Work Ontology

# Work Ontology — Flow Algebra

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

FLOW WorkOntology {

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

  PURPOSE:
    Represent mechanical work as a measurable scalar quantity describing energy transferred when a force acts through displacement, including positive, negative and zero work, constant and variable forces, path dependence, units, dimensional structure, work-energy relationships, power, conservative and non-conservative interactions, measurement conditions, uncertainty, and reference-system semantics.

  ENTITY Work {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: W
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    DEFINITION:
      work := line_integral(Force dot DifferentialDisplacement)

    GENERAL_FORM:
      W = integral_path(F dot dr)

    DIFFERENTIAL_FORM:
      dW = F dot dr

    CONSTANT_FORCE_FORM:
      W = F * s * cos(theta)

    PROPERTIES:
      is_scalar
      has_value
      has_unit
      has_dimension
      may_be_positive
      may_be_negative
      may_be_zero
      may_depend_on_path
      represents_energy_transfer
      may_have_uncertainty
  }

  ENTITY Force {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: F
    DIMENSION: M * L * T^-2
    SI_UNIT: newton
    SI_SYMBOL: N

    RELATION:
      Force dot Displacement -> Work
  }

  ENTITY Displacement {
    TYPE: VectorQuantity
    SYMBOL: delta_r
    DIMENSION: L
    SI_UNIT: metre
    SI_SYMBOL: m

    RELATION:
      Force dot Displacement -> Work
  }

  ENTITY Energy {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: E
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    RELATION:
      Work -> TRANSFERS_OR_CHANGES -> Energy
  }

  ENTITY KineticEnergy {
    TYPE: MechanicalEnergy
    SYMBOL: K

    RELATION:
      NetWork = ChangeInKineticEnergy
  }

  ENTITY PotentialEnergy {
    TYPE: MechanicalEnergy
    SYMBOL: U

    RELATION:
      WorkByConservativeForce = -ChangeInPotentialEnergy
  }

  ENTITY Power {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: P
    DIMENSION: M * L^2 * T^-3
    SI_UNIT: watt
    SI_SYMBOL: W

    RELATION:
      Power = derivative(Work, Time)
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: joule
      symbol: J

      equivalence:
        1 J = 1 N*m
        1 J = 1 kg*m^2/s^2
    }

    COMMON_ALTERNATIVES {
      kilojoule
      megajoule
      erg
      foot_pound_force
      electronvolt
    }

    SEMANTIC_UNIT_RULE:
      N*m representing_work_or_energy -> joule
      N*m representing_torque -> torque_unit
      IDENTICAL_DIMENSIONS do_not_imply_identical_semantics

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

  CLASSIFICATION {
    by_sign:
      positive_work
      negative_work
      zero_work

    by_force_behaviour:
      constant_force_work
      variable_force_work

    by_interaction:
      work_by_conservative_force
      work_by_nonconservative_force
      net_work
      external_work
      internal_work

    by_geometry:
      translational_work
      rotational_work
  }

  RELATIONSHIPS {
    Work -> DOT_PRODUCT_RELATION -> Force
    Work -> DOT_PRODUCT_RELATION -> Displacement
    Work -> HAS_DIMENSION -> M*L^2*T^-2
    Work -> MEASURED_IN -> Joule
    Work -> TRANSFERS -> Energy
    NetWork -> EQUALS -> ChangeInKineticEnergy
    ConservativeForceWork -> EQUALS -> NegativeChangeInPotentialEnergy
    Power -> RATE_OF -> Work
    ForcePerpendicularToDisplacement -> PRODUCES -> ZeroWork
    TorqueThroughAngularDisplacement -> PRODUCES -> RotationalWork
  }

  SEMANTIC_EQUIVALENCE {
    "mechanical work" ~= work WHEN mechanics_context
    "joule" ~= "J"
    "newton metre" ~= "N*m" WHEN work_context
    "force through displacement" ~= mechanical_work
    work ~= energy_transfer
    work != force
    work != power
    work != torque
    work != displacement
  }

  SIGN_MODEL {
    POSITIVE_WORK:
      ForceComponentAlongDisplacement > 0

    NEGATIVE_WORK:
      ForceComponentAlongDisplacement < 0

    ZERO_WORK:
      ForceComponentAlongDisplacement = 0

    ANGLE_INTERPRETATION:
      0 <= theta < 90_degrees -> positive_work
      theta = 90_degrees -> zero_work
      90_degrees < theta <= 180_degrees -> negative_work
  }

  CONSTANT_FORCE_MODEL {
    FORM:
      W = F*s*cos(theta)

    CONDITIONS:
      force_constant_over_displacement
      angle_defined_between_force_and_displacement

    SPECIAL_CASES:
      parallel_same_direction:
        W = F*s

      perpendicular:
        W = 0

      parallel_opposite_direction:
        W = -F*s
  }

  VARIABLE_FORCE_MODEL {
    GENERAL_FORM:
      W = integral_path(F dot dr)

    ONE_DIMENSION:
      W = integral(F_x dx)

    RULE:
      variable_force_work_requires_integration_over_path
  }

  WORK_ENERGY_MODEL {
    WORK_ENERGY_THEOREM:
      W_net = delta_K

    CONSERVATIVE_FORCE:
      W_conservative = -delta_U

    MECHANICAL_ENERGY_CHANGE:
      delta(K + U) = W_nonconservative
      UNDER appropriate_system_definition_and_sign_convention
  }

  ROTATIONAL_WORK_MODEL {
    GENERAL_FORM:
      W = integral(tau dot dtheta_vector)

    FIXED_AXIS_SCALAR_FORM:
      W = integral(tau dtheta)

    CONSTANT_TORQUE_CASE:
      W = tau * delta_theta

    RULE:
      angular_displacement_in_radians
      under_standard_SI_rotational_work_form
  }

  PATH_MODEL {
    conservative_force:
      work_between_two_points_independent_of_path

    nonconservative_force:
      work_may_depend_on_path

    closed_path:
      integral_closed(F_conservative dot dr) = 0

    RULE:
      path_independence_is_key_indicator_of_conservative_force_field
  }

  CONSTRAINTS {
    work_is_scalar_quantity = true
    dimensional_formula = M*L^2*T^-2
    SI_unit = J
    displacement_not_distance_is_required_for_vector_dot_product_definition = true
    zero_displacement_implies_zero_mechanical_work_by_finite_force = true
    force_perpendicular_to_displacement_produces_zero_work = true
    work_and_power_are_not_semantically_equivalent = true
    work_and_torque_are_not_semantically_equivalent = true
    identical_dimensions_do_not_guarantee_semantic_equivalence = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Work

    INDIRECT_MEASUREMENT:
      force_displacement_measurement
      force_path_integration
      power_time_integration
      kinetic_energy_change
      torque_angular_displacement_integration

    RECORD:
      numerical_value
      unit
      force
      displacement_or_path
      angle
      initial_state
      final_state
      system_boundary
      interaction_type
      timestamp_or_interval
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      inferred_work = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF constant_force_known AND displacement_known AND angle_known
      THEN work = force * displacement * cos(angle)

    IF force_vector_function_and_path_known
      THEN work = line_integral(force dot differential_displacement)

    IF force_perpendicular_to_displacement
      THEN work = 0

    IF net_work_known
      THEN kinetic_energy_change = net_work

    IF conservative_force_work_known
      THEN potential_energy_change = -conservative_force_work

    IF power_function_known_over_time
      THEN work_or_energy_transfer = integral(power, time)
      UNDER applicable_transfer_context

    IF constant_power AND time_interval_known
      THEN work_or_energy_transfer = power * time_interval

    IF torque_and_angular_displacement_path_known
      THEN rotational_work = integral(torque dot differential_angular_displacement)
  }

  SYSTEM_BOUNDARY_MODEL {
    REQUIRE:
      identify_object_or_system
      identify_force_source
      identify_displacement
      identify_energy_transfer_direction

    RULE:
      phrase "work done on system"
      MUST be distinguished_from
      "work done by system"
      according_to_sign_convention
  }

  REFERENCE_FRAME_MODEL {
    mechanical_work MAY depend_on_reference_frame
    because displacement_and_kinematic_quantities_may_change_between_frames

    REQUIRE:
      identify_reference_frame_when_comparing_work_values_across_motion_descriptions

    RULE:
      work_values_from_different_frames
      MUST_NOT be assumed_identical_without_analysis
  }

  POWER_RELATION_MODEL {
    instantaneous_power:
      P = dW/dt

    translational_mechanical_power:
      P = F dot v

    rotational_mechanical_power:
      P = tau dot omega

    integration:
      W = integral(P dt)
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    work_energy_relationship_confidence: 1.00
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when force, displacement, path, angle,
      system boundary, reference frame, sign convention,
      measurement method, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK force_displacement_geometry
    CHECK displacement_vs_distance_semantics
    CHECK path_for_variable_force
    CHECK sign_convention
    CHECK system_boundary
    CHECK reference_frame_when_relevant
    CHECK work_torque_semantic_distinction
    CHECK work_power_semantic_distinction
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_force
      identify_displacement_or_path
      identify_angle_or_vector_geometry
      identify_system_boundary
      identify_sign_convention
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp_or_interval
      attach_uncertainty
      update_work_state

    ON force_or_path_change:
      update_force_model
      update_displacement_path
      recompute_work
      update_energy_transfer_state

    ON energy_state_change:
      record_initial_energy
      record_final_energy
      compare_with_computed_work
      test_work_energy_consistency

    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: Work
    canonical_symbol: W
    canonical_dimension: M*L^2*T^-2
    canonical_SI_unit: J

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_force
      identify_displacement_or_path
      identify_angle_or_vector_relation
      identify_work_sign
      identify_system_boundary
      identify_reference_frame
      identify_energy_transfer_context
      identify_power_or_rotational_context
      identify_measurement_method
      identify_uncertainty
      validate_dimensions
      infer_work_energy_relationships

    ambiguity_controls:
      distinguish_work_from_energy_state
      distinguish_work_from_power
      distinguish_work_from_force
      distinguish_work_from_torque
      distinguish_displacement_from_distance
      distinguish_positive_negative_and_zero_work
      distinguish_work_on_system_from_work_by_system
      distinguish_constant_force_from_variable_force_work
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      sign_model
      constant_force_model
      variable_force_model
      work_energy_model
      rotational_work_model
      path_model
      system_boundary_model
      reference_frame_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      work_energy_model_changes
      path_model_changes
      system_boundary_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW