Resolution Ontology
Measurement Uncertainty
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Resolution Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/measurement-uncertainty/resolution-ontology.html
FLOW ResolutionOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Resolution Ontology
PURPOSE:
Represent measurement resolution as the smallest change in a quantity being measured that causes a perceptible or reportable change in the corresponding indication under specified conditions, including analogue and digital resolution, scale intervals, display increments, quantisation, least count, detector and spatial resolution, temporal and spectral resolution, resolving power, threshold effects, uncertainty contributions, calibration, signal-to-noise limitations, provenance, and strict distinctions between resolution, precision, accuracy, sensitivity, detection limit and measurement uncertainty.
ENTITY MeasurementResolution {
TYPE: MeasuringSystemCharacteristic
SYMBOL: delta_x
DEFINITION:
resolution :=
smallest_change_in_quantity_being_measured
that_causes_perceptible_change_in_corresponding_indication
under_declared_conditions
PROPERTIES:
is_quantity_dependent
depends_on_measuring_system
depends_on_operating_conditions
may_be_constant_or_range_dependent
may_be_analogue_or_digital
may_contribute_to_uncertainty
is_not_identical_to_accuracy_or_precision
}
ENTITY DisplayResolution {
TYPE: MeasurementResolution
DEFINITION:
smallest_change_representable_by_display_or_reported_digit
}
ENTITY ScaleInterval {
TYPE: IndicationIncrement
DEFINITION:
difference_between_quantity_values_corresponding_to_adjacent_scale_marks
}
ENTITY LeastCount {
TYPE: InstrumentResolutionDescriptor
DEFINITION:
smallest_scale_or_readout_increment_under_declared_instrument_context
RULE:
least_count_and_effective_resolution MAY differ
}
TERMINOLOGY_MODEL {
terms:
resolution
measurement_resolution
display_resolution
least_count
scale_interval
quantisation_step
spatial_resolution
temporal_resolution
spectral_resolution
resolving_power
RULE:
resolution_term MUST be resolved_to_quantity_and_domain_context
}
UNIT_MODEL {
absolute_resolution:
same_unit_as_measurand
relative_resolution:
delta_x/abs(x)
WHEN x != 0
resolving_power:
dimensionless_ratio
RULE:
resolution_unit MUST match_specific_resolution_definition
}
DIGITAL_RESOLUTION_MODEL {
digital_increment:
q
indication_levels:
discrete
common:
one_count_or_one_LSB
RULE:
digital_display_increment != necessarily_effective_measurement_resolution
}
ADC_MODEL {
ideal_N_bit_converter:
number_of_codes =
2^N
ideal_step:
q =
full_scale_span/2^N
under_declared_endpoint_and_code_convention
RULE:
effective_resolution_can_be_worse_due_to_noise_nonlinearity_and_effective_number_of_bits
}
QUANTISATION_MODEL {
rounding_to_nearest_step:
quantisation_error_range =
[-q/2,+q/2]
rectangular_standard_uncertainty:
u_q =
q/sqrt(12)
CONDITIONS:
error_effectively_uniform_over_quantisation_interval
RULE:
quantisation_step != standard_uncertainty
}
TRUNCATION_MODEL {
truncation_interval:
typically_one_sided_relative_to_reported_code
RULE:
truncation_error_distribution_differs_from_round_to_nearest
}
ANALOGUE_SCALE_MODEL {
scale_interval:
d
readable_fraction:
f
estimated_reading_resolution:
delta_x =
f*d
RULE:
readable_fraction_depends_on_scale_design_observer_and_conditions
}
PARALLAX_READING_MODEL {
analogue_instrument:
observer_angle_can_shift_apparent_pointer_position
RULE:
parallax_error != scale_resolution
though_it_can_limit_effective_readability
}
EFFECTIVE_RESOLUTION_MODEL {
effective_resolution:
