Density Ontology

# Density Ontology — Flow Algebra

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

FLOW DensityOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Mechanical Measurements
    -> Density Ontology

  PURPOSE:
    Represent mass density as a measurable physical quantity describing mass per unit volume, including homogeneous and non-homogeneous materials, local and average density, units, dimensional structure, temperature and pressure dependence, fluid and solid contexts, measurement conditions, uncertainty, and relationships to mass, volume, specific volume, hydrostatic pressure and buoyancy.

  ENTITY Density {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: rho
    DIMENSION: M * L^-3
    SI_UNIT: kilogram_per_cubic_metre
    SI_SYMBOL: kg/m^3

    DEFINITION:
      density := Mass / Volume

    UNIFORM_FORM:
      rho = m / V

    LOCAL_CONTINUUM_FORM:
      rho = dm/dV

    PROPERTIES:
      is_scalar
      has_value
      has_unit
      has_dimension
      may_vary_with_position
      may_vary_with_time
      may_depend_on_temperature
      may_depend_on_pressure
      may_have_uncertainty
  }

  ENTITY Mass {
    TYPE: BasePhysicalQuantity
    SYMBOL: m
    DIMENSION: M
    SI_UNIT: kilogram
    SI_SYMBOL: kg

    RELATION:
      Mass / Volume -> Density
  }

  ENTITY Volume {
    TYPE: DerivedGeometricQuantity
    SYMBOL: V
    DIMENSION: L^3
    SI_UNIT: cubic_metre
    SI_SYMBOL: m^3

    RELATION:
      Mass / Volume -> Density
  }

  ENTITY SpecificVolume {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: v_specific
    DIMENSION: L^3 * M^-1

    DEFINITION:
      specific_volume := Volume / Mass

    RELATION:
      specific_volume = 1 / Density
      WHEN density != 0
  }

  ENTITY Pressure {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: p
    DIMENSION: M * L^-1 * T^-2

    RELATION:
      fluid_density MAY_DEPEND_ON Pressure
  }

  ENTITY Temperature {
    TYPE: BasePhysicalQuantity
    SYMBOL: T

    RELATION:
      material_density MAY_DEPEND_ON Temperature
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: kilogram_per_cubic_metre
      symbol: kg/m^3
    }

    COMMON_ALTERNATIVES {
      gram_per_cubic_centimetre
      gram_per_millilitre
      kilogram_per_litre
      pound_per_cubic_foot
      pound_per_cubic_inch
    }

    COMMON_EQUIVALENCE:
      1 g/cm^3 = 1000 kg/m^3
      1 g/mL = 1000 kg/m^3

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

  CLASSIFICATION {
    by_spatial_behaviour:
      uniform_density
      nonuniform_density
      local_density
      average_density

    by_material_context:
      solid_density
      liquid_density
      gas_density
      bulk_density
      mixture_density

    related_but_distinct:
      relative_density
      specific_gravity
      number_density
      energy_density
      charge_density
  }

  RELATIONSHIPS {
    Density -> RATIO_OF -> Mass
    Density -> PER -> Volume
    Density -> HAS_DIMENSION -> M*L^-3
    Density -> MEASURED_IN -> KilogramPerCubicMetre
    Density -> INVERSE_RELATION_WITH -> SpecificVolume
    Density -> MAY_DEPEND_ON -> Temperature
    Density -> MAY_DEPEND_ON -> Pressure
    FluidDensity -> CONTRIBUTES_TO -> HydrostaticPressure
    FluidDensity -> CONTRIBUTES_TO -> BuoyantForce
    DensityField -> MAY_VARY_OVER -> Position
  }

  SEMANTIC_EQUIVALENCE {
    "mass density" ~= density WHEN mechanical_measurement_context
    "kg per cubic metre" ~= "kg/m^3"
    "g per cubic centimetre" ~= "g/cm^3"
    "specific gravity" != density
    "relative density" != absolute_mass_density
    "bulk density" != intrinsic_material_density
    density != mass
    density != volume
    density != weight_density
  }

  AVERAGE_LOCAL_MODEL {
    AVERAGE_DENSITY:
      rho_avg = total_mass / total_volume

    LOCAL_DENSITY:
      rho = dm/dV

    MASS_FROM_DENSITY_FIELD:
      m = integral_over_volume(rho dV)

    RULE:
      average_density NEED_NOT equal density_at_every_point
  }

  TEMPERATURE_PRESSURE_MODEL {
    GENERAL:
      rho = rho(T, p, composition)

    LIQUIDS_AND_SOLIDS:
      density_often_changes_with_thermal_expansion
      under_temperature_change

    GASES:
      density_can_depend_strongly_on_temperature_and_pressure

    IDEAL_GAS_CONTEXT:
      rho = p*M_molar/(R*T)
      WHEN ideal_gas_assumptions_apply

    RULE:
      density_comparisons SHOULD preserve temperature_pressure_and_composition_context
  }

  HYDROSTATIC_MODEL {
    RELATION:
      dp/dh = rho*g
      under_defined_depth_coordinate_and_sign_convention

