Conductance Ontology

# Conductance Ontology — Flow Algebra

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

FLOW ConductanceOntology {

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

  PURPOSE:
    Represent electrical conductance as a measurable electrical quantity describing the ease with which electric current flows through a component or path under defined operating conditions, including its inverse relationship to resistance, voltage-current relationships, geometry and conductivity relationships, temperature dependence, parallel and series networks, units, dimensional structure, measurement methods, uncertainty, and distinctions from conductivity, resistance, admittance and susceptance.

  ENTITY Conductance {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: G
    DIMENSION: M^-1 * L^-2 * T^3 * I^2
    SI_UNIT: siemens
    SI_SYMBOL: S

    DEFINITION:
      conductance := inverse_of_electrical_resistance

    INVERSE_FORM:
      G = 1/R
      WHEN R != 0

    OHMIC_FORM:
      G = I/V
      WHEN V != 0 AND applicable_operating_conditions

    DIFFERENTIAL_CONDUCTANCE:
      g_d = dI/dV

    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 Resistance {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: R
    SI_UNIT: ohm

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

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

    RELATION:
      I = G*V
      UNDER Ohmic_context
  }

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

    RELATION:
      I = G*V
      UNDER Ohmic_context
  }

  ENTITY Conductivity {
    TYPE: MaterialProperty
    SYMBOL: sigma
    SI_UNIT: siemens_per_metre
    SI_SYMBOL: S/m

    UNIFORM_CONDUCTOR_RELATION:
      G = sigma*A/L
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: siemens
      symbol: S

      equivalence:
        1 S = 1 A/V
        1 S = 1/ohm
    }

    HISTORICAL_NAME:
      mho

    COMMON_ALTERNATIVES {
      millisiemens
      microsiemens
      nanosiemens
      kilosiemens
    }

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

  CLASSIFICATION {
    by behaviour:
      Ohmic_conductance
      non_Ohmic_conductance
      static_conductance
      differential_conductance

    by component:
      component_conductance
      contact_conductance
      leakage_conductance
      equivalent_conductance

    by context:
      DC_conductance
      AC_effective_conductance
  }

  INVERSE_RESISTANCE_MODEL {
    RELATION:
      G = 1/R
      WHEN R != 0

    INVERSE:
      R = 1/G
      WHEN G != 0

    RULE:
      resistance_and_conductance
      are_inverse_quantities_not_semantic_synonyms
  }

  OHMIC_MODEL {
    IDEAL_LINEAR:
      I = G*V

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

    CONDITIONS:
      linear_current_voltage_relation
      stable_operating_conditions

    RULE:
      I_over_V_at_single_operating_point
      MUST_NOT automatically_imply_linear_Ohmic_behaviour
  }

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

    STATIC_CONDUCTANCE:
      G_static = I/V
      WHEN V != 0

    DIFFERENTIAL_CONDUCTANCE:
      g_d = dI/dV

    RULE:
      static_and_differential_conductance
      MUST_NOT be treated_as_interchangeable
  }

  GEOMETRY_CONDUCTIVITY_MODEL {
    UNIFORM_CONDUCTOR:
      G = sigma*A/L

    CONDITIONS:
      homogeneous_material
      uniform_cross_section
      approximately_uniform_current_distribution
      defined_temperature
      L != 0

    INFERENCES:
      sigma = G*L/A
      WHEN A != 0

    RULE:
      conductance_is_geometry_dependent
      conductivity_is_material_property
  }

  TEMPERATURE_MODEL {
    GENERAL:
      G = G(T, material_state, geometry)

    RESISTANCE_RELATION:
      G(T) = 1/R(T)
      WHEN R(T) != 0

    RULE:
      temperature_dependence_of_conductance
      follows_material_and_resistance_behaviour
      and_need_not_be_linear
  }

  PARALLEL_MODEL {
    CONDUCTANCES_IN_PARALLEL:
      G_eq = sum(G_i)

    CONDITIONS:
      same_voltage_across_branches
      lumped_component_model

    RULE:
      parallel_conductance_addition
      is_direct_for_independent_linear_branches
  }

  SERIES_MODEL {
    RESISTIVE_BRANCHES_IN_SERIES:
      R_eq = sum(1/G_i)
      WHEN all_G_i != 0

      G_eq = 1/R_eq

    TWO_CONDUCTANCE_FORM:
      G_eq = (G_1*G_2)/(G_1 + G_2)
      WHEN denominator != 0

    RULE:
      conductances_do_not_generally_add_directly_in_series
  }

  POWER_MODEL {
    GENERAL:
      P = V*I

    OHMIC_CONDUCTANCE_FORMS:
      P = V^2*G
      P = I^2/G
      WHEN applicable_and_G != 0

    RULE:
      conductance_value
      MUST_NOT be confused_with_power_rating_or_dissipation
  }

  ADMITTANCE_DISTINCTION_MODEL {
    CONDUCTANCE:
      real_component_of_admittance
      in_common_linear_AC_representation

    ADMITTANCE:
      Y = G + jB

    SUSCEPTANCE:
      B = imaginary_component_of_admittance

    RULE:
      conductance != admittance
      except_when_susceptive_component_is_zero_under_defined_frequency_context
  }

  RELATIONSHIPS {
    Conductance -> INVERSE_OF -> Resistance
    Conductance -> RELATES -> CurrentAndVoltage
    Conductance -> HAS_DIMENSION -> M^-1*L^-2*T^3*I^2
    Conductance -> MEASURED_IN -> Siemens
    Conductance -> DEPENDS_ON -> Conductivity
    Conductance -> DEPENDS_ON -> CrossSectionArea
    Conductance -> INVERSELY_DEPENDS_ON -> Length
    Conductance -> MAY_DEPEND_ON -> Temperature
    Conductance -> CONTRIBUTES_TO -> ElectricalPowerDissipation
    Conductance -> REAL_COMPONENT_OF -> Admittance
  }