determined_by_combination_of
display_increment
noise
stability
hysteresis
signal_processing
calibration
threshold
RULE:
nominal_resolution SHOULD_NOT automatically_be_equated_with_effective_resolution
}
NOISE_LIMIT_MODEL {
signal_change:
delta_signal
noise:
sigma_noise
resolvable:
may_require
delta_signal >= k*sigma_noise
under_declared_detection_criterion
RULE:
resolution_depends_on_signal_to_noise_criterion_when_noise_limited
}
SENSITIVITY_MODEL {
sensitivity:
S =
change_in_indication/change_in_input
input_resolution_from_output_increment:
delta_x =
delta_y/S
WHEN S != 0
under_linear_local_model
RULE:
sensitivity != resolution
}
THRESHOLD_MODEL {
threshold:
minimum_input_change_required_to_produce_detectable_response
RULE:
threshold MAY influence_resolution
but_threshold_and_resolution_are_not_universally_identical
}
HYSTERESIS_MODEL {
effect:
indication_depends_on_input_history
RULE:
hysteresis_can_limit_effective_resolution_and_repeatability
}
DEAD_BAND_MODEL {
dead_band:
range_of_input_change_that_produces_no_detectable_output_change
RULE:
dead_band != resolution
though_large_dead_band_degrades_effective_resolution
}
RANGE_DEPENDENCE_MODEL {
resolution:
delta_x =
f(range, gain, operating_mode)
examples:
autoranging_multimeter
variable_gain_sensor
logarithmic_display
RULE:
instrument_range MUST be preserved
}
RELATIVE_RESOLUTION_MODEL {
relative:
r =
delta_x/abs(x)
WHEN x != 0
percentage:
100*r
RULE:
relative_resolution_is_undefined_at_zero_without_alternative_reference
}
SIGNIFICANT_DIGIT_MODEL {
displayed_digits:
constrain_reported_resolution
RULE:
number_of_digits != accuracy
and_extra_digits_do_not_guarantee_real_information
}
PRECISION_DISTINCTION_MODEL {
precision:
agreement_among_replicate_measurements
resolution:
smallest_discernible_change_in_indication
RULE:
resolution != precision
though_resolution_can_limit_observed_precision
}
ACCURACY_DISTINCTION_MODEL {
accuracy:
closeness_to_true_or_reference_value
resolution:
ability_to_distinguish_small_changes
RULE:
high_resolution_does_not_imply_high_accuracy
}
UNCERTAINTY_DISTINCTION_MODEL {
uncertainty:
quantified_dispersion_of_values_attributed_to_measurand
resolution:
instrument_or_system_characteristic
RULE:
resolution MAY contribute_to_uncertainty
but_resolution != uncertainty
}
DETECTION_LIMIT_DISTINCTION_MODEL {
detection_limit:
smallest_quantity_or_signal_detectable_with_declared_false_positive_false_negative_or_statistical_criterion
resolution:
smallest distinguishable_change
RULE:
detection_limit != resolution
}
DYNAMIC_RANGE_MODEL {
dynamic_range:
ratio_or_span_between_minimum_and_maximum_usable_signal
RULE:
dynamic_range != resolution
}
SPATIAL_RESOLUTION_MODEL {
context:
imaging
mapping
remote_sensing
microscopy
possible_definitions:
pixel_spacing
ground_sample_distance
point_spread_function_width
minimum_resolvable_separation
RULE:
pixel_size != optical_spatial_resolution_in_general
}
POINT_SPREAD_MODEL {
point_spread_function:
system_response_to_point_source
metrics:
FWHM
encircled_energy
modulation_transfer_function
RULE:
spatial_resolution_metric MUST be declared
}
RAYLEIGH_MODEL {
circular_aperture:
angular_resolution approximately_equals
1.22*lambda/D
REQUIRE:
diffraction_limited_context
wavelength
aperture_diameter
RULE:
Rayleigh_criterion_is_specific_resolution_definition
}
TEMPORAL_RESOLUTION_MODEL {
possible:
sampling_interval
integration_time
response_time
minimum_resolvable_event_separation
RULE:
sampling_interval != effective_temporal_resolution_in_all_systems
}
SAMPLING_RATE_MODEL {
sampling_frequency:
f_s
interval:
delta_t =
1/f_s
WHEN f_s > 0
RULE:
high_sampling_rate_does_not_guarantee_high_temporal_resolution_if_sensor_response_is_slow
}
SPECTRAL_RESOLUTION_MODEL {
wavelength:
delta_lambda
frequency:
delta_nu
resolving_power:
R =
lambda/delta_lambda
or
nu/delta_nu
RULE:
resolving_power_and_resolution_width_are_inverse_style_metrics
}
MASS_RESOLUTION_MODEL {
mass_spectrometry:
resolving_power =
m/delta_m
RULE:
definition_of_delta_m_and_peak_criterion MUST be declared
}
FREQUENCY_RESOLUTION_MODEL {
finite_observation:
nominal_Fourier_bin_width approximately_equals
1/T_observation
RULE:
spectral_estimator_windowing_and_signal_to_noise_affect_effective_frequency_resolution
}
ANGULAR_RESOLUTION_MODEL {
angular_separation:
theta_min
possible_limits:
diffraction
seeing
detector_sampling
signal_to_noise
RULE:
angular_resolution != angular_accuracy
}
VERTICAL_RESOLUTION_MODEL {
context:
depth_profile
atmosphere
ocean
subsurface
RULE:
vertical_sampling_interval_and_vertical_resolution MUST be distinguished
}
MEASUREMENT_UNCERTAINTY_MODEL {
resolution_increment:
q
common_rounding_standard_uncertainty:
u_res =
q/sqrt(12)
REQUIRE:
rounding_to_nearest
uniform_phase_assumption
RULE:
uncertainty_model MUST match_actual_readout_process
}
CALIBRATION_MODEL {
calibration:
maps_indication_to_quantity
effect:
determines_scale_factor_and_may_affect_resolution_in_input_units
RULE:
calibration_uncertainty_and_resolution_uncertainty_are_distinct_components
}
FILTERING_MODEL {
filtering:
may_reduce_noise
but_also_reduce_bandwidth_or_temporal_spatial_detail
RULE:
resolution_after_filtering MUST preserve_filter_parameters
}
AVERAGING_MODEL {
averaging:
may_improve_estimation_of_constant_signal_below_single_readout_noise
RULE:
sub-resolution_statistical_estimation_does_not_change_nominal_display_increment
}
SUPER_RESOLUTION_MODEL {
context:
computational_imaging_or_signal_processing
principle:
combine_multiple_observations_and_prior_model_to_infer_detail_beyond_single_sample_grid
RULE:
reconstructed_resolution_requires_model_validation
and_MUST_NOT be_equated_with_raw_sensor_sampling
}
INTERPOLATION_MODEL {
interpolated_grid:
more_output_points
RULE:
interpolation_does_not_by_itself_increase_true_measurement_resolution
}
CALIBRATION_GRID_MODEL {
lookup_table_spacing:
may_limit_correction_interpolation
RULE:
calibration_point_spacing != measurement_resolution
}
REPORTING_MODEL {
REQUIRED:
resolution_value_or_metric
quantity_or_domain
unit
operating_range_or_mode
resolution_definition
RECOMMENDED:
sensor
sampling
bandwidth
noise
filter
environmental_conditions
calibration
uncertainty_model
provenance
RULE:
resolution_statement MUST identify_metric_and_conditions
}
RELATIONSHIPS {
MeasurementResolution -> QUALIFIES -> MeasuringSystem
DisplayResolution -> IS_A -> MeasurementResolution
ScaleInterval -> RELATES_TO -> AnalogueResolution
QuantisationStep -> RELATES_TO -> DigitalResolution
Resolution -> MAY_CONTRIBUTE_TO -> MeasurementUncertainty
Sensitivity -> MAPS -> OutputIncrementToInputResolution
Noise -> MAY_LIMIT -> EffectiveResolution
Bandwidth -> QUALIFIES -> TemporalOrSpectralResolution
PointSpreadFunction -> QUALIFIES -> SpatialResolution
SamplingRate -> RELATES_TO -> TemporalResolution
SpectralResolution -> RELATES_TO -> ResolvingPower
}
SEMANTIC_EQUIVALENCE {
"measurement resolution" ~= smallest_discernible_quantity_change_under_defined_conditions
"least count" ~= nominal_smallest_instrument_increment WHEN instrument_context
resolution != precision
resolution != accuracy
resolution != measurement_uncertainty
resolution != sensitivity
resolution != detection_limit
resolution != dynamic_range
pixel_size != spatial_resolution
sampling_interval != effective_temporal_resolution
quantisation_step != quantisation_standard_uncertainty
}
CONSTRAINTS {
resolution_quantity_or_domain_must_be_defined = true
resolution_metric_must_be_defined = true
operating_range_or_mode_should_be_defined = true
resolution_and_precision_are_not_semantically_equivalent = true
resolution_and_accuracy_are_not_semantically_equivalent = true
resolution_and_uncertainty_are_not_semantically_equivalent = true
resolution_and_sensitivity_are_not_semantically_equivalent = true
resolution_and_detection_limit_are_not_semantically_equivalent = true
uncertainty_from_resolution_requires_distribution_assumption = true
processing_and_filtering_history_should_be_preserved = true
}
MEASUREMENT_MODEL {
RECORD:
measurand
resolution_type
resolution_value
unit
instrument
display_increment
scale_interval
ADC_bits
full_scale_range
operating_range
sensitivity
noise_level
bandwidth
sampling_rate
integration_time
spatial_sampling
point_spread_metric
spectral_width
resolving_power
filter
calibration
environmental_conditions
uncertainty_contribution
provenance
RULE:
nominal_and_effective_resolution SHOULD be_distinguished
}
REASONING_RULES {
IF digital_full_scale_span_and_bits_known
THEN ideal_quantisation_step =
full_scale_span/(2^bits)
under_declared_code_convention
IF rounding_quantisation_step_known
AND uniform_rounding_model_valid
THEN resolution_standard_uncertainty =
quantisation_step/sqrt(12)
IF output_increment_and_local_sensitivity_known
AND sensitivity != 0
THEN input_resolution =
output_increment/abs(sensitivity)
IF wavelength_and_aperture_diameter_known
AND diffraction_limited_circular_aperture_context
THEN Rayleigh_angular_resolution approximately_equals
1.22*wavelength/aperture_diameter
IF sampling_frequency_known AND sampling_frequency > 0
THEN sampling_interval =
1/sampling_frequency
IF spectral_central_wavelength_and_resolution_width_known
AND resolution_width != 0
THEN resolving_power =
central_wavelength/resolution_width
IF observation_duration_known AND observation_duration > 0
THEN nominal_Fourier_frequency_spacing approximately_equals
1/observation_duration
IF interpolation_only_increases_output_grid_density
THEN do_not_infer_improved_physical_resolution
IF noise_or_filtering_dominates
THEN effective_resolution_may_be_worse_than_nominal_increment
}
VALIDATION {
CHECK resolution_type
CHECK quantity_or_domain
CHECK unit
CHECK nominal_vs_effective_resolution
CHECK instrument_range
CHECK display_increment
CHECK scale_interval
CHECK quantisation_model
CHECK sensitivity
CHECK noise_and_bandwidth
CHECK sampling_rate_and_response_time
CHECK spatial_resolution_metric
CHECK spectral_resolution_metric
CHECK resolving_power_definition
CHECK resolution_vs_precision
CHECK resolution_vs_accuracy
CHECK resolution_vs_uncertainty
CHECK resolution_vs_detection_limit
CHECK filtering_and_interpolation
CHECK calibration
CHECK uncertainty_distribution_assumption
CHECK provenance
}
CONFIDENCE {
definition_confidence: 1.00
precision_distinction_confidence: 1.00
accuracy_distinction_confidence: 1.00
uncertainty_distinction_confidence: 1.00
quantisation_model_confidence: 1.00
spatial_resolution_confidence: 0.99
temporal_resolution_confidence: 0.99
spectral_resolution_confidence: 0.99
RULE:
confidence decreases when resolution metric, range, sensitivity,
noise, bandwidth, sampling, filtering, calibration
or uncertainty assumptions are missing or ambiguous
