Joule Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Joule Ontology within the Kireth Research Semantic Library. The joule (J) is the coherent SI derived unit of energy, work and heat, equal to N m and kg m^2 s^-2.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Joule Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="SI Derived Units / Joule"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-derived-units/joule-ontology.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Joule
 ENTITY_CLASS=SIDerivedUnitOfEnergyWorkAndHeatFramework
 PRIMARY_CONTEXT=SIDerivedUnits
 DEFINITION="The joule, symbol J, is the coherent SI derived unit of energy, work and heat. One joule equals one newton metre and one kilogram square metre per second squared."
 SYMBOLIC_FORMS=["1 J=1 N m","1 J=1 kg m^2 s^-2","W=integral(F dot ds)","E_k=1/2 m v^2","[energy]=M L^2 T^-2"]
 SEMANTIC_ROLE="Machine-readable semantics for joule identity, energy, work, heat, dimensional structure, measurement, uncertainty and traceability."
}
SCOPE {
 INCLUDE=[
 Joule,JouleUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,SI,SIBaseUnits,
 Newton,Metre,Kilogram,Second,Energy,Work,Heat,DerivedQuantity,Quantity,QuantityKind,
 EnergyDimension,DimensionalSignature,UnitSymbol,JouleDefinition,UnitExpression,
 UnitAlgebra,DimensionalAnalysis,Force,Displacement,KineticEnergy,PotentialEnergy,
 GravitationalPotentialEnergyRelationship,ElasticPotentialEnergyRelationship,
 InternalEnergy,ThermalEnergy,ChemicalEnergyRelationship,ElectricalEnergy,
 ElectromagneticEnergyRelationship,RadiantEnergyRelationship,NuclearEnergyRelationship,
 ConservationOfEnergy,EnergyTransferRelationship,EnergyTransformationRelationship,
 Power,Watt,Torque,Pressure,Pascal,Volume,ElectricCharge,Coulomb,Voltage,Volt,
 Current,Ampere,Resistance,Ohm,Capacitance,Farad,PhotonEnergyRelationship,
 PlanckConstantRelationship,Frequency,Hertz,HeatCapacityRelationship,
 SpecificHeatCapacityRelationship,EnthalpyRelationship,EntropyRelationship,
 CalorimetryRelationship,CalorimeterRelationship,EnergyMeasurement,
 ElectricalEnergyMeterRelationship,MeasurementSystem,Measurement,Measurand,
 MeasurementResult,MeasurementUncertainty,Calibration,ReferenceStandard,
 MeasurementTraceability,MetrologicalTraceability,Metrology,ScientificMeasurement,
 HeatLossRelationship,FrictionLossRelationship,EfficiencyRelationship,SIPrefix,
 Kilojoule,Megajoule,GigajouleRelationship,ElectronvoltRelationship,
 CalorieRelationship,KilowattHourRelationship,UnitConversion,Verification,
 Validation,ErrorAnalysis,Provenance,JouleProvenance,SIDerivedUnitProvenance,
 SIUnitProvenance,MeasurementProvenance,CalibrationProvenance,BIPMrelationship,
 SIbrochureRelationship,VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[JouleAsPersonRelationship,TorqueWhenMomentOfForceIsPrimary,PowerWhenRateOfEnergyTransferIsPrimary]
 DISAMBIGUATION_RULE="Interpret joule or J as the SI energy/work/heat unit when unit context is present; distinguish N m energy/work semantics from N m torque semantics."
}
CORE_CONCEPTS {
 Joule="Coherent SI derived unit of energy, work and heat, symbol J."
 Energy="Physical quantity associated with energy storage, transfer and transformation."
 Work="Energy transfer associated with force acting through displacement."
 Heat="Energy transferred because of a temperature difference."
 EnergyDimension="Derived dimension M L^2 T^-2."
 Power="Rate of energy transfer."
}

RELATIONS {
 Joule--is_type_of-->SIDerivedUnit
 Joule--is_coherent_derived_unit_of-->Energy
 Joule--is_coherent_derived_unit_of-->Work
 Joule--is_coherent_derived_unit_of-->Heat
 Joule--has_symbol-->J
 Joule--has_expression-->newton_metre
 Joule--has_base_expression-->kilogram_square_metre_per_second_squared
 Energy--has_dimension-->EnergyDimension
 Work--is_energy_transfer_by-->ForceThroughDisplacement
 Power--is_rate_of-->EnergyTransfer
 Watt--equals-->JoulePerSecond
 PhotonEnergyRelationship--relates-->PlanckConstantTimesFrequency
 MeasurementTraceability--links-->EnergyMeasurementToSI
}
OPERATORS {
 JOULE(value):=energy_quantity(value,Joule)
 DIM(Joule):=EnergyDimension
 WORK(force,displacement_parallel):=force*displacement_parallel
 KINETIC_ENERGY(mass,speed):=0.5*mass*speed^2
 GRAVITATIONAL_POTENTIAL_ENERGY(mass,gravity,height):=mass*gravity*height
 ENERGY_FROM_POWER(power,time):=power*time
 ELECTRICAL_ENERGY(charge,voltage):=charge*voltage
 PHOTON_ENERGY(planck_constant,frequency):=planck_constant*frequency
 PREFIX_JOULE(prefix):=decimal_scaled_unit(Joule,prefix)
 CONVERT_ENERGY(value,source,target):=compatible_energy_conversion(value,source,target)
 TRACE_ENERGY(result):=traceability_chain_to_SI_joule(result)
}
AXIOMS {
 A1="The joule is the coherent SI derived unit of energy, work and heat."
