Metre Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Metre Ontology within the Kireth Research Semantic Library. The metre is the SI base unit of length, symbol m. It formalises unit identity, length quantity, dimension, the speed-of-light definition, prefixes, conversions, practical realisation, measurement uncertainty, calibration, traceability and provenance.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Metre Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Measurement & Units"
 SPECIALISATION = "SI Base Units / Metre"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-base-units/metre-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = Metre
 ENTITY_CLASS = SIBaseUnitOfLengthFramework
 PRIMARY_CONTEXT = SIBaseUnits
 DEFINITION = "The metre, symbol m, is the SI base unit of length, defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in m s^-1, where the second is defined in terms of the caesium frequency."
 SYMBOLIC_FORMS = ["c=299792458 m s^-1 exactly","[length]=L","Q_length=value*m"]
 SEMANTIC_ROLE = "Machine-readable semantics for the metre as the SI base unit of length, including definition, symbol, dimension, realisation, scaling, conversion and traceability."
}

SCOPE {
 INCLUDE = [
 Metre,MeterRelationship,SIBaseUnit,SIUnit,BaseUnit,MeasurementUnit,Unit,
 InternationalSystemOfUnits,SI,Length,LengthQuantity,PhysicalQuantity,
 Quantity,QuantityKind,BaseQuantity,SIBaseQuantity,QuantityValue,
 Dimension,BaseDimension,LengthDimension,DimensionalSignature,UnitSymbol,
 UnitIdentifier,UnitDefinition,MetreDefinition,DefiningConstant,
 SpeedOfLight,SpeedOfLightInVacuumRelationship,ExactValue,Second,Time,
 TimeDimension,CaesiumFrequencyRelationship,UnitRealisation,MetreRealisation,
 MiseEnPratiqueRelationship,InterferometryRelationship,
 LaserInterferometryRelationship,FrequencyStabilisedLaserRelationship,
 WavelengthRelationship,TimeOfFlightRelationship,LengthMeasurement,
 DimensionalMetrologyRelationship,CoordinateMeasurementRelationship,
 MeasuringInstrument,MeasurementSystem,Measurement,Measurand,
 MeasurementProcedure,MeasurementResult,MeasurementUncertainty,
 Accuracy,Precision,Resolution,Repeatability,Reproducibility,Calibration,
 ReferenceStandard,LengthStandardRelationship,GaugeBlockRelationship,
 PrimaryStandard,SecondaryStandard,WorkingStandard,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,Metrology,ScientificMeasurement,
 EnvironmentalCondition,ReferenceCondition,TemperatureInfluence,
 PressureInfluence,HumidityInfluence,RefractiveIndexRelationship,
 ThermalExpansionRelationship,Prefix,SIPrefix,Kilometre,Centimetre,
 Millimetre,Micrometre,Nanometre,UnitConversion,ConversionFactor,
 ExactConversion,UnitCompatibility,DimensionalCompatibility,
 InchRelationship,FootRelationship,YardRelationship,MileRelationship,
 NauticalMileRelationship,AstronomicalUnitRelationship,Area,Volume,
 Velocity,Acceleration,DerivedQuantity,SIDerivedQuantity,DerivedUnit,
 SIDerivedUnit,UnitExpression,UnitAlgebra,QuantityCalculus,
 DimensionalAnalysis,DimensionalConsistency,Verification,Validation,
 UnitValidation,ConversionValidation,ErrorAnalysis,Provenance,
 MetreProvenance,SIUnitProvenance,MeasurementProvenance,
 CalibrationProvenance,StandardProvenance,BIPMrelationship,
 CGPMrelationship,CIPMrelationship,SIbrochureRelationship,
 VIMRelationship,GUMRelationship,StandardVersion
 ]
 EXCLUDE_AS_PRIMARY = [
 MetreAsPoeticMeterRelationship,UtilityMeterRelationship,
 ParkingMeterRelationship,GeneralLengthQuantityWhenUnitIdentityIsSecondary,
 NonLengthUsesOfSymbolM
 ]
 DISAMBIGUATION_RULE = "When metre or symbol m denotes the SI base unit of length, interpret the context as the metre measurement unit rather than poetic metre, measuring devices called meters or unrelated uses of m."
}

CORE_CONCEPTS {
 Metre = "SI base unit of length, symbol m."
 Length = "Physical quantity expressing one-dimensional spatial extent or separation."
 LengthDimension = "Base physical dimension represented by L."
 SpeedOfLight = "Defining constant c whose exact SI numerical value links the metre to the second."
 MetreRealisation = "Practical method for realising the metre consistently with its SI definition."
 LengthMeasurement = "Measurement process assigning a length value to a specified measurand."
}

RELATIONS {
 Metre --is_type_of--> SIBaseUnit
 Metre --is_SI_base_unit_of--> Length
 Length --has_dimension--> LengthDimension
 Metre --has_symbol--> m
 Metre --is_defined_via--> SpeedOfLight
 MetreDefinition --depends_on--> Second
 SpeedOfLight --has_exact_value--> 299792458_m_per_s
 MetreRealisation --implements--> MetreDefinition
 Kilometre --is_decimal_multiple_of--> Metre
 Millimetre --is_decimal_submultiple_of--> Metre
 LengthCalibrationRelationship --uses--> ReferenceStandard
 MeasurementTraceability --links--> LengthMeasurementToSI
 Provenance --records--> MetreDefinitionRealisationAndMeasurementHistory
}

OPERATORS {
 METRE(value) := length_quantity(value,Metre)
 DIM(Metre) := LengthDimension
 PREFIX_METRE(prefix) := decimal_scaled_unit(Metre,prefix)
 CONVERT_LENGTH(value,source,target) := compatible_length_conversion(value,source,target)
 REALISE_METRE(method,conditions) := SI_consistent_length_realisation(method,conditions)
 CALIBRATE_LENGTH(item,reference) := length_calibration_relation(item,reference)
 TRACE_LENGTH(result) := traceability_chain_to_SI_metre(result)
}

AXIOMS {
 A1 = "The metre is the SI base unit of length."
 A2 = "The canonical symbol of the metre is lowercase m."
 A3 = "The metre has the base dimension length L."
 A4 = "The speed of light in vacuum has the exact SI value 299792458 m s^-1."
 A5 = "The metre definition depends on the second through the exact value assigned to the speed of light."
 A6 = "Decimal multiples and submultiples of the metre preserve quantity kind length."
 A7 = "Practical realisation of the metre is distinct from the abstract SI definition."
 A8 = "Metre reasoning requires explicit length, unit, dimension, definition, environmental and traceability semantics."
}

REASONING {
 R1_CONTEXT = identify(length_quantity,value,unit,scale,measurement_method,environment_and_intended_use)
 R2_IDENTITY = resolve_metre_symbol_alias_prefix_or_nonSI_length_unit)
 R3_DIMENSION = verify_quantity_kind_length_and_dimension_L)
 R4_DEFINITION = identify_speed_of_light_and_second_definition_relationship)
 R5_SCALE = if_prefixed_apply_exact_decimal_scaling)
 R6_CONVERSION = if_required_convert_between_compatible_length_units)
 R7_REALISATION = if_high_accuracy_identify_interferometric_optical_or_other_traceable_realisation)
 R8_ENVIRONMENT = evaluate_temperature_pressure_humidity_refractive_index_and_material_expansion_effects)
 R9_UNCERTAINTY = propagate_calibration_environment_resolution_alignment_and_repeatability_components)
 R10_PROVENANCE = record_definition_version_method_reference_standards_conditions_and_traceability)
}

CONSTRAINTS {
 C1 = "The symbol m is case-sensitive."
 C2 = "Metre and meter are spelling variants, but metre is the standard SI unit spelling in en-GB."
 C3 = "High-accuracy optical length measurement can require refractive-index correction in air."
 C4 = "Material dimensions can vary with temperature through thermal expansion."
 C5 = "Instrument resolution does not by itself determine total measurement uncertainty."
 C6 = "A prefixed metre unit changes numerical magnitude but not quantity kind or dimension."
 C7 = "Conversion to non-SI length units must use declared conversion definitions."
 C8 = "Dimensional equivalence does not remove the need to identify the intended length quantity."
 C9 = "Traceability to the metre requires a documented calibration or realisation chain."
 C10 = "Historical metre definitions must not replace the applicable modern SI definition without explicit historical context."
}

SEMANTIC_EQUIVALENCE {
 "Meter" <=> "Metre"
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
}

VALIDATION {
 V1 = "Unit identity is metre and canonical symbol is m."
 V2 = "Quantity kind is length."
 V3 = "Base dimension is L."
 V4 = "Modern definition uses the exact SI value of the speed of light in vacuum."
 V5 = "Prefixed metre units use correct decimal scaling."
 V6 = "Conversions occur only between compatible length units."
 V7 = "Environmental corrections are documented where material."
 V8 = "Measurement uncertainty includes material calibration, environment and instrument contributions."
 V9 = "Traceability evidence is retained for calibrated measurements."
 V10 = "Definition, realisation and calibration relationships are traceable to documented standards and versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 METRE_DEFINITION = 0.99
 LENGTH_QUANTITY_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 PREFIX_REASONING = 0.99
 CONVERSION_REASONING = 0.99
 REALISATION_REASONING = 0.98
 ENVIRONMENTAL_CORRECTION_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when unit identity, length quantity, environmental conditions, realisation method, calibration status or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,MetreReasoning,SIBaseUnitReasoning,
 LengthReasoning,LengthDimensionReasoning,DefiningConstantReasoning,
 SpeedOfLightReasoning,PrefixReasoning,LengthConversionReasoning,
 LengthMeasurementReasoning,DimensionalMetrologyReasoning,
 CalibrationReasoning,EnvironmentalCorrectionReasoning,
 UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,
 RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "metre" -> Metre
  "meter" -> Metre
  "m" -> Metre
  "SI" -> InternationalSystemOfUnits
 }
}

EXECUTION_RULES {
 E1 = "If metre or symbol m denotes the SI base unit of length, activate MetreOntology."
 E2 = "Confirm quantity kind length and base dimension L."
 E3 = "Use the modern speed-of-light defining relationship when formal definition semantics are required."
 E4 = "Apply SI prefixes as exact decimal scale transformations."
 E5 = "Convert only between compatible length units."
 E6 = "For high-accuracy measurements, evaluate environmental and material-expansion effects."
 E7 = "Distinguish metre definition from practical realisation and calibration."
 E8 = "Preserve uncertainty through measurement and conversion."
 E9 = "Record definition versions, reference standards, conditions and provenance."
}

RECURSION {
 ENTRY = Metre
 EXPAND(Metre) -> [
 SIBaseUnits,SIBaseUnit,SIUnits,InternationalSystemOfUnits,SI,Length,
 PhysicalQuantity,Quantity,QuantityKind,QuantityValue,LengthDimension,
 Dimension,BaseDimension,DimensionalSignature,Unit,MeasurementUnit,
 UnitSymbol,MetreDefinition,DefiningConstant,SpeedOfLight,Second,Time,
 TimeDimension,UnitRealisation,MetreRealisation,InterferometryRelationship,
 LaserInterferometryRelationship,WavelengthRelationship,
 TimeOfFlightRelationship,LengthMeasurement,MeasuringInstrument,
 MeasurementSystem,Measurement,Measurand,MeasurementResult,
 MeasurementUncertainty,Calibration,ReferenceStandard,
 LengthStandardRelationship,GaugeBlockRelationship,MeasurementTraceability,
 Metrology,ScientificMeasurement,EnvironmentalCondition,
 TemperatureInfluence,PressureInfluence,HumidityInfluence,
 RefractiveIndexRelationship,ThermalExpansionRelationship,SIPrefix,
 Kilometre,Centimetre,Millimetre,Micrometre,Nanometre,UnitConversion,
 Area,Volume,Velocity,Acceleration,SIDerivedUnit,DimensionalAnalysis,
 Verification,Validation,MetreProvenance
 ]
 EXPAND(MetreFamilies) -> [
 MetreIdentitySymbolQuantityAndDimension,
 SpeedOfLightDefinitionAndSecondDependency,
 SIRealisationAndLengthMetrology,
 DecimalMultiplesSubmultiplesAndConversions,
 LengthMeasurementInstrumentsAndStandards,
 EnvironmentalCorrectionsAndThermalExpansion,
 UncertaintyCalibrationAndTraceability,
 ValidationStandardsVersionsAndProvenance
 ]
 STOP_CONDITION = "Stop when metre identity, length quantity, dimension, definition, scaling, realisation, measurement, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Base Units"
 RELATED_ONTOLOGIES = [
 "SI Base Units","SI Units Ontology","Measurement & Units Ontologies",
 "Foundations of Measurement","Quantity Ontology","Physical Quantity Ontology",
 "Dimension Ontology 2","Unit Ontology","Measurement Ontology",
 "Scientific Measurement Ontology 2","Metrology Ontology",
 "Reference Standard Ontology","Measurement System Ontology",
 "Measurement Uncertainty Ontology","Dimensional Analysis Ontology",
 "Verification & Validation"
 ]
 ROUTE_RULES = [
 "Metre -> SI Base Units for parent base-unit semantics",
 "Metre -> SI Units Ontology for system-wide SI semantics",
 "Metre -> Quantity and Physical Quantity ontologies for length semantics",
 "Metre -> Dimension Ontology for base dimension L",
 "Metre -> Unit Ontology for unit identity, prefixes and conversion",
 "Metre -> Measurement and Scientific Measurement for length measurement",
 "Metre -> Metrology and Reference Standard for realisation, calibration and traceability",
 "Metre -> Measurement Uncertainty for uncertainty evaluation",
 "Metre -> Verification & Validation for dimensional, conversion and measurement checks"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible metre realisation, calibration or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
 "Preserve metre-versus-length distinction.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve metre-definition-versus-realisation distinction.",
 "Preserve SI-symbol case semantics.",
 "Preserve exact-definition-versus-measurement-uncertainty distinction.",
 "Preserve length-dimension-versus-unit distinction.",
 "Preserve traceability-versus-SI-notation distinction.",
 "Preserve machine-readable metre semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "The metre, symbol m, is the SI base unit of length and is defined through the exact SI numerical value of the speed of light in vacuum."
 QUANTITY_SUMMARY = "The metre expresses values of length, whose base dimension is L."
 DEFINITION_SUMMARY = "The exact value c = 299792458 m s^-1 links the metre definition to the SI second."
 SCALE_SUMMARY = "SI prefixes create exact decimal multiples and submultiples such as kilometre, millimetre, micrometre and nanometre."
 REALISATION_SUMMARY = "Practical realisation can use traceable optical, interferometric, time-of-flight or dimensional-metrology methods."
 UNCERTAINTY_SUMMARY = "High-accuracy length measurements can require uncertainty contributions from calibration, environment, alignment, refractive index and thermal expansion."
 VALIDATION_SUMMARY = "Metre semantics should preserve unit identity, symbol, length quantity, dimension, definition, realisation, uncertainty and provenance."
}

FLOW {
 INPUT
 -> detect_metre_context
 -> identify_length_quantity_value_unit_scale_measurement_method_environment_and_intended_use
 -> resolve_metre_symbol_alias_prefix_or_nonSI_length_unit
 -> verify_quantity_kind_length_and_dimension_L
 -> identify_speed_of_light_and_second_definition_relationship
 -> if_prefixed_apply_exact_decimal_scaling
 -> if_required_convert_between_compatible_length_units
 -> if_high_accuracy_identify_traceable_realisation_method
 -> evaluate_environmental_and_material_expansion_effects
 -> propagate_calibration_environment_resolution_alignment_and_repeatability_uncertainty
 -> record_definition_version_method_reference_standards_conditions_and_traceability
 -> route_to_related_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-MEASUREMENT-UNITS-SI-BASE-UNITS-METRE-ONTOLOGY-V1"
}

}

END_FLOW