}
UPDATE_MODEL {
ON new_resolution_record:
identify_resolution_type
identify_quantity_or_domain
attach_value_and_unit
attach_operating_range
identify_nominal_or_effective_status
attach_sensor_sampling_noise_and_bandwidth
attach_processing_and_calibration
derive_uncertainty_contribution_when_valid
preserve_provenance
ON range_change:
preserve_previous_resolution
update_gain_or_operating_mode
recompute_display_or_input_resolution
update_uncertainty_model
ON calibration_revision:
preserve_raw_indication_increment
update_scale_or_sensitivity
recompute_resolution_in_input_units
preserve_calibration_uncertainty_separately
ON processing_revision:
preserve_raw_data
update_filter_averaging_or_reconstruction
reassess_effective_resolution
preserve_processing_history
ON noise_revision:
update_noise_statistics
reassess_noise_limited_resolution
preserve_detection_criterion
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: MeasurementResolution
canonical_role: MeasuringSystemCharacteristic
interpretation_order:
identify_resolution_domain
identify_resolution_metric
identify_value_and_unit
identify_instrument_and_operating_range
identify_display_scale_or_quantisation_increment
identify_sensitivity
identify_noise_and_bandwidth
identify_sampling_or_integration_time
identify_spatial_spectral_or_temporal_context
identify_filtering_or_processing
identify_calibration
identify_uncertainty_contribution
identify_provenance
validate_resolution_semantics
infer_resolution_relationships
ambiguity_controls:
distinguish_resolution_from_precision
distinguish_resolution_from_accuracy
distinguish_resolution_from_measurement_uncertainty
distinguish_resolution_from_sensitivity
distinguish_resolution_from_detection_limit
distinguish distinguish_nominal_from_effective_resolution
distinguish_pixel_size_from_optical_spatial_resolution
distinguish_sampling_interval_from_effective_temporal_resolution
distinguish_quantisation_step_from_uncertainty
preserve_domain_metric_range_sampling_noise_processing_calibration_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_uncertainty_and_resolution_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Resolution Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
unit_model
digital_resolution_model
ADC_model
quantisation_model
truncation_model
analogue_scale_model
parallax_reading_model
effective_resolution_model
noise_limit_model
sensitivity_model
threshold_model
hysteresis_model
dead_band_model
range_dependence_model
relative_resolution_model
significant_digit_model
precision_distinction_model
accuracy_distinction_model
uncertainty_distinction_model
detection_limit_distinction_model
dynamic_range_model
spatial_resolution_model
point_spread_model
Rayleigh_model
temporal_resolution_model
sampling_rate_model
spectral_resolution_model
mass_resolution_model
frequency_resolution_model
angular_resolution_model
vertical_resolution_model
measurement_uncertainty_model
calibration_model
filtering_model
averaging_model
super_resolution_model
interpolation_model
calibration_grid_model
reporting_model
relationships
constraints
measurement_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
resolution_definition_or_metric_changes
digital_or_analogue_resolution_model_changes
quantisation_or_ADC_model_changes
noise_sensitivity_or_threshold_model_changes
spatial_temporal_or_spectral_resolution_changes
processing_filtering_or_reconstruction_changes
calibration_or_range_changes
uncertainty_contribution_model_changes
measurement_record_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW