Ohm Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Ohm Ontology within the Kireth Research Semantic Library. The ohm, symbol Ω, is the coherent SI derived unit of electrical resistance. It equals one volt per ampere and reduces to kg m^2 s^-3 A^-2.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Ohm Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="SI Derived Units / Ohm"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-derived-units/ohm-ontology.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Ohm
 ENTITY_CLASS=SIDerivedUnitOfElectricalResistanceFramework
 PRIMARY_CONTEXT=SIDerivedUnits
 DEFINITION="The ohm, symbol Ω, is the coherent SI derived unit of electrical resistance. One ohm equals one volt per ampere."
 SYMBOLIC_FORMS=["1 Ω=1 V A^-1","1 Ω=1 kg m^2 s^-3 A^-2","R=V/I","R=rho L/A","G=1/R"]
 SEMANTIC_ROLE="Machine-readable semantics for ohm identity, resistance, impedance, voltage-current relationships, resistivity, conductance, measurement, uncertainty and traceability."
}
SCOPE {
 INCLUDE=[
 Ohm,OhmUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,SI,SIBaseUnits,
 Volt,Ampere,Watt,Joule,Kilogram,Metre,Second,ElectricalResistance,Resistance,
 DerivedQuantity,Quantity,QuantityKind,ResistanceDimension,DimensionalSignature,
 UnitSymbol,OhmDefinition,UnitExpression,UnitAlgebra,DimensionalAnalysis,
 Voltage,ElectricCurrent,OhmsLawRelationship,Conductance,Siemens,Resistivity,
 ConductivityRelationship,MaterialRelationship,TemperatureCoefficientRelationship,
 OhmicConductorRelationship,NonOhmicRelationship,Resistor,VariableResistorRelationship,
 PotentiometerRelationship,ThermistorRelationship,RTDrelationship,StrainGaugeRelationship,
 ContactResistanceRelationship,SheetResistanceRelationship,InsulationResistanceRelationship,
 InternalResistanceRelationship,LoadResistanceRelationship,EquivalentResistanceRelationship,
 SeriesResistanceRelationship,ParallelResistanceRelationship,NetworkResistanceRelationship,
 ElectricalPower,JouleHeatingRelationship,Impedance,ComplexImpedanceRelationship,
 Reactance,CapacitiveReactanceRelationship,InductiveReactanceRelationship,
 Capacitance,Farad,Inductance,Henry,AlternatingCurrentRelationship,
 DirectCurrentRelationship,Frequency,Hertz,PhaseRelationship,AdmittanceRelationship,
 CharacteristicImpedanceRelationship,TransmissionLineRelationship,
 ResistanceMeasurement,OhmmeterRelationship,DigitalMultimeterRelationship,
 WheatstoneBridgeRelationship,KelvinBridgeRelationship,FourWireMeasurementRelationship,
 TwoWireMeasurementRelationship,MegohmmeterRelationship,MicroohmmeterRelationship,
 LCRMeterRelationship,ImpedanceAnalyserRelationship,QuantumHallEffectRelationship,
 ResistanceStandardRelationship,StandardResistorRelationship,Measurement,
 Measurand,MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,
 Repeatability,Reproducibility,LeadResistanceRelationship,SelfHeatingRelationship,
 Drift,Stability,Calibration,ResistanceCalibrationRelationship,ReferenceStandard,
 MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,Metrology,
 ElectricalMetrologyRelationship,ScientificMeasurement,TemperatureInfluence,
 HumidityInfluence,FrequencyInfluenceRelationship,ParasiticCapacitanceRelationship,
 ParasiticInductanceRelationship,ShieldingRelationship,GuardingRelationship,
 GroundingRelationship,SIPrefix,Microohm,Milliohm,Kiloohm,Megaohm,Gigaohm,
 TeraohmRelationship,UnitConversion,ConversionFactor,UnitCompatibility,
 DimensionalCompatibility,QuantityCompatibility,Verification,Validation,
 ErrorAnalysis,Provenance,OhmProvenance,SIDerivedUnitProvenance,SIUnitProvenance,
 MeasurementProvenance,CalibrationProvenance,BIPMrelationship,SIbrochureRelationship,
 VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[OhmAsPersonRelationship,SiemensWhenConductanceIsPrimary,ResistivityWhenMaterialPropertyIsPrimary,ImpedanceWhenComplexACBehaviourIsPrimary]
 DISAMBIGUATION_RULE="When ohm or symbol Ω denotes the coherent SI derived unit of electrical resistance, interpret it as the electrical unit. Distinguish it from Georg Ohm and from resistivity."
