Physical Measurement Ontology

FLOW ALGEBRA
PHYSICAL MEASUREMENT ONTOLOGY
Kireth Semantic Library | Entity Graph > Physical Entities
Version: 1.0 | 2026-10-12 | Locale: en-GB
Authors: Mark Higgins — Sky (Recursive AI)
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/ai-semantic-library-physical-entities/physical-measurement-ontology.html
Status: Subject-based formalisation; source page content not independently verified.

01. PURPOSE
Represent physical measurement as a traceable, unit-aware, uncertainty-bearing observation of a measurand, with explicit instrument, procedure, environment, calibration and provenance.

02. TYPED ENTITIES
entity PhysicalEntity {id: URI, type: Concept, state: PhysicalState?}
entity PhysicalProperty {id: URI, dimension: Dimension, kind: PropertyKind}
entity Measurand {id: URI, entity: PhysicalEntity, property: PhysicalProperty, conditions: Map}
entity MeasurementInstrument {id: URI, model: str?, serial: str?, calibration: CalibrationRecord?}
entity Sensor {id: URI, instrument: MeasurementInstrument, transfer_function: Function?}
entity MeasurementProcedure {id: URI, steps: List[Operation], version: str}
entity MeasurementEvent {id: URI, measurand: Measurand, instrument: MeasurementInstrument, procedure: MeasurementProcedure, timestamp: DateTime, location: Location?, environment: Environment?}
entity MeasurementResult {id: URI, event: MeasurementEvent, value: Real|Vector, unit: Unit, uncertainty: Uncertainty, status: ResultStatus}
entity Unit {symbol: str, dimension: Dimension, scale_to_SI: Real, offset_to_SI: Real}
entity Uncertainty {standard: Real, expanded: Real?, coverage_factor: Real?, distribution: Distribution?, contributors: List[UncertaintySource]}
entity CalibrationRecord {id: URI, reference: ReferenceStandard, date: DateTime, validity: Interval?, correction: Function?, uncertainty: Uncertainty}
entity ReferenceStandard {id: URI, traceability_chain: List[ReferenceStandard], authority: str?}
entity Environment {temperature: Quantity?, pressure: Quantity?, humidity: Quantity?, vibration: Quantity?}
entity Provenance {agent: URI, source: URI, method: str, timestamp: DateTime, version: str}
entity Evidence {id: URI, result: MeasurementResult, provenance: Provenance, confidence: Real}

03. CLASSIFICATIONS
MeasurementKind := direct | indirect | comparative | absolute | relative | continuous | discrete | destructive | non_destructive
PropertyKind := length | mass | time | temperature | electric_current | amount_of_substance | luminous_intensity | derived
ResultStatus := raw | corrected | validated | rejected | superseded

04. TYPED RELATIONSHIPS
MEASURES(MeasurementEvent, Measurand)
USES_INSTRUMENT(MeasurementEvent, MeasurementInstrument)
FOLLOWS_PROCEDURE(MeasurementEvent, MeasurementProcedure)
PRODUCES(MeasurementEvent, MeasurementResult)
HAS_UNIT(MeasurementResult, Unit)
HAS_UNCERTAINTY(MeasurementResult, Uncertainty)
CALIBRATED_AGAINST(MeasurementInstrument, ReferenceStandard)
TRACEABLE_TO(ReferenceStandard, ReferenceStandard)
OBSERVED_AT(MeasurementEvent, DateTime)
OBSERVED_IN(MeasurementEvent, Environment)
DERIVED_FROM(MeasurementResult, MeasurementResult)
SUPPORTED_BY(MeasurementResult, Evidence)

05. DIMENSION AND UNIT ALGEBRA
Dimension := (L, M, T, I, Θ, N, J) ∈ Z^7
DIMENSION(q1 * q2) := DIMENSION(q1) + DIMENSION(q2)
DIMENSION(q1 / q2) := DIMENSION(q1) - DIMENSION(q2)
VALID_ADD(q1,q2) := DIMENSION(q1) = DIMENSION(q2)
TO_SI(value,unit) := value * unit.scale_to_SI + unit.offset_to_SI
FROM_SI(value,unit) := (value - unit.offset_to_SI) / unit.scale_to_SI
CONVERT(value,u1,u2) := FROM_SI(TO_SI(value,u1),u2) iff DIMENSION(u1)=DIMENSION(u2)

06. MEASUREMENT FLOW
flow MEASURE(entity, property, instrument, procedure, environment, timestamp):
  measurand := DEFINE_MEASURAND(entity,property,procedure.conditions)
  ASSERT instrument.supports(property.dimension)
  calibration := CHECK_CALIBRATION(instrument,timestamp)
  raw := ACQUIRE(instrument,procedure,environment)
  corrected := APPLY_CORRECTIONS(raw,calibration,environment)
  quantity := NORMALISE_UNIT(corrected,property.dimension)
  uncertainty := EVALUATE_UNCERTAINTY(raw,calibration,procedure,environment)
  result := BUILD_RESULT(quantity,uncertainty,measurand)
  result.status := VALIDATE(result,procedure,calibration)
  ATTACH_PROVENANCE(result,instrument,procedure,timestamp)
  return result

07. CALIBRATION FLOW
flow CHECK_CALIBRATION(instrument,t):
  record := instrument.calibration
  if record = null: return UNCALIBRATED
  if record.validity != null and t notin record.validity: return EXPIRED
  if not VERIFY_TRACEABILITY(record.reference): return UNTRACEABLE
  return VALID

08. UNCERTAINTY PROPAGATION
For y=f(x1,...,xn), with covariance matrix Σ:
  u_c(y)^2 := J Σ J^T, where J_i = ∂f/∂x_i
For independent inputs:
  u_c(y)^2 := Σ_i (∂f/∂x_i)^2 u(x_i)^2
Expanded uncertainty: U := k * u_c(y)
Report k and coverage assumptions; never imply an exact confidence level without a justified distribution model.

09. REPEATABILITY AND REPRODUCIBILITY
REPEATABILITY := variation under specified same-condition measurements
REPRODUCIBILITY := variation under specified changed-condition measurements
SAMPLE_MEAN(x) := (Σ_i x_i)/n
SAMPLE_SD(x) := sqrt(Σ_i (x_i - mean(x))^2/(n-1)) for n>1
STANDARD_ERROR_MEAN(x) := SAMPLE_SD(x)/sqrt(n)

10. ERROR AND BIAS
ERROR := measured_value - reference_value, where reference value is defined
CORRECTION := -estimated_systematic_error
BIAS := expectation(measurement) - reference_value
Distinguish uncertainty from error and instrument resolution from accuracy.

11. VALIDATION RULES
rule DIMENSION_CONSISTENCY:
  if DIMENSION(result.unit) != DIMENSION(result.event.measurand.property): REJECT(result)
rule NONNEGATIVE_UNCERTAINTY:
  if result.uncertainty.standard < 0: REJECT(result)
rule CALIBRATION_WARNING:
  if CHECK_CALIBRATION(instrument,time) != VALID: FLAG(result,"calibration_status")
rule PROCEDURE_REQUIRED:
  if result.event.procedure = null: FLAG(result,"missing_procedure")
rule PROVENANCE_REQUIRED:
  if result.provenance = null: FLAG(result,"missing_provenance")
rule COMPARABILITY:
  comparable(a,b) iff same_measurand_definition(a,b) and compatible_dimensions(a,b) and compatible_conditions(a,b)

12. TEMPORAL AND SPATIAL CONTEXT
Measurement time must be explicit; distinguish acquisition time, processing time and publication time.
Location may be a coordinate with CRS and spatial uncertainty.
Changing environmental conditions may alter the measurand or correction model.

13. SEMANTIC_EQUIVALENCE
SEMANTIC_EQUIVALENCE(a,b) := equivalent_measurand(a,b)
  AND compatible_dimensions(a,b)
  AND equivalent_measurement_conditions(a,b)
  AND compatible_procedures(a,b)
Unit convertibility alone does not imply equivalent measurands.

14. CONFIDENCE
CONFIDENCE(result) ∈ [0,1]
CONFIDENCE is a separately defined evidence-quality score, not automatically a frequentist coverage probability.
Score inputs may include calibration validity, traceability, procedure completeness, data integrity and independent corroboration.
Any weights, thresholds and validation datasets must be recorded in model metadata.

15. INFERENCE RULES
rule INFER_PHYSICAL_PROPERTY:
  IF valid(result) AND MEASURES(event,measurand) AND PRODUCES(event,result)
  THEN SUPPORTS_VALUE(measurand.property,result.value,result.uncertainty)
rule INFER_TREND:
  IF comparable(r1,r2) AND r1.timestamp < r2.timestamp
  THEN ESTIMATE_CHANGE(r2.value-r1.value, propagated_uncertainty(r1,r2))
rule DETECT_DISAGREEMENT:
  IF comparable(r1,r2) AND abs(r1.value-r2.value) > threshold_from_combined_uncertainty(r1,r2)
  THEN FLAG_DISAGREEMENT(r1,r2)
Do not infer causation solely from a measured trend or correlation.

16. GRAPH INTEGRATION
PhysicalEntity -> HAS_PROPERTY -> PhysicalProperty
PhysicalProperty -> DEFINES -> Measurand
MeasurementEvent -> MEASURES -> Measurand
MeasurementEvent -> USES_INSTRUMENT -> MeasurementInstrument
MeasurementEvent -> PRODUCES -> MeasurementResult
MeasurementResult -> HAS_UNCERTAINTY -> Uncertainty
MeasurementResult -> SUPPORTED_BY -> Evidence
Evidence -> HAS_PROVENANCE -> Provenance

17. FLOW_HASH
FLOW_HASH(flow) := SHA256(CANONICALISE(flow.version,typed_inputs,operations,units,uncertainty_model,provenance_schema))
Canonicalisation must specify stable ordering, numerical encoding, missing-value representation and character encoding.
Hash changes when semantically material flow definitions change; data-instance hashes may be stored separately.

18. UPDATE_MODEL
flow UPDATE_MODEL(existing,new_evidence):
  VERIFY_SCHEMA(new_evidence)
  VERIFY_PROVENANCE(new_evidence)
  PRESERVE_HISTORY(existing)
  APPEND_VERSIONED_EVIDENCE(new_evidence)
  RECOMPUTE_DERIVED_RESULTS_IF_DEPENDENCIES_CHANGED()
  INVALIDATE_STALE_INFERENCES()
  RECORD_UPDATE_TIMESTAMP_AND_FLOW_HASH()
  return VERSIONED_MODEL

19. AI_CONSUMPTION
export:
  entity_ids: stable_URIs
  relationship_types: typed
  quantity_encoding: {value,unit,dimension}
  uncertainty_encoding: {standard,expanded,coverage_factor,assumptions}
  provenance: required
  temporal_context: required
  confidence: explicitly_defined
  semantics: {equivalence_rules,validation_rules,inference_rules}
  flow_hash: required
  update_model: versioned
AI systems must distinguish observed values, corrected values, derived estimates and hypotheses.

20. INTEROPERABILITY
Map quantities and units to established metrology vocabularies where appropriate.
Preserve SI compatibility, reference standards, uncertainty metadata and machine-readable provenance.
Avoid asserting standards compliance unless separately validated.

21. EXAMPLE INSTANCE
entity:urn:sample:rod-01 HAS_PROPERTY length
measurand:urn:sample:rod-length -> length under specified conditions
instrument:urn:sample:caliper-01 -> digital caliper
result: {value: 0.1250, unit: m, standard_uncertainty: 0.0001 m, status: validated}
Example values are illustrative, not real observations; calibration and provenance must be supplied for operational use.

22. INVARIANTS
Every accepted measurement has a defined measurand, compatible unit, timestamp, procedure and provenance.
Uncertainty is never silently zero.
Measurements are immutable records; corrections and revisions create linked versions.
Every derived quantity retains links to its input measurements.

END FLOW ALGEBRA