Watt Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Watt Ontology within the Kireth Research Semantic Library. The watt, symbol W, is the coherent SI derived unit of power and radiant flux. It equals one joule per second and reduces to kg m^2 s^-3.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY=Watt
 ENTITY_CLASS=SIDerivedUnitOfPowerFramework
 PRIMARY_CONTEXT=SIDerivedUnits
 DEFINITION="The watt, symbol W, is the coherent SI derived unit of power. One watt equals one joule per second and one kilogram square metre per second cubed."
 SYMBOLIC_FORMS=["1 W=1 J s^-1","1 W=1 kg m^2 s^-3","P=dE/dt","P=F dot v","P=V I","[power]=M L^2 T^-3"]
 SEMANTIC_ROLE="Machine-readable semantics for watt identity, power, energy-rate relationships, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE=[
 Watt,WattUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,MeasurementUnit,Unit,
 InternationalSystemOfUnits,SI,SIBaseUnits,Joule,Second,Newton,Metre,Kilogram,
 Ampere,Volt,Ohm,Power,DerivedQuantity,Quantity,QuantityKind,QuantityValue,
 PowerDimension,DimensionalSignature,UnitSymbol,WattDefinition,UnitExpression,
 UnitAlgebra,DimensionalAnalysis,Energy,Work,Heat,EnergyTransferRelationship,
 MechanicalPower,ElectricalPower,ThermalPower,RadiantPower,RadiantFluxRelationship,
 AcousticPowerRelationship,HydraulicPowerRelationship,ShaftPowerRelationship,
 InputPowerRelationship,OutputPowerRelationship,DissipatedPowerRelationship,
 AveragePower,InstantaneousPower,PeakPowerRelationship,ActivePower,ReactivePower,
 ApparentPower,PowerFactor,VoltAmpereRelationship,ElectricalEnergy,ElectricCurrent,
 Voltage,Resistance,JoulesLawRelationship,OhmsLawRelationship,Force,Velocity,Torque,
 AngularVelocity,RotationalPowerRelationship,Pressure,Pascal,VolumeFlowRateRelationship,
 HeatFlowRateRelationship,IrradianceRelationship,PowerDensityRelationship,
 PowerMeasurement,Wattmeter,PowerMeterRelationship,EnergyMeterRelationship,
 PowerAnalyserRelationship,DynamometerRelationship,TorqueSensorRelationship,
 TachometerRelationship,CalorimeterRelationship,RadiometerRelationship,
 OpticalPowerMeterRelationship,MeasurementSystem,Measurement,Measurand,
 MeasurementProcedure,MeasurementModel,MeasurementResult,MeasurementUncertainty,
 Accuracy,Precision,Resolution,Repeatability,Reproducibility,LinearityRelationship,
 BandwidthRelationship,PhaseErrorRelationship,Drift,Stability,Calibration,
 PowerCalibrationRelationship,ElectricalCalibrationRelationship,
 OpticalPowerCalibrationRelationship,ReferenceStandard,PowerStandardRelationship,
 MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,Metrology,
 PowerMetrologyRelationship,ScientificMeasurement,TemperatureInfluence,
 FrequencyInfluenceRelationship,HarmonicDistortionRelationship,WaveformRelationship,
 LoadingEffectRelationship,Efficiency,EnergyEfficiencyRelationship,SIPrefix,
 Milliwatt,MicrowattRelationship,Kilowatt,Megawatt,Gigawatt,TerawattRelationship,
 UnitConversion,ConversionFactor,ExactConversion,UnitCompatibility,
 DimensionalCompatibility,QuantityCompatibility,HorsepowerRelationship,
 BTUPerHourRelationship,KilowattHourRelationship,Verification,Validation,
 UnitValidation,DimensionalValidation,ConversionValidation,ErrorAnalysis,
 Provenance,WattProvenance,SIDerivedUnitProvenance,SIUnitProvenance,
 MeasurementProvenance,CalibrationProvenance,StandardProvenance,
 BIPMrelationship,SIbrochureRelationship,VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[
 WattAsSurnameRelationship,
 EnergyWhenAccumulatedEnergyRatherThanRateIsPrimary,
 ReactivePowerWhenVarUnitSemanticsArePrimary,
 ApparentPowerWhenVoltAmpereSemanticsArePrimary
 ]
 DISAMBIGUATION_RULE="When watt or W denotes the coherent SI derived unit of power or radiant flux, interpret it as the watt measurement unit. Distinguish power in watts from energy in joules or watt-hours."
}

CORE_CONCEPTS {
 Watt="Coherent SI derived unit of power, symbol W, equal to J s^-1."
 Power="Rate at which energy is transferred, transformed or used."
 PowerDimension="Derived physical dimension M L^2 T^-3."
 Joule="SI derived unit of energy used in W=J/s."
 MechanicalPower="Rate of mechanical work or energy transfer."
 ElectricalPower="Rate of electrical energy transfer."
 ThermalPower="Rate of thermal energy transfer."
 RadiantPower="Radiant energy transferred per unit time."
 PowerMeasurement="Measurement process assigning a power value to a measurand."
}

RELATIONS {
 Watt--is_type_of-->SIDerivedUnit
 Watt--is_coherent_derived_unit_of-->Power
 Watt--is_coherent_derived_unit_of-->RadiantPower
 Watt--has_symbol-->W
 Watt--has_expression-->joule_per_second
 Watt--has_base_expression-->kilogram_square_metre_per_second_cubed
 Power--has_dimension-->PowerDimension
 Power--is_rate_of-->EnergyTransfer
 MechanicalPower--can_equal-->ForceDotVelocity
 RotationalPowerRelationship--can_equal-->TorqueTimesAngularVelocity
 ElectricalPower--for_DC_can_equal-->VoltageTimesCurrent
 Kilowatt--is_decimal_multiple_of-->Watt
 Megawatt--is_decimal_multiple_of-->Watt
 MeasurementTraceability--links-->PowerMeasurementToSI
 Provenance--records-->WattDefinitionMeasurementAndCalibrationHistory
}

OPERATORS {
 WATT(value):=power_quantity(value,Watt)
 DIM(Watt):=PowerDimension
 POWER_FROM_ENERGY(energy,time):=energy/time
 MECHANICAL_POWER(force,velocity_parallel):=force*velocity_parallel
 ROTATIONAL_POWER(torque,angular_velocity):=torque*angular_velocity
 DC_ELECTRICAL_POWER(voltage,current):=voltage*current
 RESISTIVE_POWER(current,resistance):=current^2*resistance
 EFFICIENCY(output_power,input_power):=output_power/input_power
 PREFIX_WATT(prefix):=decimal_scaled_unit(Watt,prefix)
 CONVERT_POWER(value,source,target):=compatible_power_conversion(value,source,target)
 TRACE_POWER(result):=traceability_chain_to_SI_watt(result)
}

AXIOMS {
 A1="The watt is the coherent SI derived unit of power."
 A2="One watt equals one joule per second."
 A3="One watt is equivalent to kg m^2 s^-3."
 A4="The canonical symbol is uppercase W."
 A5="Power is a rate and must remain distinct from energy."
 A6="Mechanical power can be represented by force dotted with velocity."
 A7="For direct-current circuits, electrical power can be represented by voltage multiplied by current."
 A8="Active, reactive and apparent electrical power are distinct quantities."
 A9="Power measurement traceability requires documented reference standards and calibration."
}

REASONING {
 R1_CONTEXT=identify(power_quantity,value,unit,energy_domain,time_basis,measurement_method_and_intended_use)
 R2_IDENTITY=resolve_watt_prefixed_watt_nonSI_power_unit_or_symbol_W_ambiguity)
 R3_QUANTITY=distinguish_power_energy_active_reactive_apparent_or_related_quantity)
 R4_DIMENSION=verify_dimension_M_L_squared_T_minus_3)
 R5_DERIVATION=expand_watt_to_J_s_minus_1_and_kg_m_squared_s_minus_3)
 R6_EQUATION=choose_energy_rate_mechanical_rotational_electrical_thermal_radiant_or_valid_power_relationship)
 R7_SCALE=if_prefixed_apply_exact_decimal_scaling)
 R8_MEASUREMENT=identify_wattmeter_power_analyser_dynamometer_calorimetric_radiometric_or_other_method)
 R9_UNCERTAINTY=evaluate_reference_voltage_current_phase_frequency_waveform_loading_temperature_resolution_and_repeatability)
 R10_PROVENANCE=record_unit_expression_quantity_kind_equation_method_reference_standard_calibration_and_traceability)
}

CONSTRAINTS {
 C1="The symbol W is case-sensitive."
 C2="Power in watts must not be conflated with energy in joules or watt-hours."
 C3="Watt-hour is a unit of energy, not power."
 C4="Active power in watts must be distinguished from reactive power and apparent power."
 C5="The relation P=V I requires appropriate circuit semantics; AC contexts can require phase and waveform information."
 C6="Mechanical power calculations require consistent force-velocity or torque-angular-velocity relationships."
 C7="Efficiency is dimensionless and requires clearly defined input and output boundaries."
 C8="Instrument resolution alone does not determine total power-measurement uncertainty."
 C9="Traceability to the watt requires a documented electrical, mechanical, thermal or radiometric reference chain."
 C10="Dimensional correctness alone does not establish the intended power quantity kind."
}

SEMANTIC_EQUIVALENCE {
 "WattUnit"<=>"Watt"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
 "RealPower"<=>"ActivePower"
}

VALIDATION {
 V1="Unit identity is watt and canonical symbol is W."
 V2="Quantity kind is power, radiant flux or another explicitly identified compatible quantity."
 V3="Derived dimension is M L^2 T^-3."
 V4="Coherent SI expressions are J s^-1 and kg m^2 s^-3."
 V5="Power and energy semantics remain distinct."
 V6="Active, reactive and apparent power semantics remain distinct in AC systems."
 V7="Prefixed watt units use correct decimal scaling."
 V8="Conversions to non-SI power units use declared conversion definitions."
 V9="Measurement uncertainty includes relevant electrical, mechanical, thermal, optical and environmental effects."
 V10="Power calibration and traceability evidence are retained."
}

CONFIDENCE {
 BASE_CONFIDENCE=0.99
 WATT_DEFINITION=0.99
 POWER_REASONING=0.99
 DIMENSION_REASONING=0.99
 MECHANICAL_POWER_REASONING=0.98
 ELECTRICAL_POWER_REASONING=0.98
 POWER_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when power quantity kind, time basis, AC phase, waveform, system boundaries, measurement method, calibration status or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES=[
 SemanticSearch,OntologyGrounding,WattReasoning,SIDerivedUnitReasoning,
 PowerReasoning,EnergyRateReasoning,MechanicalPowerReasoning,ElectricalPowerReasoning,
 ThermalPowerReasoning,RadiantPowerReasoning,EfficiencyReasoning,
 PowerMeasurementReasoning,PowerMetrologyReasoning,CalibrationReasoning,
 DimensionalReasoning,UncertaintyReasoning,TraceabilityReasoning,
 KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "watt"->Watt
  "W"->Watt
  "mW"->Milliwatt
  "kW"->Kilowatt
  "MW"->Megawatt
  "GW"->Gigawatt
 }
}

EXECUTION_RULES {
 E1="If watt or W denotes the SI derived unit of power or radiant flux, activate WattOntology."
 E2="Confirm quantity kind rather than relying only on dimensional form."
 E3="Map watt coherently to J s^-1 and kg m^2 s^-3."
 E4="Distinguish power from accumulated energy."
 E5="Distinguish active, reactive and apparent electrical power."
 E6="Choose a power equation appropriate to the physical domain."
 E7="Apply SI prefixes as exact decimal scale transformations."
 E8="For measurement contexts, evaluate phase, waveform, loading, environment, calibration and uncertainty."
 E9="Record power-reference, calibration and traceability provenance."
}

RECURSION {
 ENTRY=Watt
 EXPAND(Watt)->[
 SIDerivedUnits,DerivedUnit,SIDerivedUnit,CoherentDerivedUnit,SIUnits,SIBaseUnits,
 Joule,Second,Newton,Metre,Kilogram,Ampere,Volt,Ohm,Power,PowerDimension,
 Energy,Work,Heat,Quantity,QuantityKind,Dimension,DimensionalSignature,Unit,
 UnitSymbol,WattDefinition,UnitExpression,UnitAlgebra,DimensionalAnalysis,
 MechanicalPower,ElectricalPower,ThermalPower,RadiantPower,AveragePower,
 InstantaneousPower,ActivePower,ReactivePower,ApparentPower,PowerFactor,
 ElectricCurrent,Voltage,Resistance,Force,Velocity,Torque,AngularVelocity,
 Pressure,Pascal,HeatFlowRateRelationship,IrradianceRelationship,
 PowerMeasurement,Wattmeter,PowerAnalyserRelationship,DynamometerRelationship,
 CalorimeterRelationship,OpticalPowerMeterRelationship,MeasurementSystem,
 Measurement,MeasurementUncertainty,Calibration,ReferenceStandard,
 PowerStandardRelationship,MeasurementTraceability,Metrology,
 FrequencyInfluenceRelationship,HarmonicDistortionRelationship,
 WaveformRelationship,Efficiency,SIPrefix,Milliwatt,Kilowatt,Megawatt,
 Gigawatt,TerawattRelationship,HorsepowerRelationship,UnitConversion,
 Verification,Validation,WattProvenance
 ]
 EXPAND(WattFamilies)->[
 WattIdentitySymbolQuantityAndDimension,
 JouleSecondAndBaseUnitExpansion,
 EnergyRateMechanicalAndRotationalPower,
 ElectricalActiveReactiveApparentAndPowerFactorSemantics,
 ThermalRadiantAcousticHydraulicAndOtherPowerDomains,
 PowerMeasurementMetersAnalysersStandardsAndCalibration,
 PhaseWaveformLoadingEfficiencyUncertaintyAndTraceability,
 ValidationConversionSemanticDisambiguationAndProvenance
 ]
 STOP_CONDITION="Stop when watt identity, power quantity, dimensional expression, domain relationship, measurement semantics, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY="SI Derived Units"
 RELATED_ONTOLOGIES=[
 "SI Derived Units","Derived Units Ontology","SI Base Units","SI Units Ontology",
 "Joule Ontology","Second Ontology","Newton Ontology","Metre Ontology",
 "Kilogram Ontology","Ampere Ontology","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","Physics Ontology","Thermodynamics Ontology",
 "Verification & Validation"
 ]
 ROUTE_RULES=[
 "Watt -> SI Derived Units for parent derived-unit semantics",
 "Watt -> Derived Units Ontology for general derived-unit algebra",
 "Watt -> Joule and Second ontologies for J s^-1 semantics",
 "Watt -> Kilogram, Metre and Second ontologies for base-unit expansion",
 "Watt -> Quantity and Physical Quantity ontologies for power semantics",
 "Watt -> Dimension Ontology for M L^2 T^-3 dimensional structure",
 "Watt -> Physics and Thermodynamics for mechanical, electrical, thermal and radiant power",
 "Watt -> Measurement and Scientific Measurement for power measurement",
 "Watt -> Metrology and Reference Standard for calibration and traceability",
 "Watt -> Measurement Uncertainty for uncertainty evaluation",
 "Watt -> Verification & Validation for power, dimensional and semantic checks"
 ]
}

UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible power, measurement or reasoning relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=[
 "Preserve watt-versus-power distinction.",
 "Preserve power-versus-energy distinction.",
 "Preserve active-versus-reactive-versus-apparent-power distinction.",
 "Preserve mechanical-versus-electrical-versus-thermal-versus-radiant context.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve dimensional-correctness-versus-quantity-meaning distinction.",
 "Preserve measurement-reference-versus-unit-definition distinction.",
 "Preserve machine-readable watt semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION="The watt, symbol W, is the coherent SI derived unit of power and equals J s^-1 or kg m^2 s^-3."
 QUANTITY_SUMMARY="Power is the rate of energy transfer or transformation and has derived dimension M L^2 T^-3."
 ENERGY_SUMMARY="One watt represents one joule of energy transferred per second."
 MECHANICAL_SUMMARY="Mechanical power can be expressed through force and velocity or torque and angular velocity."
 ELECTRICAL_SUMMARY="Electrical power requires explicit active, reactive or apparent-power semantics where relevant."
 MEASUREMENT_SUMMARY="Power measurement can use wattmeters, power analysers, dynamometers, calorimetric methods and optical power meters."
 UNCERTAINTY_SUMMARY="Precision power measurement can require uncertainty contributions from voltage, current, phase, frequency, waveform, loading, calibration and environment."
 VALIDATION_SUMMARY="Watt semantics should preserve unit identity, power quantity, dimensional structure, domain relationships, uncertainty, traceability and provenance."
}

FLOW {
 INPUT
 -> detect_watt_context
 -> identify_power_quantity_value_unit_energy_domain_time_basis_measurement_method_and_intended_use
 -> resolve_watt_prefixed_watt_nonSI_power_unit_or_symbol_W_ambiguity
 -> distinguish_power_energy_active_reactive_apparent_or_related_quantity
 -> verify_dimension_M_L_squared_T_minus_3
 -> expand_watt_to_J_s_minus_1_and_kg_m_squared_s_minus_3
 -> choose_energy_rate_mechanical_rotational_electrical_thermal_radiant_or_valid_power_relationship
 -> if_prefixed_apply_exact_decimal_scaling
 -> identify_wattmeter_power_analyser_dynamometer_calorimetric_radiometric_or_other_method
 -> evaluate_reference_voltage_current_phase_frequency_waveform_loading_temperature_resolution_and_repeatability
 -> record_unit_expression_quantity_kind_equation_method_reference_standard_calibration_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-DERIVED-UNITS-WATT-ONTOLOGY-V1"
}

}

END_FLOW