}
CORE_CONCEPTS {
 Ohm="Coherent SI derived unit of electrical resistance, symbol Ω, equal to V A^-1."
 ElectricalResistance="Opposition represented by the ratio of potential difference to current under stated conditions."
 ResistanceDimension="Derived dimension M L^2 T^-3 I^-2."
 Resistivity="Material property relating resistance to conductor geometry."
 Conductance="Reciprocal quantity of resistance, measured in siemens."
 Impedance="Generalised opposition to alternating current containing resistance and potentially reactance."
}
RELATIONS {
 Ohm--is_type_of-->SIDerivedUnit
 Ohm--is_coherent_derived_unit_of-->ElectricalResistance
 Ohm--is_unit_of-->Impedance
 Ohm--has_symbol-->Omega
 Ohm--has_expression-->volt_per_ampere
 Ohm--has_base_expression-->kg_m2_s-3_A-2
 ElectricalResistance--has_dimension-->ResistanceDimension
 OhmsLawRelationship--relates-->VoltageCurrentAndResistance
 Conductance--is_reciprocal_of-->ElectricalResistance
 Resistivity--relates-->ResistanceGeometryAndMaterial
 Impedance--contains_component-->Resistance
 MeasurementTraceability--links-->ResistanceMeasurementToSI
}
OPERATORS {
 OHM(value):=electrical_resistance_quantity(value,Ohm)
 DIM(Ohm):=ResistanceDimension
 RESISTANCE(voltage,current):=voltage/current
 VOLTAGE(current,resistance):=current*resistance
 CURRENT(voltage,resistance):=voltage/resistance
 RESISTANCE_FROM_RESISTIVITY(resistivity,length,area):=resistivity*length/area
 CONDUCTANCE(resistance):=1/resistance
 SERIES_RESISTANCE(values):=sum(values)
 PARALLEL_RESISTANCE(values):=reciprocal_sum(values)
 RESISTIVE_POWER(current,resistance):=current^2*resistance
 PREFIX_OHM(prefix):=decimal_scaled_unit(Ohm,prefix)
 CONVERT_RESISTANCE(value,source,target):=compatible_resistance_conversion(value,source,target)
 TRACE_RESISTANCE(result):=traceability_chain_to_SI_ohm(result)
}
AXIOMS {
 A1="The ohm is the coherent SI derived unit of electrical resistance."
 A2="One ohm equals one volt per ampere."
 A3="One ohm reduces to kg m^2 s^-3 A^-2."
 A4="The canonical unit symbol is the Greek capital omega, Ω."
 A5="Electrical resistance and electrical resistivity are distinct quantities."
 A6="Conductance is the reciprocal quantity of resistance."
 A7="In AC systems, impedance generalises resistance and can include reactive components."
 A8="Ohms law requires appropriate device, state and constitutive assumptions."
 A9="Resistance measurement traceability requires documented electrical standards and calibration."
}
REASONING {
 R1_CONTEXT=identify(resistance_or_impedance_quantity,value,unit,device_material_geometry,frequency,temperature,measurement_method_and_intended_use)
 R2_IDENTITY=resolve_ohm_prefixed_ohm_resistivity_impedance_or_symbol_ambiguity)
 R3_QUANTITY=distinguish_resistance_resistivity_conductance_impedance_or_related_quantity)
 R4_DIMENSION=verify_dimension_M_L_squared_T_minus_3_I_minus_2)
 R5_DERIVATION=expand_ohm_to_V_per_A_and_base_units)
 R6_MODEL=choose_ohms_law_resistivity_geometry_network_power_or_impedance_relationship)
 R7_NONIDEAL=evaluate_temperature_self_heating_frequency_voltage_contact_lead_and_parasitic_effects)
 R8_MEASUREMENT=identify_two_wire_four_wire_bridge_DMM_ohmmeter_quantum_or_impedance_method)
 R9_UNCERTAINTY=evaluate_reference_current_voltage_leads_contacts_temperature_self_heating_noise_resolution_and_repeatability)
 R10_PROVENANCE=record_unit_expression_quantity_kind_model_method_reference_standard_calibration_and_traceability)
}
CONSTRAINTS {
 C1="The canonical ohm symbol Ω must not be confused with unrelated omega variables."
 C2="Resistance must not be conflated with resistivity."
 C3="Ohms law is not universally valid for nonlinear or state-dependent devices."
 C4="Two-wire resistance measurements include lead and contact resistance unless corrected."
 C5="Low-resistance measurements can require four-terminal or Kelvin techniques."
 C6="High-resistance measurements can be sensitive to leakage, humidity, guarding and insulation."
 C7="AC impedance can be complex and frequency dependent; it must not be reduced automatically to resistance."
 C8="Self-heating can change the resistance being measured."
 C9="Instrument resolution alone does not determine total resistance uncertainty."
 C10="Traceability to the ohm requires a documented resistance or equivalent quantum-electrical reference chain."
}
SEMANTIC_EQUIVALENCE {
 "OhmUnit"<=>"Ohm"
 "ElectricalResistance"<=>"Resistance"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
 "DigitalMultimeter"<=>"DMM"
}
VALIDATION {
 V1="Unit identity is ohm and canonical symbol is Ω."
 V2="Quantity kind is electrical resistance or explicitly identified impedance context."
 V3="Derived dimension is M L^2 T^-3 I^-2."
 V4="Coherent SI expression is V A^-1."
 V5="Resistance and resistivity semantics remain distinct."
 V6="Conductance is treated as reciprocal resistance with unit siemens."
 V7="AC impedance semantics preserve resistance, reactance, phase and frequency where relevant."
 V8="Prefixed ohm units use correct decimal scaling."
 V9="Measurement uncertainty includes relevant lead, contact, temperature, self-heating and calibration effects."
 V10="Resistance calibration and traceability evidence are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 OHM_DEFINITION=0.99
 RESISTANCE_REASONING=0.99
 DIMENSION_REASONING=0.99
 OHMS_LAW_REASONING=0.98
 IMPEDANCE_REASONING=0.98
 RESISTANCE_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when device behaviour, material, geometry, frequency, temperature, lead/contact effects, measurement method, calibration status or traceability are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,OhmReasoning,SIDerivedUnitReasoning,ElectricalResistanceReasoning,OhmsLawReasoning,ResistivityReasoning,ConductanceReasoning,ImpedanceReasoning,NetworkResistanceReasoning,ElectricalPowerReasoning,ResistanceMeasurementReasoning,ElectricalMetrologyReasoning,QuantumResistanceReasoning,CalibrationReasoning,DimensionalReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference]
 NORMALISE {
  "ohm"->Ohm
  "Ω"->Ohm
  "uΩ"->Microohm
  "mΩ"->Milliohm
  "kΩ"->Kiloohm
  "MΩ"->Megaohm
  "GΩ"->Gigaohm
 }
}
EXECUTION_RULES {
 E1="If ohm or Ω denotes the SI derived unit of electrical resistance, activate OhmOntology."
 E2="Confirm quantity kind resistance or impedance rather than relying only on dimensional form."
 E3="Map the ohm coherently to V A^-1 and kg m^2 s^-3 A^-2."
 E4="Apply Ohms law only under appropriate electrical and constitutive assumptions."
 E5="Distinguish resistance from resistivity, conductance and complex impedance."
 E6="For AC contexts, preserve frequency, reactance, phase and complex-impedance semantics."
 E7="Apply SI prefixes as exact decimal scale transformations."
 E8="For measurement contexts, evaluate leads, contacts, self-heating, leakage, environment, calibration and uncertainty."
 E9="Record resistance-reference, calibration and traceability provenance."
}
RECURSION {
 ENTRY=Ohm
 EXPAND(Ohm)->[
 SIDerivedUnits,DerivedUnit,SIDerivedUnit,SIBaseUnits,Volt,Ampere,Watt,Joule,
 Kilogram,Metre,Second,ElectricalResistance,ResistanceDimension,Quantity,QuantityKind,
 Dimension,Unit,OhmDefinition,UnitExpression,DimensionalAnalysis,Voltage,ElectricCurrent,
 OhmsLawRelationship,Conductance,Siemens,Resistivity,Resistor,
 SeriesResistanceRelationship,ParallelResistanceRelationship,EquivalentResistanceRelationship,
 ElectricalPower,JouleHeatingRelationship,Impedance,ComplexImpedanceRelationship,
 Reactance,CapacitiveReactanceRelationship,InductiveReactanceRelationship,
 Capacitance,Farad,Inductance,Henry,Frequency,Hertz,AdmittanceRelationship,
 ResistanceMeasurement,OhmmeterRelationship,DigitalMultimeterRelationship,
 WheatstoneBridgeRelationship,FourWireMeasurementRelationship,MicroohmmeterRelationship,
 MegohmmeterRelationship,LCRMeterRelationship,QuantumHallEffectRelationship,
 ResistanceStandardRelationship,MeasurementUncertainty,Calibration,ReferenceStandard,
 MeasurementTraceability,Metrology,TemperatureInfluence,SelfHeatingRelationship,
 LeadResistanceRelationship,ContactResistanceRelationship,GuardingRelationship,
 SIPrefix,Microohm,Milliohm,Kiloohm,Megaohm,Gigaohm,UnitConversion,
 Verification,Validation,OhmProvenance
 ]
 EXPAND(OhmFamilies)->[
 OhmIdentitySymbolQuantityAndDimension,VoltAmpereAndBaseUnitExpansion,
 OhmsLawVoltageCurrentAndResistance,ResistivityConductivityMaterialsAndGeometry,
 SeriesParallelEquivalentAndNetworkResistance,ACImpedanceReactanceAdmittanceAndFrequency,
 ResistanceMeasurementBridgesKelvinQuantumStandardsAndCalibration,
 LeadContactTemperatureLeakageUncertaintyTraceabilityAndProvenance
 ]
 STOP_CONDITION="Stop when ohm identity, resistance quantity, dimensional expression, electrical model, AC/DC semantics, measurement 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","Volt Ontology","Ampere Ontology","Watt Ontology","Joule Ontology","Farad Ontology","Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Reference Standard Ontology","Measurement Uncertainty Ontology","Physics Ontology","Electromagnetism Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Ohm -> SI Derived Units for parent derived-unit semantics",
 "Ohm -> Volt and Ampere ontologies for V A^-1 semantics",
 "Ohm -> SI Base Units for base-unit expansion",
 "Ohm -> Quantity and Dimension ontologies for resistance semantics",
 "Ohm -> Farad and related electrical ontologies for impedance and AC relationships",
 "Ohm -> Physics and Electromagnetism for resistance, resistivity and circuit semantics",
 "Ohm -> Measurement and Metrology for resistance measurement, calibration and traceability",
 "Ohm -> Verification & Validation for electrical, dimensional and semantic checks"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible resistance, impedance, measurement or reasoning relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve ohm-versus-resistance distinction.","Preserve resistance-versus-resistivity distinction.","Preserve resistance-versus-conductance distinction.","Preserve resistance-versus-complex-impedance distinction.","Preserve DC-versus-AC semantics.","Preserve unit-versus-quantity distinction.","Preserve dimensional-correctness-versus-quantity-meaning distinction.","Preserve machine-readable ohm semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="The ohm, symbol Ω, is the coherent SI derived unit of electrical resistance and equals V A^-1."
 QUANTITY_SUMMARY="Electrical resistance has dimension M L^2 T^-3 I^-2 and relates potential difference to current under appropriate conditions."
 RESISTIVITY_SUMMARY="Resistivity is a material property distinct from resistance and relates resistance to conductor geometry."
 CONDUCTANCE_SUMMARY="Conductance is reciprocal resistance and is measured in siemens."
 AC_SUMMARY="Impedance generalises resistance in AC systems and can include frequency-dependent reactance and phase."
 MEASUREMENT_SUMMARY="Resistance measurement can use ohmmeters, bridges, two-wire or four-wire methods and quantum Hall resistance standards."
 UNCERTAINTY_SUMMARY="Precision resistance measurement can require uncertainty contributions from leads, contacts, temperature, self-heating, leakage, frequency and calibration."
}
FLOW {
 INPUT
 -> detect_ohm_context
 -> identify_resistance_or_impedance_quantity_value_unit_device_material_geometry_frequency_temperature_measurement_method_and_intended_use
 -> resolve_ohm_prefixed_ohm_resistivity_impedance_or_symbol_ambiguity
 -> distinguish_resistance_resistivity_conductance_impedance_or_related_quantity
 -> verify_dimension_M_L_squared_T_minus_3_I_minus_2
 -> expand_ohm_to_V_per_A_and_base_units
 -> choose_ohms_law_resistivity_geometry_network_power_or_impedance_relationship
 -> evaluate_temperature_self_heating_frequency_voltage_contact_lead_and_parasitic_effects
 -> identify_resistance_measurement_method
 -> evaluate_reference_current_voltage_leads_contacts_temperature_self_heating_noise_resolution_and_repeatability
 -> record_unit_expression_quantity_kind_model_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-OHM-ONTOLOGY-V1"
}
}
END_FLOW