  SEMANTIC_EQUIVALENCE {
    "electrical conductance" ~= conductance
    "siemens" ~= "S"
    "ampere per volt" ~= "A/V"
    "mho" ~= siemens_unit

    conductance != conductivity
    conductance != resistance
    conductance != admittance
    conductance != susceptance
    conductance != power
  }

  CONSTRAINTS {
    dimensional_formula = M^-1*L^-2*T^3*I^2
    SI_unit = S
    resistance_inverse_requires_nonzero_resistance = true
    conductance_inverse_requires_nonzero_conductance = true
    I_over_V_requires_nonzero_voltage = true
    conductance_and_conductivity_are_not_semantically_equivalent = true
    conductance_and_admittance_are_not_generally_semantically_equivalent = true
    static_and_differential_conductance_must_be_distinguished_for_nonlinear_devices = true
    temperature_and_operating_point_may_be_required_for_complete_measurement_semantics = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Conductance

    COMMON_INSTRUMENTS:
      digital_multimeter
      conductance_meter
      source_measure_unit
      resistance_bridge
      impedance_analyser

    METHODS:
      current_voltage_ratio
      inverse_resistance_measurement
      current_voltage_curve_analysis
      bridge_measurement

    RECORD:
      numerical_value
      unit
      component_or_path
      terminal_definition
      measurement_current
      measurement_voltage
      temperature
      operating_point
      DC_or_AC
      frequency_when_relevant
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_conductance = best_estimate +/- uncertainty
  }

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

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

    IF current_known AND voltage_known AND voltage != 0
      AND applicable_conductance_definition
      THEN static_conductance = current/voltage

    IF conductance_known AND voltage_known
      AND Ohmic_conditions_apply
      THEN current = conductance*voltage

    IF current_known AND conductance_known AND conductance != 0
      AND Ohmic_conditions_apply
      THEN voltage = current/conductance

    IF conductivity_known AND area_known AND length_known AND length != 0
      AND uniform_conductor_conditions_apply
      THEN conductance = conductivity*area/length

    IF parallel_conductances_known
      THEN equivalent_conductance = sum(parallel_conductances)

    IF voltage_known AND conductance_known
      AND Ohmic_conditions_apply
      THEN power_dissipation = voltage^2*conductance
  }

  CONTACT_AND_LEAKAGE_MODEL {
    contact_conductance:
      inverse_of_contact_resistance
      WHEN contact_resistance != 0

    leakage_conductance:
      represents_unwanted_or_intended_finite_conductive_path
      across_nominally_insulating_structure

    RULE:
      measurement_configuration_and_parallel_leakage_paths
      MUST be considered_for_high_resistance_low_conductance_measurements
  }

  MATERIAL_CONTEXT_MODEL {
    dependencies:
      conductivity
      geometry
      temperature
      composition
      strain
      electric_field
      frequency

    RULE:
      conductance_value SHOULD_NOT be treated_as_intrinsic_material_constant
  }

  UNCERTAINTY_MODEL {
    sources:
      voltage_measurement_uncertainty
      current_measurement_uncertainty
      resistance_measurement_uncertainty
      contact_effects
      leakage_paths
      self_heating
      temperature_variation
      instrument_resolution
      calibration_uncertainty
      geometry_uncertainty

    PROPAGATION:
      derived_conductance_uncertainty
      <- measurement_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    inverse_resistance_relationship_confidence: 1.00
    geometry_conductivity_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when operating point, temperature,
      AC/DC context, frequency, geometry, leakage paths,
      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_conductance
    CHECK conductance_vs_conductivity_distinction
    CHECK conductance_vs_admittance_distinction
    CHECK temperature_and_operating_point
    CHECK series_parallel_topology
    CHECK leakage_and_contact_paths_when_relevant
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_component_or_path
      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_siemens
      preserve_original_value_and_unit
      attach_uncertainty
      update_conductance_state

    ON resistance_change:
      update_resistance
      recompute_conductance_when_valid
      preserve_previous_state

    ON temperature_change:
      update_temperature
      recompute_conductance_when_valid_model_available
      preserve_material_state

    ON geometry_or_material_change:
      update_length
      update_area
      update_conductivity
      recompute_conductance_when_uniform_conductor_model_valid
      preserve_material_provenance

    ON circuit_topology_change:
      identify_series_and_parallel_groups
      recompute_equivalent_conductance
      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: Conductance
    canonical_symbol: G
    canonical_dimension: M^-1*L^-2*T^3*I^2
    canonical_SI_unit: S

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_component_or_path
      identify_current_voltage_context
      identify_resistance_relationship
      identify_Ohmic_or_nonlinear_behaviour
      identify_static_or_differential_conductance
      identify_temperature_and_operating_point
      identify_geometry_and_conductivity_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_conductance_from_conductivity
      distinguish_conductance_from_resistance
      distinguish_conductance_from_admittance
      distinguish_conductance_from_susceptance
      distinguish_static_from_differential_conductance
      distinguish_component_conductance_from_equivalent_conductance
      distinguish_geometry_dependent_conductance_from_intrinsic_material_conductivity
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      inverse_resistance_model
      Ohmic_model
      nonlinear_model
      geometry_conductivity_model
      temperature_model
      parallel_model
      series_model
      power_model
      admittance_distinction_model
      contact_and_leakage_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
      resistance_inverse_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