    CONSTANT_DENSITY_APPROXIMATION:
      delta_p = rho*g*delta_h

    CONDITIONS:
      fluid_at_rest
      gravitational_field_defined
  }

  BUOYANCY_MODEL {
    ARCHIMEDES_RELATION:
      buoyant_force = displaced_fluid_density * gravitational_acceleration * displaced_volume

    FORM:
      F_b = rho_fluid * g * V_displaced

    RULE:
      buoyancy_analysis requires_fluid_density_and_displaced_volume
  }

  RELATIVE_DENSITY_MODEL {
    DEFINITION:
      relative_density = material_density / reference_density

    PROPERTY:
      dimensionless = true

    COMMON_CONTEXT:
      specific_gravity often_uses_water_as_reference_for_liquids_and_solids

    RULE:
      reference_material_and_reference_conditions MUST be identified
  }

  CONSTRAINTS {
    density_is_scalar_quantity = true
    dimensional_formula = M*L^-3
    SI_unit = kg/m^3
    volume_must_be_nonzero_for_average_density_calculation = true
    density_and_mass_are_not_semantically_equivalent = true
    density_and_specific_gravity_are_not_semantically_equivalent = true
    density_value_may_require_temperature_pressure_and_composition_context = true
    local_density_and_average_density_must_not_be_assumed_equal_in_nonuniform_material = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Density

    DIRECT_OR_INSTRUMENTAL_MEASUREMENT:
      densitometer
      hydrometer
      pycnometer
      digital_density_meter

    INDIRECT_MEASUREMENT:
      mass_divided_by_volume
      displacement_volume_method
      hydrostatic_weighing
      equation_of_state_inference

    RECORD:
      numerical_value
      unit
      density_type
      material_or_medium
      mass
      volume
      temperature
      pressure
      composition_when_relevant
      spatial_location_when_local
      timestamp
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_density = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF mass_known AND volume_known AND volume != 0
      THEN average_density = mass / volume

    IF density_known AND volume_known
      THEN mass = density * volume
      WHEN density_uniform_or_density_represents_average_for_volume

    IF mass_known AND density_known AND density != 0
      THEN volume = mass / density

    IF density_field_known
      THEN total_mass = integral_over_volume(density dV)

    IF density_known AND density != 0
      THEN specific_volume = 1 / density

    IF fluid_density_constant AND depth_difference_known
      THEN hydrostatic_pressure_difference = density * g * depth_difference

    IF displaced_fluid_density_known AND displaced_volume_known
      THEN buoyant_force = density * g * displaced_volume

    IF material_density_known AND reference_density_known AND reference_density != 0
      THEN relative_density = material_density / reference_density
  }

  FIELD_MODEL {
    density_field:
      rho = rho(x, y, z, t)

    total_mass:
      m = integral_V(rho dV)

    conservation_context:
      density MAY participate_in mass_continuity_equations

    RULE:
      spatially_varying_density requires_location_or_field_representation
  }

  MATERIAL_CONTEXT_MODEL {
    REQUIRE_WHEN_RELEVANT:
      material_identity
      phase
      composition
      temperature
      pressure

    RULE:
      tabulated_density_value SHOULD_NOT be treated_as_universal_constant
      unless applicable_conditions_are_preserved
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    mass_volume_relationship_confidence: 1.00
    environmental_dependence_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when unit, material, volume definition,
      temperature, pressure, composition, measurement method,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK volume_nonzero_for_ratio_calculation
    CHECK average_vs_local_density_semantics
    CHECK material_or_medium_identity
    CHECK temperature_and_pressure_when_relevant
    CHECK composition_when_relevant
    CHECK density_relative_density_distinction
    CHECK bulk_vs_intrinsic_density_distinction
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_density_type
      identify_material_or_medium
      validate_mass_and_volume_when_used
      attach_temperature_and_pressure_when_relevant
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp
      attach_uncertainty
      update_density_state

    ON environmental_condition_change:
      update_temperature
      update_pressure
      update_phase_or_composition_when_required
      recompute_density_if_model_available
      preserve_previous_state

    ON spatial_sampling_update:
      attach_location
      update_density_field
      recompute_average_density_when_required
      recompute_total_mass_when_required

    ON revised_calibration:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Density
    canonical_symbol: rho
    canonical_dimension: M*L^-3
    canonical_SI_unit: kg/m^3

    interpretation_order:
      identify_quantity
      identify_density_type
      identify_value
      identify_unit
      identify_mass_and_volume_context
      identify_material_or_medium
      identify_phase_and_composition
      identify_temperature
      identify_pressure
      identify_local_or_average_context
      identify_measurement_method
      identify_uncertainty
      validate_dimensions
      infer_relationships

    ambiguity_controls:
      distinguish_density_from_mass
      distinguish_density_from_volume
      distinguish_mass_density_from_weight_density
      distinguish_density_from_specific_gravity
      distinguish_absolute_density_from_relative_density
      distinguish_bulk_from_intrinsic_material_density
      distinguish_local_from_average_density
      distinguish_mass_density_from_other_density_types
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Mechanical Measurements
      -> Density Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      average_local_model
      temperature_pressure_model
      hydrostatic_model
      buoyancy_model
      relative_density_model
      field_model
      material_context_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      environmental_context_model_changes
      field_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW