Accuracy Ontology
Measurement Uncertainty
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Accuracy Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/measurement-uncertainty/accuracy-ontology.html
FLOW AccuracyOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Accuracy Ontology
PURPOSE:
Represent measurement accuracy as the qualitative closeness of agreement between a measured quantity value and a true quantity value or accepted reference value under a declared measurement context. The ontology distinguishes accuracy from precision, trueness, bias, error, uncertainty, resolution and tolerance; represents the roles of random and systematic effects, calibration, validation, reference values, traceability, method comparison, classification accuracy where explicitly separate, uncertainty-informed interpretation, provenance, and machine-consumable reasoning without treating accuracy itself as a universal numerical quantity.
ENTITY MeasurementAccuracy {
TYPE: MeasurementPerformanceCharacteristic
DEFINITION:
accuracy :=
closeness_of_agreement
between_measured_quantity_value
and_true_quantity_value_or_accepted_reference_value
PROPERTIES:
is_qualitative_in_metrological_definition
depends_on_measurement_context
affected_by_random_error
affected_by_systematic_error
related_to_precision
related_to_trueness
not_identical_to_uncertainty
not_identical_to_error
}
ENTITY MeasuredQuantityValue {
TYPE: QuantityEstimate
SYMBOL: x_m
}
ENTITY ReferenceQuantityValue {
TYPE: ReferenceValue
SYMBOL: x_ref
POSSIBLE:
certified_reference_value
calibration_standard_value
conventional_quantity_value
accepted_reference_value
higher_accuracy_method_value
RULE:
reference_value_uncertainty MUST be_preserved
}
ENTITY TrueQuantityValue {
TYPE: IdealMetrologicalConcept
RULE:
true_value_is_generally_unknown_in_practical_measurement
}
TERMINOLOGY_MODEL {
terms:
accuracy
measurement_accuracy
trueness
precision
error
bias
uncertainty
resolution
tolerance
RULE:
accuracy MUST_NOT be_used_as_direct_synonym_for_any_single_term_above
}
QUALITATIVE_MODEL {
accuracy:
qualitative_characteristic
possible_descriptions:
higher_accuracy
lower_accuracy
fit_for_declared_purpose
agreement_with_reference_within_declared_evidence
RULE:
a_single_numeric_accuracy_value_requires_explicit_operational_definition
}
ERROR_RELATION_MODEL {
measurement_error:
e =
x_m-x_ref
when_reference_used_as_proxy_for_true_value
ideal:
smaller_absolute_error
suggests_closer_agreement_for_that_observation
RULE:
observed_error_against_uncertain_reference_is_not_identical_to_metrological_accuracy
}
ABSOLUTE_ERROR_MODEL {
absolute_error:
abs(e) =
abs(x_m-x_ref)
RULE:
absolute_error_has_same_unit_as_measurand
}
RELATIVE_ERROR_MODEL {
relative_error:
e_r =
(x_m-x_ref)/x_ref
WHEN x_ref != 0
absolute_relative_error:
abs(e_r)
RULE:
relative_error_is_dimensionless
}
PERCENT_ERROR_MODEL {
percent_error:
100*(x_m-x_ref)/x_ref
WHEN x_ref != 0
RULE:
percent_error_is_not_measurement_accuracy_percentage
}
PRECISION_DISTINCTION_MODEL {
precision:
closeness_of_agreement_among_replicate_measurements
accuracy:
closeness_to_true_or_reference_value
RULE:
high_precision != high_accuracy
and_low_precision_does_not_by_itself_define_accuracy
}
TRUENESS_MODEL {
trueness:
closeness_of_agreement_between_average_of_large_number_of_replicate_results
and_reference_or_true_quantity_value
relationship:
trueness_is_associated_with_systematic_effects
RULE:
trueness != precision
and_trueness_is_related_to_but_not_identical_with_overall_accuracy
}
BIAS_MODEL {
bias:
b =
E[x_m]-x_ref
under_declared_model
estimated_bias:
b_hat =
x_bar-x_ref
RULE:
bias_estimate_has_uncertainty
and_bias != accuracy
}
RANDOM_ERROR_MODEL {
random_error:
unpredictable_measurement_error_component
effect:
contributes_to_dispersion_and_can_reduce_closeness_of_individual_results_to_reference
RULE:
random_error != accuracy
}
SYSTEMATIC_ERROR_MODEL {
systematic_error:
constant_or_predictable_measurement_error_component
effect:
shifts_results_relative_to_reference
RULE:
systematic_error != accuracy
}
COMBINED_PERFORMANCE_MODEL {
accuracy_context:
influenced_by
trueness
precision
reference_quality
measurement_conditions
RULE:
accuracy SHOULD be interpreted_from_multiple_evidence_sources
rather_than_collapsed_into_undefined_single_score
}
UNCERTAINTY_DISTINCTION_MODEL {
measurement_uncertainty:
nonnegative_parameter_characterising_dispersion_of_values_attributed_to_measurand
accuracy:
qualitative_closeness_characteristic
RULE:
smaller_uncertainty MAY support_stronger_accuracy_claim
but_uncertainty != accuracy
}
UNCERTAINTY_AWARE_ACCURACY_MODEL {
measured_result:
x_m +/- U_m
reference:
x_ref +/- U_ref
comparison:
must_consider_both_uncertainties_and_possible_correlation
RULE:
apparent_numeric_agreement_without_uncertainty_context MAY be_misleading
}
COMPARISON_DIFFERENCE_MODEL {
difference:
d =
x_m-x_ref
variance:
u^2(d) =
u^2(x_m)+u^2(x_ref)-2*cov(x_m,x_ref)
RULE:
shared_traceability_or_calibration_can_create_correlation
}
NORMALIZED_ERROR_MODEL {
common_proficiency_context:
E_n =
(x_m-x_ref)/
sqrt(U_m^2+U_ref^2)
under_declared_expanded_uncertainty_and_independence_context
RULE:
normalized_error_is_specific_comparison_metric
not_general_definition_of_accuracy
}
Z_SCORE_MODEL {
proficiency_testing_context:
z =
(x-x_assigned)/sigma_for_proficiency_assessment
RULE:
proficiency_z_score != measurement_accuracy
}
RESOLUTION_DISTINCTION_MODEL {
resolution:
smallest_change_or_display_increment_resolved_by_system
RULE:
high_resolution_does_not_guarantee_high_accuracy
}
SENSITIVITY_DISTINCTION_MODEL {
sensitivity:
change_in_indication_per_change_in_input_quantity
RULE:
sensitivity != accuracy
}
LINEARITY_MODEL {
response:
y =
f(x)
linearity_error:
deviation_from_declared_linear_reference
RULE:
good_linearity_is_one_instrument_characteristic
but_does_not_by_itself_establish_measurement_accuracy
}
CALIBRATION_MODEL {
purpose:
establish_relation_between_indications_and_reference_values
outputs:
calibration_function
correction
uncertainty
validity_range
RULE:
calibration_supports_accuracy_but_calibration != accuracy
}
CORRECTION_MODEL {
corrected:
x_corr =
x_ind+C
uncertainty:
includes_uncertainty_of_C
RULE:
correction_for_known_systematic_effect_can_improve_closeness_to_reference
but_corrected_result_still_has_uncertainty
}
TRACEABILITY_MODEL {
chain:
measurement_result
-> calibration
-> reference_standard
-> higher_standard
-> SI_or_declared_reference
RULE:
traceability_supports_comparability_and_reference_quality
but_traceability_alone_does_not_guarantee_accuracy
}
REFERENCE_QUALITY_MODEL {
attributes:
uncertainty
stability
commutability
matrix_match
calibration_status
traceability
RULE:
accuracy_assessment_cannot_exceed_quality_of_reference_evidence_without_additional_model
}
VALIDATION_MODEL {
purpose:
demonstrate_measurement_procedure_performance_for_intended_use
evidence:
bias_study
precision_study
recovery
linearity
range
selectivity
robustness
reference_comparison
uncertainty
RULE:
validation_context_and_acceptance_criteria MUST be preserved
}
METHOD_COMPARISON_MODEL {
methods:
candidate_method
reference_method
data:
paired_measurements
analyses:
mean_difference
regression
agreement_interval
bias_by_range
uncertainty_comparison
RULE:
correlation_coefficient_alone_does_not_demonstrate_accuracy_or_agreement
}
REGRESSION_MODEL {
candidate:
y
reference:
x
ideal_agreement:
intercept approximately_equals 0
slope approximately_equals 1
RULE:
ordinary_least_squares_may_be_inappropriate_when_both_methods_have_measurement_error
}
DEMING_REGRESSION_MODEL {
use:
method_comparison_with_error_in_both_axes
REQUIRE:
variance_ratio_or_model
RULE:
regression_model_assumptions MUST be preserved
}
BLAND_ALTMAN_CONTEXT_MODEL {
difference:
d_i =
method_A_i-method_B_i
mean_difference:
bias_estimate
agreement_limits:
mean_difference +/- k*s_d
under_declared_distribution_and_k
RULE:
agreement_limits_are_not_accuracy_definition
}
RECOVERY_MODEL {
recovery:
R =
measured_increment/
known_added_increment
percent:
100*R
RULE:
recovery_is_specific_validation_metric
not_general_accuracy_percentage
}
REFERENCE_MATERIAL_MODEL {
certified_reference_material:
has_certified_quantity_value
uncertainty
traceability_statement
RULE:
matrix_and_commutability SHOULD match_measurement_application
}
INTERLABORATORY_MODEL {
comparison:
results_from_multiple_laboratories
use:
assess_method_or_laboratory_performance
RULE:
consensus_value_must_not_be_assumed_true_without_reference_basis
}
PROFICIENCY_TESTING_MODEL {
assigned_value:
x_assigned
participant_result:
x_lab
evaluation:
declared_performance_statistic
RULE:
proficiency_performance != direct_metrological_accuracy_measure
}
RANGE_MODEL {
measurement_range:
interval_of_quantity_values
accuracy_related_performance:
may_change_across_range
RULE:
validation_at_one_level_does_not_establish_performance_across_full_range
}
MATRIX_MODEL {
sample_matrix:
may_affect_bias_precision_and_recovery
RULE:
accuracy_evidence SHOULD match_matrix_and_measurand_context
}
ENVIRONMENTAL_MODEL {
influences:
temperature
humidity
pressure
vibration
electromagnetic_interference
orientation
RULE:
accuracy_claim_requires_conditions_within_validated_or_corrected_range
}
TEMPORAL_STABILITY_MODEL {
effects:
drift
ageing
recalibration
reference_change
RULE:
accuracy_evidence_has_temporal_validity
}
SAMPLING_MODEL {
sampling:
may introduce_bias_and_variability_before_measurement
RULE:
analytical_accuracy_does_not_guarantee_accuracy_of_population_or_field_estimate
}
MODEL_BASED_MEASUREMENT_MODEL {
derived_quantity:
inferred_using_model
accuracy_evidence:
depends_on
input_measurements
model_validity
parameter_accuracy
calibration
validation
RULE:
model_error_can_reduce_accuracy_even_when_input_measurements_are_precise
}
CLASSIFICATION_ACCURACY_DISTINCTION_MODEL {
machine_learning_or_diagnostic_classification_accuracy:
proportion_correct =
correct_predictions/total_predictions
metrological_measurement_accuracy:
closeness_of_measured_quantity_to_true_or_reference_value
RULE:
classification_accuracy != measurement_accuracy
}
DIGITAL_ACCURACY_SPECIFICATION_MODEL {
instrument_specification:
may_be_stated_as
plus_minus_percent_reading
plus_minus_digits
plus_minus_full_scale
combined_terms
RULE:
manufacturer_accuracy_specification_is_operational_error_limit_or_uncertainty_input
not_metrological_accuracy_quantity_itself
}
TOLERANCE_DISTINCTION_MODEL {
tolerance:
allowed_product_or_process_deviation
accuracy:
measurement_performance_characteristic
RULE:
tolerance != accuracy
}
FITNESS_FOR_PURPOSE_MODEL {
decision:
measurement_performance_sufficient_for_declared_use
depends_on:
uncertainty
tolerance
risk
decision_rule
required_accuracy_context
RULE:
fitness_for_purpose_is_application_specific
}
DECISION_RULE_MODEL {
comparison:
measurement_result_and_uncertainty
versus_specification_limit
possible:
guard_band
shared_risk
consumer_risk
producer_risk
RULE:
conformance_decision != accuracy_measurement
}
RELATIONSHIPS {
MeasurementAccuracy -> QUALIFIES -> MeasurementResultOrProcedure
MeasurementAccuracy -> RELATES_TO -> Trueness
MeasurementAccuracy -> RELATES_TO -> Precision
MeasurementError -> AFFECTS -> Accuracy
SystematicError -> AFFECTS -> Trueness
RandomError -> AFFECTS -> Precision
Calibration -> SUPPORTS -> AccuracyAssessment
ReferenceValue -> ENABLES -> ErrorOrBiasAssessment
MeasurementUncertainty -> QUALIFIES -> AccuracyEvidence
Validation -> PROVIDES -> PerformanceEvidence
Traceability -> SUPPORTS -> ReferenceComparability
}
SEMANTIC_EQUIVALENCE {
"measurement accuracy" ~= closeness_to_true_or_reference_value
accuracy != precision
accuracy != trueness
accuracy != bias
accuracy != measurement_error
accuracy != measurement_uncertainty
accuracy != resolution
accuracy != tolerance
measurement_accuracy != classification_accuracy
percent_error != percent_accuracy
}
CONSTRAINTS {
accuracy_is_qualitative_metrological_characteristic = true
accuracy_assessment_requires_reference_or_model_context = true
precision_and_accuracy_are_not_semantically_equivalent = true
trueness_and_accuracy_are_not_semantically_equivalent = true
uncertainty_and_accuracy_are_not_semantically_equivalent = true
resolution_and_accuracy_are_not_semantically_equivalent = true
manufacturer_accuracy_specification_requires_operational_interpretation = true
reference_uncertainty_must_be_preserved = true
measurement_conditions_and_range_should_be_preserved = true
numerical_accuracy_metric_requires_explicit_definition = true
}
MEASUREMENT_MODEL {
RECORD:
measurand
measured_value
unit
reference_value
reference_uncertainty
measurement_uncertainty
difference
relative_difference
bias_estimate
precision_metric
calibration_state
correction
correction_uncertainty
measurement_method
validation_method
measurement_range
sample_matrix_or_object
environmental_conditions
timestamp
traceability
decision_rule_when_relevant
provenance
RULE:
accuracy_evidence MUST preserve_reference_uncertainty_and_measurement_context
}
REASONING_RULES {
IF measured_value_and_reference_value_known
THEN difference =
measured_value-reference_value
IF reference_value != 0
THEN relative_difference =
difference/reference_value
IF repeated_measurements_and_reference_known
THEN estimated_bias =
mean(measurements)-reference_value
IF measurement_and_reference_uncertainties_known
THEN uncertainty_of_difference =
sqrt(
u_measurement^2
+ u_reference^2
- 2*covariance
)
IF correction_known
THEN corrected_value =
indicated_value+correction
AND preserve_correction_uncertainty
IF precision_high_but_bias_large
THEN do_not_infer_high_accuracy
IF bias_small_but_precision_poor
THEN do_not_infer_high_accuracy_for_individual_measurements_without_context
IF reference_uncertainty_large
THEN limit_strength_of_accuracy_assessment
IF manufacturer_accuracy_specification_given
THEN parse_as_declared_operational_limit_or_uncertainty_input
not_as_universal_numeric_accuracy
IF classification_accuracy_metric_detected
THEN route_to_classification_metric_semantics
not_measurement_accuracy_semantics
}
VALIDATION {
CHECK measurand
CHECK measured_value_and_unit
CHECK reference_value
CHECK reference_uncertainty
CHECK accuracy_vs_precision
CHECK accuracy_vs_trueness
CHECK accuracy_vs_uncertainty
CHECK accuracy_vs_error
CHECK accuracy_vs_resolution
CHECK bias_and_correction
CHECK measurement_range
CHECK method_validation
CHECK matrix_or_object_context
CHECK environmental_conditions
CHECK temporal_validity
CHECK traceability
CHECK manufacturer_specification_semantics
CHECK classification_accuracy_distinction
CHECK numerical_metric_definition
CHECK provenance
}
CONFIDENCE {
definition_confidence: 1.00
precision_distinction_confidence: 1.00
trueness_distinction_confidence: 1.00
uncertainty_distinction_confidence: 1.00
error_distinction_confidence: 1.00
reference_comparison_confidence: 0.99
validation_context_confidence: 0.99
measurement_context_confidence: 0.99
RULE:
confidence decreases when reference value, reference uncertainty,
measurement range, calibration, precision, validation,
environmental context or provenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_measurement:
identify_measurand
preserve_measured_value
attach_reference_value_when_available
attach_measurement_and_reference_uncertainty
compute_difference_when_valid
attach_calibration_and_correction
attach_precision_evidence
attach_measurement_conditions
update_accuracy_evidence
ON new_reference_measurement:
preserve_candidate_result
update_reference_value_and_uncertainty
recompute_difference_and_bias_evidence
update_traceability update_accuracy_evidence
ON calibration_revision:
preserve_raw_indication
update_calibration_function
update_correction_and_uncertainty
recompute_corrected_value
update_accuracy_evidence
ON precision_study_update:
preserve_replicate_data
update_repeatability_or_reproducibility_metrics
reassess_combined_accuracy_evidence
preserve_precision_accuracy_distinction
ON validation_revision:
preserve_previous_validation
update_reference_method_range_matrix_and_conditions
recompute_bias_and_agreement_statistics
update_confidence_and_provenance
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: MeasurementAccuracy
canonical_role: MeasurementPerformanceCharacteristic
interpretation_order:
identify_measurand
identify_measured_value_and_unit
identify_reference_or_true_value_context
identify_reference_uncertainty
identify_measurement_uncertainty
identify_difference_or_bias_evidence
identify_precision_and_trueness_evidence
identify_calibration_and_corrections
identify_measurement_range_and_conditions
identify_validation_and_traceability
identify_operational_numeric_metric_if_present
distinguish_classification_accuracy_when_relevant
validate_accuracy_semantics
infer_accuracy_evidence_without_creating_undefined_score
ambiguity_controls:
distinguish_accuracy_from_precision
distinguish_accuracy_from_trueness
distinguish_accuracy_from_bias
distinguish_accuracy_from_measurement_error
distinguish_accuracy_from_measurement_uncertainty
distinguish_accuracy_from_resolution
distinguish_accuracy_from_tolerance
distinguish_measurement_accuracy_from_classification_accuracy
distinguish_percent_error_from_percent_accuracy
preserve_measurand_reference_uncertainty_calibration_range_conditions_validation_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_uncertainty_and_accuracy_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Accuracy Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
qualitative_model
error_relation_model
absolute_error_model
relative_error_model
percent_error_model
precision_distinction_model
trueness_model
bias_model
random_error_model
systematic_error_model
combined_performance_model
uncertainty_distinction_model
uncertainty_aware_accuracy_model
comparison_difference_model
normalized_error_model
z_score_model
resolution_distinction_model
sensitivity_distinction_model
linearity_model
calibration_model
correction_model
traceability_model
reference_quality_model
validation_model
method_comparison_model
regression_model
Deming_regression_model
Bland_Altman_context_model
recovery_model
reference_material_model
interlaboratory_model
proficiency_testing_model
range_model
matrix_model
environmental_model
temporal_stability_model
sampling_model
model_based_measurement_model
classification_accuracy_distinction_model
digital_accuracy_specification_model
tolerance_distinction_model
fitness_for_purpose_model
decision_rule_model
relationships
constraints
measurement_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
accuracy_definition_or_reference_context_changes
precision_trueness_or_uncertainty_distinction_changes
calibration_or_correction_model_changes
reference_value_or_traceability_changes
validation_or_method_comparison_model_changes
measurement_range_or_environment_changes
operational_accuracy_metric_semantics_change
measurement_record_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW