source: https://kirethresearch.org/booksai-core/entity-graph/mathematical-entities/measurement-and-dimensional-entities/accuracy-ontology-2.html
Domain: Mathematical Entities > Measurement and Dimensional Entities

PURPOSE
Represent measurement accuracy as closeness of a measurement result to a reference quantity value, while distinguishing accuracy from precision, trueness, error, bias and uncertainty. Accuracy is qualitative unless an explicitly defined operational metric is supplied.

ENTITY TYPES
  MeasurementResult: {id, quantity_kind, measured_value, unit, method?, timestamp?}
  ReferenceValue: {id, quantity_kind, value, unit, provenance, reference_uncertainty?}
  AccuracyAssessment: {id, measurement_id, reference_id, criterion, outcome, evidence, confidence?}
  MeasurementError: {measured_value, reference_value, signed_error, absolute_error, unit}
  RelativeError: {ratio, reference_nonzero: true}
  MeasurementBias: {estimate, unit, sample_size?, method?}
  Trueness: {assessment_method, systematic_error_evidence?}
  Precision: {repeatability?, reproducibility?, dispersion_metric?}
  MeasurementUncertainty: {standard_uncertainty?, expanded_uncertainty?, coverage_factor?, coverage_probability?}
  CalibrationRecord: {instrument_id, reference_standard, date, traceability_chain?}
  Tolerance: {lower_limit, upper_limit, unit, decision_rule?}

RELATIONSHIPS
  MeasurementResult --compared_with--> ReferenceValue
  MeasurementResult --has_error--> MeasurementError
  AccuracyAssessment --assesses--> MeasurementResult
  AccuracyAssessment --uses_reference--> ReferenceValue
  AccuracyAssessment --uses_criterion--> Tolerance
  MeasurementResult --associated_with--> MeasurementUncertainty
  CalibrationRecord --supports_traceability_of--> MeasurementResult
  Trueness --concerns--> systematic_error
  Precision --concerns--> dispersion_of_repeated_results
  Accuracy --distinct_from--> Precision
  Accuracy --distinct_from--> MeasurementUncertainty

FLOW RULES
  R1 ALIGN_UNITS:
    require compatible quantity kinds and dimensions;
    convert measured and reference values to a common unit before comparison.
  R2 SIGNED_ERROR:
    e = x_measured - x_reference.
  R3 ABSOLUTE_ERROR:
    E_abs = abs(e).
  R4 RELATIVE_ERROR:
    if x_reference != 0, E_rel = abs(e) / abs(x_reference);
    else relative error is undefined.
  R5 BIAS_ESTIMATE:
    for repeated comparable measurements, estimated_bias = mean(x_i) - x_reference;
    qualify estimate by sampling and reference uncertainty.
  R6 ACCURACY_ASSESSMENT:
    an operational accuracy verdict requires a declared criterion and decision rule;
    do not infer universal accuracy from a numerical error alone.
  R7 TOLERANCE_DECISION:
    check stated acceptance interval and uncertainty-aware decision rule;
    avoid treating simple in-range observation as proof of conformance when uncertainty matters.
  R8 PRECISION_SEPARATION:
    low dispersion does not imply low bias; low bias does not imply low dispersion.
  R9 UNCERTAINTY_SEPARATION:
    uncertainty characterises dispersion of values reasonably attributable to the measurand;
    it is not identical to actual error.
  R10 REFERENCE_QUALIFICATION:
    a reference value may itself have uncertainty and must not automatically be labelled an exact true value.

VALIDATION CONSTRAINTS
  V1 measurement and reference dimensions must match.
  V2 conversion must respect offset units (e.g. Celsius/Kelvin).
  V3 absolute error must be nonnegative.
  V4 relative error requires a nonzero reference value.
  V5 assessments must identify their reference and criterion.
  V6 uncertainty values and coverage factors, when supplied, must be nonnegative and valid respectively.
  V7 confidence in an ontology assertion must not be conflated with measurement confidence/coverage probability.
  V8 distinguish an accuracy specification from an empirically verified accuracy result.

WORKED EXAMPLES
  Example A: measured length 10.2 m, reference 10.0 m.
    signed_error = +0.2 m; absolute_error = 0.2 m;
    relative_error = 0.02 = 2%.
    Accuracy acceptance is undecided until a criterion is supplied.
  Example B: five measurements [9.8, 9.8, 9.8, 9.8, 9.8] m against reference 10.0 m.
    Repeatability dispersion = 0 for this sample; estimated bias = -0.2 m.
    High repeatability does not establish high accuracy.
  Example C: nominal 100.0 mm with tolerance [99.5, 100.5] mm;
    measured 100.4 mm, expanded uncertainty 0.3 mm.
    The observed value lies within limits, but a conformance verdict depends on the stated decision rule.

SEMANTIC_EQUIVALENCE
  measurement accuracy ~ closeness to a reference quantity value (context-dependent)
  measurement trueness != measurement precision
  accuracy != precision
  measurement error != measurement uncertainty
  accuracy != number of significant figures

CONFIDENCE
  ontology_assertion_confidence: 0.97
  basis: standard metrology definitions and explicit mathematical rules
  note: this score is metadata about the formalisation, not a measurement coverage probability.

FLOW_HASH
  method: SHA-256 over canonical UTF-8 normalised ontology payload, excluding the FLOW_HASH field
  value: compute_at_ingestion

UPDATE_MODEL
  version: 1.0
  change_policy: increment version for modified definitions, equations, constraints or mappings
  provenance: source URL; formalisation based on standard measurement concepts
  review_triggers: changes in VIM, GUM, relevant ISO/IEC guidance, or source-page content

AI_CONSUMPTION
  tasks: [semantic_retrieval, measurement_comparison, error_calculation, conformance_support, unit_validation, uncertainty_reasoning]
  required_context: [measured_value, unit, reference_value, reference_unit]
  optional_context: [measurement_uncertainty, reference_uncertainty, acceptance_criterion, decision_rule]
  output: [normalised_values, error_metrics, qualified_accuracy_assessment, provenance, validation_flags]
  safeguards:
    - never label a measurement accurate without an operational criterion when a pass/fail judgement is requested
    - do not confuse precision with accuracy or uncertainty with error
    - report undefined relative errors rather than divide by zero
    - preserve traceability and units

END FLOW ALGEBRA