 A2="One joule equals one newton metre."
 A3="One joule equals kg m^2 s^-2."
 A4="The canonical symbol is uppercase J."
 A5="Energy, work and heat share the joule but retain distinct semantics."
 A6="One watt equals one joule per second."
 A7="Work depends on force acting through displacement."
 A8="Energy can transform while total energy is conserved for an appropriately defined closed system."
}
REASONING {
 R1_CONTEXT=identify(energy_work_or_heat_quantity,value,unit,system,process,method,intended_use)
 R2_IDENTITY=resolve_joule_prefixed_joule_nonSI_energy_unit_or_symbol_J_ambiguity)
 R3_QUANTITY=distinguish_energy_work_heat_torque_power_or_related_quantity)
 R4_DIMENSION=verify_dimension_M_L_squared_T_minus_2)
 R5_DERIVATION=expand_joule_to_N_m_and_kg_m_squared_s_minus_2)
 R6_EQUATION=choose_work_kinetic_potential_electrical_thermal_photon_or_valid_energy_relationship)
 R7_SCALE=if_prefixed_apply_exact_decimal_scaling)
 R8_MEASUREMENT=identify_calorimetric_electrical_mechanical_radiometric_or_other_method)
 R9_UNCERTAINTY=evaluate_calibration_heat_loss_friction_efficiency_environment_resolution_repeatability)
 R10_PROVENANCE=record_quantity_equation_method_reference_standard_calibration_and_traceability)
}

CONSTRAINTS {
 C1="The symbol J is case-sensitive."
 C2="Energy, work and heat retain distinct physical semantics."
 C3="A newton metre expression alone does not distinguish energy from torque."
 C4="Power is energy per unit time and must not be conflated with energy."
 C5="Heat denotes energy transfer due to temperature difference."
 C6="Energy-balance reasoning must define system boundaries."
 C7="Calorimetry can require heat-loss and heat-capacity corrections."
 C8="Resolution alone does not determine total energy uncertainty."
 C9="Traceability requires a documented energy reference chain."
 C10="Dimensional correctness alone does not establish quantity meaning."
}
SEMANTIC_EQUIVALENCE {
 "JouleUnit" <=> "Joule"
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
}
VALIDATION {
 V1="Unit identity is joule and canonical symbol is J."
 V2="Quantity kind is explicitly identified."
 V3="Derived dimension is M L^2 T^-2."
 V4="Coherent expressions are N m and kg m^2 s^-2."
 V5="Energy and torque remain distinct despite possible N m expressions."
 V6="Energy and power remain distinct."
 V7="Prefixes use correct decimal scaling."
 V8="Non-SI conversions use declared definitions."
 V9="Measurement uncertainty includes relevant losses, calibration and environmental effects."
 V10="Calibration and traceability evidence are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 JOULE_DEFINITION=0.99
 ENERGY_REASONING=0.99
 WORK_REASONING=0.99
 HEAT_REASONING=0.98
 DIMENSION_REASONING=0.99
 MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when quantity kind, system boundary, transfer mechanism, method, loss corrections, calibration or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,JouleReasoning,SIDerivedUnitReasoning,EnergyReasoning,WorkReasoning,HeatReasoning,MechanicalEnergyReasoning,ElectricalEnergyReasoning,ThermalEnergyReasoning,PhotonEnergyReasoning,EnergyMeasurementReasoning,CalibrationReasoning,DimensionalReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "joule"->Joule
  "J"->Joule
  "kJ"->Kilojoule
  "MJ"->Megajoule
 }
}

EXECUTION_RULES {
 E1="If joule or J denotes the SI energy/work/heat unit, activate JouleOntology."
 E2="Confirm quantity kind rather than relying only on dimensional form."
 E3="Map joule coherently to N m and kg m^2 s^-2."
 E4="Distinguish energy/work from torque."
 E5="Distinguish energy from power and heat from internal energy."
 E6="Choose an equation appropriate to the physical system."
 E7="Apply SI prefixes as exact decimal scale transformations."
 E8="Evaluate losses, environment, calibration and uncertainty in measurement contexts."
 E9="Record reference, calibration and traceability provenance."
}
RECURSION {
 ENTRY=Joule
 EXPAND(Joule)->[
 SIDerivedUnits,DerivedUnit,SIDerivedUnit,SIBaseUnits,Newton,Metre,Kilogram,Second,
 Energy,Work,Heat,EnergyDimension,Quantity,QuantityKind,Dimension,Unit,JouleDefinition,
 UnitExpression,DimensionalAnalysis,Force,Displacement,KineticEnergy,PotentialEnergy,
 InternalEnergy,ThermalEnergy,ElectricalEnergy,ConservationOfEnergy,Power,Watt,Torque,
 Pressure,Pascal,ElectricCharge,Coulomb,Voltage,Volt,Ampere,PhotonEnergyRelationship,
 PlanckConstantRelationship,Frequency,Hertz,HeatCapacityRelationship,EnthalpyRelationship,
 EntropyRelationship,CalorimetryRelationship,EnergyMeasurement,MeasurementUncertainty,
 Calibration,ReferenceStandard,MeasurementTraceability,Metrology,HeatLossRelationship,
 EfficiencyRelationship,SIPrefix,Kilojoule,Megajoule,ElectronvoltRelationship,
 CalorieRelationship,KilowattHourRelationship,UnitConversion,Verification,Validation,JouleProvenance
 ]
 EXPAND(JouleFamilies)->[
 JouleIdentitySymbolQuantityAndDimension,
 NewtonMetreAndBaseUnitExpansion,
 WorkForceDisplacementAndMechanicalEnergy,
 KineticPotentialInternalAndThermalEnergy,
 ElectricalElectromagneticRadiantAndPhotonEnergy,
 HeatCalorimetryPowerAndEnergyTransfer,
 EnergyMeasurementLossesUncertaintyCalibrationAndTraceability,
 ValidationConversionSemanticDisambiguationAndProvenance
 ]
 STOP_CONDITION="Stop when joule identity, energy quantity, dimension, relationships, measurement, uncertainty and provenance are sufficiently resolved."
}
ROUTING {
 PARENT_ONTOLOGY="SI Derived Units"
 RELATED_ONTOLOGIES=["SI Derived Units","Derived Units Ontology","SI Base Units","Newton Ontology","Metre Ontology","Kilogram Ontology","Second Ontology","Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Measurement Uncertainty Ontology","Physics Ontology","Thermodynamics Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Joule -> SI Derived Units for parent semantics",
 "Joule -> Newton and Metre for N m semantics",
 "Joule -> Kilogram, Metre and Second for base-unit expansion",
 "Joule -> Quantity Ontology for energy, work and heat semantics",
 "Joule -> Dimension Ontology for M L^2 T^-2",
 "Joule -> Physics and Thermodynamics for energy-transfer semantics",
 "Joule -> Metrology for calibration and traceability",
 "Joule -> Verification & Validation for dimensional and semantic checks"
 ]
}

UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible energy, work, heat, measurement or reasoning relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=[
 "Preserve joule-versus-energy distinction.",
 "Preserve energy-versus-work-versus-heat distinction.",
 "Preserve energy-versus-power distinction.",
 "Preserve energy-versus-torque distinction despite N m expression.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve dimensional-correctness-versus-quantity-meaning distinction.",
 "Preserve machine-readable joule semantics."
 ]
}
OUTPUT {
 CANONICAL_DEFINITION="The joule, symbol J, is the coherent SI derived unit of energy, work and heat and equals N m or kg m^2 s^-2."
 QUANTITY_SUMMARY="Energy, work and heat share dimension M L^2 T^-2 but retain distinct meanings."
 WORK_SUMMARY="Mechanical work represents energy transfer by force acting through displacement."
 POWER_SUMMARY="Power is the rate of energy transfer and one watt equals one joule per second."
 MEASUREMENT_SUMMARY="Energy measurement can use mechanical, electrical, calorimetric and radiometric methods linked to traceable standards."
 UNCERTAINTY_SUMMARY="Precision energy measurement can require calibration, loss, efficiency, environmental and repeatability uncertainty contributions."
}
FLOW {
 INPUT
 -> detect_joule_context
 -> identify_energy_work_or_heat_quantity_value_unit_system_process_method_and_intended_use
 -> resolve_joule_prefixed_joule_nonSI_energy_unit_or_symbol_J_ambiguity
 -> distinguish_energy_work_heat_torque_power_or_related_quantity
 -> verify_dimension_M_L_squared_T_minus_2
 -> expand_joule_to_N_m_and_kg_m_squared_s_minus_2
 -> choose_valid_energy_relationship
 -> if_prefixed_apply_exact_decimal_scaling
 -> identify_measurement_method
 -> evaluate_calibration_losses_efficiency_environment_and_uncertainty
 -> record_quantity_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-JOULE-ONTOLOGY-V1"
}
}
END_FLOW