Resistance Ontology

# Resistance Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/electromagnetic-measurements/resistance-ontology.html

FLOW ResistanceOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Electromagnetic Measurements
    -> Resistance Ontology

  PURPOSE:
    Represent electrical resistance as a measurable electrical quantity describing the relationship between potential difference and electric current under defined operating conditions, including Ohmic and non-Ohmic behaviour, geometry and resistivity relationships, temperature dependence, series and parallel combinations, power dissipation, units, dimensional structure, measurement methods, uncertainty, and distinctions from resistivity, impedance and reactance.

  ENTITY Resistance {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: R
    DIMENSION: M * L^2 * T^-3 * I^-2
    SI_UNIT: ohm
    SI_SYMBOL: ohm

    OHMIC_DEFINITION:
      R = V/I
      WHEN I != 0 AND applicable_operating_conditions

    DIFFERENTIAL_RESISTANCE:
      r_d = dV/dI

    PROPERTIES:
      is_scalar_in_lumped_two_terminal_context
      has_value
      has_unit
      has_dimension
      may_depend_on_temperature
      may_depend_on_geometry
      may_depend_on_material
      may_depend_on_operating_point
      may_be_nonlinear
      may_have_uncertainty
  }

  ENTITY Voltage {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: V
    SI_UNIT: volt
    SI_SYMBOL: V

    RELATION:
      V = I*R
      UNDER Ohmic_context
  }

  ENTITY ElectricCurrent {
    TYPE: SIBaseQuantity
    SYMBOL: I
    SI_UNIT: ampere
    SI_SYMBOL: A

    RELATION:
      I = V/R
      WHEN R != 0 AND Ohmic_context
  }

  ENTITY Resistivity {
    TYPE: MaterialProperty
    SYMBOL: rho_e
    SI_UNIT: ohm_metre
    SI_SYMBOL: ohm*m

    UNIFORM_CONDUCTOR_RELATION:
      R = rho_e*L/A
  }

  ENTITY Conductance {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: G
    SI_UNIT: siemens
    SI_SYMBOL: S

    RELATION:
      G = 1/R
      WHEN R != 0
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: ohm
      symbol: ohm

      equivalence:
        1 ohm = 1 V/A
        1 ohm = 1 kg*m^2/(A^2*s^3)
    }

    COMMON_ALTERNATIVES {
      milliohm
      kiloohm
      megaohm
      gigaohm
    }

    CONVERSION_RULE:
      resistance_value(target_unit)
        = resistance_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by_behaviour:
      Ohmic_resistance
      non_Ohmic_resistance
      static_resistance
      differential_resistance

    by component:
      fixed_resistance
      variable_resistance
      contact_resistance
      internal_resistance
      insulation_resistance

    by context:
      DC_resistance
      AC_effective_resistance
  }

  OHMS_LAW_MODEL {
    IDEAL_LINEAR:
      V = I*R

    CONDITIONS:
      resistance_constant_over_operating_range
      temperature_and_material_state_defined

    INFERENCES:
      R = V/I WHEN I != 0
      I = V/R WHEN R != 0

    RULE:
      V_over_I_at_single_operating_point
      MUST_NOT automatically_imply_linear_Ohmic_behaviour
  }

  NONLINEAR_MODEL {
    GENERAL:
      V = f(I, T, state)

    STATIC_RESISTANCE:
      R_static = V/I
      WHEN I != 0

    DIFFERENTIAL_RESISTANCE:
      r_d = dV/dI

    RULE:
      static_and_differential_resistance
      MUST_NOT be treated_as_interchangeable
  }

  GEOMETRY_RESISTIVITY_MODEL {
    UNIFORM_CONDUCTOR:
      R = rho_e*L/A

    CONDITIONS:
      homogeneous_material
      uniform_cross_section
      approximately_uniform_current_distribution
      defined_temperature

    INFERENCES:
      rho_e = R*A/L
      WHEN L != 0

      A = rho_e*L/R
      WHEN R != 0

    RULE:
      resistance_is_component_or_geometry_dependent
      resistivity_is_material_property
  }

  TEMPERATURE_MODEL {
    LINEAR_APPROXIMATION:
      R(T) = R_0*[1 + alpha*(T - T_0)]

    PARAMETERS:
      R_0 = resistance_at_reference_temperature
      alpha = temperature_coefficient_of_resistance
      T_0 = reference_temperature

    CONDITIONS:
      applicable_temperature_range
      material_state_unchanged

    RULE:
      temperature_coefficient_and_reference_temperature
      MUST be preserved
  }

  SERIES_MODEL {
    RESISTORS_IN_SERIES:
      R_eq = sum(R_i)

    CONDITIONS:
      same_current_path
      lumped_component_model

    RULE:
      equivalent_series_resistance >= each_nonnegative_component_resistance
  }

  PARALLEL_MODEL {
    RESISTORS_IN_PARALLEL:
      1/R_eq = sum(1/R_i)

    TWO_RESISTOR_FORM:
      R_eq = (R_1*R_2)/(R_1 + R_2)
      WHEN denominator != 0

    CONDITIONS:
      same_voltage_across_branches
      lumped_component_model

    RULE:
      for_positive_finite_resistances
      R_eq < smallest_branch_resistance
  }

  POWER_MODEL {
    GENERAL_DC:
      P = V*I

    OHMIC_FORMS:
      P = I^2*R
      P = V^2/R
      WHEN applicable_and_R != 0

    ENERGY_DISSIPATION:
      E = integral(P dt)

    RULE:
      resistor_power_rating
      MUST_NOT be confused_with_resistance_value
  }

  CONDUCTANCE_MODEL {
    DEFINITION:
      G = 1/R
      WHEN R != 0

    UNIT:
      siemens

    PARALLEL_RELATION:
      G_eq = sum(G_i)

    RULE:
      resistance_and_conductance_are_inverse_quantities
      not_semantic_synonyms
  }

  IMPEDANCE_DISTINCTION_MODEL {
    RESISTANCE:
      real_dissipative_component_of_impedance
      in_common_linear_AC_circuit_representation

    IMPEDANCE:
      Z = R + jX

    REACTANCE:
      X = imaginary_component_of_impedance

    RULE:
      resistance != impedance
      except_when_reactive_component_is_zero_under_defined_frequency_context
  }

  RELATIONSHIPS {
    Resistance -> RELATES -> VoltageAndCurrent
    Resistance -> HAS_DIMENSION -> M*L^2*T^-3*I^-2
    Resistance -> MEASURED_IN -> Ohm
    Resistance -> INVERSE_OF -> Conductance
    Resistance -> DEPENDS_ON -> Resistivity
    Resistance -> DEPENDS_ON -> ConductorLength
    Resistance -> INVERSELY_DEPENDS_ON -> CrossSectionArea
    Resistance -> MAY_DEPEND_ON -> Temperature
    Resistance -> CONTRIBUTES_TO -> ElectricalPowerDissipation
    Resistance -> REAL_COMPONENT_OF -> Impedance
  }

  SEMANTIC_EQUIVALENCE {
    "electrical resistance" ~= resistance
    "ohm" ~= resistance_unit
    "V/A" ~= ohm

    resistance != resistivity
    resistance != conductance
    resistance != impedance
    resistance != reactance
    resistance != power
  }

  CONSTRAINTS {
    dimensional_formula = M*L^2*T^-3*I^-2
    SI_unit = ohm
    V_over_I_requires_nonzero_current = true
    conductance_inverse_requires_nonzero_resistance = true
    resistance_and_resistivity_are_not_semantically_equivalent = true
    resistance_and_impedance_are_not_generally_semantically_equivalent = true
    static_and_differential_resistance_must_be_distinguished_for_nonlinear_devices = true
    temperature_and_operating_point_may_be_required_for_complete_measurement_semantics = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Resistance

    COMMON_INSTRUMENTS:
      ohmmeter
      digital_multimeter
      resistance_bridge
      four_wire_Kelvin_meter
      megohmmeter
      source_measure_unit

    METHODS:
      direct_ohmmeter_measurement
      voltage_current_ratio
      four_wire_measurement
      bridge_measurement
      current_voltage_curve_analysis

    RECORD:
      numerical_value
      unit
      component_or_material
      terminal_definition
      measurement_current
      measurement_voltage
      temperature
      operating_point
      DC_or_AC
      frequency_when_relevant
      two_wire_or_four_wire_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_resistance = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF voltage_known AND current_known AND current != 0
      AND applicable_resistance_definition
      THEN static_resistance = voltage/current

    IF resistance_known AND current_known
      AND Ohmic_conditions_apply
      THEN voltage = current*resistance

    IF voltage_known AND resistance_known AND resistance != 0
      AND Ohmic_conditions_apply
      THEN current = voltage/resistance

    IF resistivity_known AND length_known AND area_known AND area != 0
      AND uniform_conductor_conditions_apply
      THEN resistance = resistivity*length/area

    IF resistance_known AND resistance != 0
      THEN conductance = 1/resistance

    IF series_resistances_known
      THEN equivalent_resistance = sum(series_resistances)

    IF parallel_resistances_known AND all_required_denominators_valid
      THEN inverse_equivalent_resistance =
        sum(inverse(branch_resistance))

    IF current_known AND resistance_known AND Ohmic_conditions_apply
      THEN power_dissipation = current^2*resistance

    IF voltage_known AND resistance_known AND resistance != 0
      AND Ohmic_conditions_apply
      THEN power_dissipation = voltage^2/resistance
  }

  CONTACT_AND_LEAD_MODEL {
    TWO_WIRE_MEASUREMENT:
      measured_resistance MAY_INCLUDE
        device_resistance
        lead_resistance
        contact_resistance

    FOUR_WIRE_MEASUREMENT:
      reduces_effect_of_lead_and_contact_resistance
      for_low_resistance_measurement

    RULE:
      measurement_topology MUST be preserved
      when precision_or_low_resistance_context_matters
  }

  MATERIAL_CONTEXT_MODEL {
    dependencies:
      material
      temperature
      geometry
      strain
      composition
      frequency
      current_density

    RULE:
      resistance_value SHOULD_NOT be treated_as_intrinsic_material_constant
  }

  UNCERTAINTY_MODEL {
    sources:
      voltage_measurement_uncertainty
      current_measurement_uncertainty
      lead_resistance
      contact_resistance
      self_heating
      temperature_variation
      instrument_resolution
      calibration_uncertainty
      noise
      geometry_uncertainty

    PROPAGATION:
      derived_resistance_uncertainty
      <- measurement_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    Ohmic_relationship_confidence: 0.99
    geometry_resistivity_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when operating point, temperature,
      measurement topology, AC/DC context, frequency,
      geometry, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK nonzero_denominator_for_ratio_or_inverse
    CHECK Ohmic_vs_non_Ohmic_context
    CHECK static_vs_differential_resistance
    CHECK resistance_vs_resistivity_distinction
    CHECK resistance_vs_impedance_distinction
    CHECK temperature_and_operating_point
    CHECK series_parallel_topology
    CHECK two_wire_vs_four_wire_measurement_when_relevant
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_component_or_material
      identify_terminals
      identify_measurement_method
      attach_voltage_and_current_when_relevant
      attach_temperature
      identify_operating_point
      identify_DC_or_AC_context
      attach_frequency_when_relevant
      normalize_to_ohm
      preserve_original_value_and_unit
      attach_uncertainty
      update_resistance_state

    ON temperature_change:
      update_temperature
      recompute_resistance_when_valid_temperature_model_available
      preserve_reference_temperature_and_coefficient
      preserve_previous_state

    ON geometry_or_material_change:
      update_length
      update_area
      update_resistivity
      recompute_resistance_when_uniform_conductor_model_valid
      preserve_material_provenance

    ON circuit_topology_change:
      identify_series_and_parallel_groups
      recompute_equivalent_resistance
      preserve_component_values

    ON calibration_revision:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Resistance
    canonical_symbol: R
    canonical_dimension: M*L^2*T^-3*I^-2
    canonical_SI_unit: ohm

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_component_or_material
      identify_voltage_current_context
      identify_Ohmic_or_nonlinear_behaviour
      identify_static_or_differential_resistance
      identify_temperature_and_operating_point
      identify_geometry_and_resistivity_context
      identify_DC_or_AC_context
      identify_frequency_when_relevant
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_circuit_relationships

    ambiguity_controls:
      distinguish_resistance_from_resistivity
      distinguish_resistance_from_conductance
      distinguish_resistance_from_impedance
      distinguish_resistance_from_reactance
      distinguish_static_from_differential_resistance
      distinguish_component_resistance_from_equivalent_resistance
      distinguish_intrinsic_material_property_from_geometry_dependent_resistance
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Electromagnetic Measurements
      -> Resistance Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      Ohms_law_model
      nonlinear_model
      geometry_resistivity_model
      temperature_model
      series_model
      parallel_model
      power_model
      conductance_model
      impedance_distinction_model
      contact_and_lead_model
      material_context_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      Ohmic_or_nonlinear_model_changes
      geometry_or_material_model_changes
      temperature_model_changes
      circuit_topology_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW