Measurement Value Ontology

FLOW ALGEBRA
Measurement Value Ontology — Kireth Semantic Library
Version: 1.0 | Date: 2026-10-14
Source: https://kirethresearch.org/booksai-core/entity-graph/mathematical-entities/measurement-and-dimensional-entities/measurement-value-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)

ONTOLOGY_ID: measurement_value_ontology
PARENT: measurement_and_dimensional_entities
ENTITY_TYPE: MeasurementValue

DEFINITION
A measurement value is a reported result of measuring a specified measurand, expressed through a quantity value and accompanied, where available, by uncertainty and measurement context. A measured value is not automatically the true value.

TYPED ENTITIES
MeasurementValue(id:str, measurand:Measurand, magnitude:real, unit:Unit, uncertainty:Uncertainty?, timestamp:datetime?, method:Method?, provenance:Source?, status:Status)
Measurand(id:str, quantity_kind:QuantityKind, subject:Entity, conditions:Context?)
Unit(symbol:str, dimension:Dimension, scale:real, offset:real?)
Uncertainty(standard:real?, expanded:real?, coverage_factor:real?, coverage_probability:real?, distribution:str?)
Method(id:str, instrument:Instrument?, calibration:Calibration?)
Source(id:str, citation:str?, recorded_at:datetime?)
Status := observed | estimated | calculated | corrected

RELATIONSHIPS
MeasurementValue --measures--> Measurand
MeasurementValue --expressed_in--> Unit
MeasurementValue --has_uncertainty--> Uncertainty
MeasurementValue --obtained_using--> Method
MeasurementValue --derived_from--> Source
Unit --has_dimension--> Dimension
Method --uses_instrument--> Instrument
Instrument --has_calibration--> Calibration

FLOW OPERATIONS
flow measurement_record(measurand, magnitude, unit, uncertainty?, method?, provenance?) -> MeasurementValue
  require compatible(unit.dimension, measurand.quantity_kind.dimension)
  require finite(magnitude)
  require uncertainty is absent or uncertainty.standard >= 0
  emit MeasurementValue(...)

flow convert_measurement(m, target_unit) -> MeasurementValue
  require compatible(m.unit.dimension, target_unit.dimension)
  # For affine units, convert through a reference unit.
  reference = m.magnitude * m.unit.scale + (m.unit.offset or 0)
  target_magnitude = (reference - (target_unit.offset or 0)) / target_unit.scale
  # Standard uncertainty is scaled, never offset.
  target_standard_uncertainty = m.uncertainty.standard * abs(m.unit.scale / target_unit.scale) if available
  preserve measurand, method, provenance, and status

flow combine_independent_additive(a, b, operation) -> MeasurementValue
  require operation in {add, subtract}
  require dimension_compatible(a, b)
  require uncertainties are standard and independent
  result = a.value (+ or -) b.value in common units
  u_result = sqrt(u_a^2 + u_b^2)
  emit result with derivation provenance

flow compare_measurements(a, b) -> Comparison
  require dimension_compatible(a, b)
  normalise units
  report difference and uncertainty context
  do not infer agreement solely from rounded equality

MATHEMATICAL RULES
R1: Quantity value = numerical magnitude × unit (for multiplicative units).
R2: Standard uncertainty u >= 0; expanded uncertainty U = k*u when a valid coverage factor k is specified.
R3: Independent additive uncertainty: u(x ± y) = sqrt(u(x)^2 + u(y)^2).
R4: With covariance: u(x ± y)^2 = u(x)^2 + u(y)^2 ± 2*cov(x,y).
R5: For differentiable y=f(x), first-order uncertainty propagation uses covariance matrix Σ: u(y)^2 ≈ J Σ J^T.
R6: Unit conversion must preserve physical quantity and dimension.
R7: Accuracy is not synonymous with precision or uncertainty.
R8: Significant figures reflect reporting policy; rounding must not manufacture precision.

INFERENCE
IF compatible units AND equal measurand identity THEN measurements may be compared.
IF instrument calibration is expired THEN flag calibration_review; do not automatically invalidate historical observations.
IF uncertainty missing THEN uncertainty_status = unreported, not zero.
IF measurement derived by calculation THEN preserve source lineage.
IF temperature uses Celsius or Fahrenheit THEN use affine conversions for values and scale-only conversions for uncertainty intervals.

VALIDATION
V01 required measurand, finite magnitude, recognised unit
V02 unit dimension matches measurand dimension
V03 uncertainty components non-negative and finite
V04 coverage factor positive when expanded uncertainty is reported
V05 conversion scale nonzero
V06 preserve original observation and transformation provenance
V07 prohibit arithmetic on incompatible dimensions
V08 distinguish observations, estimates, and calculations
V09 identify correlation assumptions in propagation
V10 never assert measured value equals unknowable true value

WORKED EXAMPLES
E1 length: 2.50 m ± 0.01 m (standard uncertainty) -> 250 cm ± 1 cm.
E2 independent lengths: (2.00 ± 0.03) m + (1.00 ± 0.04) m = (3.00 ± 0.05) m.
E3 temperature: 20 °C = 293.15 K; standard uncertainty 0.2 °C = 0.2 K.
E4 uncertainty omitted: 5.0 kg -> uncertainty_status: unreported.

SEMANTIC_EQUIVALENCE
measurement value ~ measured quantity value (context dependent)
measurement value != measurand
measurement value != unit
measurement value != true quantity value
standard uncertainty != expanded uncertainty

CONFIDENCE
confidence_model: provenance_and_method_based
confidence_label: contextual; not a substitute for stated measurement uncertainty
confidence_checks: unit validity, calibration traceability, uncertainty model, repeatability, provenance

FLOW_HASH
algorithm: SHA-256
canonicalisation: UTF-8, normalised line endings, deterministic field ordering
hash_input: canonical ontology content excluding generated hash field
hash_value: compute at publication; not fabricated

UPDATE_MODEL
version: 1.0
change_policy: append versioned revisions, preserve prior provenance and semantic mappings
review_triggers: SI revisions, uncertainty guidance updates, ontology relationship changes

AI_CONSUMPTION
mode: typed-semantic-execution
parse: entities -> relationships -> rules -> validation -> inference
require: dimension checking, explicit uncertainty semantics, provenance preservation
output: validated measurement records and explainable derived values
failure_mode: report validation errors; never silently coerce incompatible units

END FLOW ALGEBRA