Velocity Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Velocity Ontology within the Kireth Research Semantic Library. Velocity is a vector kinematic quantity representing rate of change of position with respect to time. Its dimension is L T^-1 and its coherent SI derived unit is metre per second, symbol m/s.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Velocity Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Mechanical Measurements / Velocity"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/velocity-ontology.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Velocity
 ENTITY_CLASS=DerivedVectorKinematicQuantityFramework
 DEFINITION="Velocity is a vector quantity describing the rate of change of position with respect to time in a specified reference frame. Its dimension is L T^-1 and coherent SI derived unit is metre per second, symbol m/s."
 SYMBOLIC_FORMS=["dim(v)=L*T^-1","SI_unit(v)=m/s","v=dr/dt","v_avg=Delta_r/Delta_t","speed=|v|"]
 SEMANTIC_ROLE="Machine-readable semantics for velocity, direction, reference frames, kinematics, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE=[
 Velocity,VelocityQuantity,DerivedQuantity,VectorQuantity,KinematicQuantity,
 MechanicalMeasurement,PhysicalQuantity,Quantity,QuantityKind,QuantityValue,
 VelocityDimension,LengthDimension,TimeDimension,MetrePerSecondRelationship,
 Metre,Second,SI,Unit,UnitSymbol,Position,PositionVectorRelationship,
 Displacement,DisplacementVectorRelationship,Distance,Time,DurationRelationship,
 RateOfChangeRelationship,InstantaneousVelocityRelationship,AverageVelocityRelationship,
 LinearVelocityRelationship,TranslationalVelocityRelationship,
 RelativeVelocityRelationship,AbsoluteVelocityRelationship,
 ReferenceFrameVelocityRelationship,RadialVelocityRelationship,
 TangentialVelocityRelationship,TransverseVelocityRelationship,
 LongitudinalVelocityRelationship,LateralVelocityRelationship,
 VerticalVelocityRelationship,HorizontalVelocityRelationship,
 ComponentVelocityRelationship,VelocityVectorRelationship,
 VelocityMagnitudeRelationship,DirectionRelationship,VectorRelationship,
 VectorComponentRelationship,CartesianVelocityRelationship,
 PolarVelocityRelationship,CylindricalVelocityRelationship,
 SphericalVelocityRelationship,CoordinateSystem,ReferenceFrame,
 InertialReferenceFrameRelationship,NonInertialReferenceFrameRelationship,
 GalileanTransformationRelationship,RelativeMotionRelationship,
 VelocityAdditionRelationship,RelativisticVelocityRelationship,
 Speed,SpeedMagnitudeRelationship,Acceleration,AngularVelocityRelationship,
 RotationalMotionRelationship,LinearMotionRelationship,CircularMotionRelationship,
 UniformMotionRelationship,UniformVelocityRelationship,VariableVelocityRelationship,
 TrajectoryRelationship,PathRelationship,MotionRelationship,
 ParticleKinematicsRelationship,RigidBodyKinematicsRelationship,
 ContinuumVelocityRelationship,VelocityFieldRelationship,
 FlowVelocityRelationship,FluidVelocityRelationship,ParticleVelocityRelationship,
 PhaseVelocityRelationship,GroupVelocityRelationship,WaveVelocityRelationship,
 TerminalVelocityRelationship,EscapeVelocityRelationship,OrbitalVelocityRelationship,
 DriftVelocityRelationship,MeanVelocityRelationship,BulkVelocityRelationship,
 LocalVelocityRelationship,VelocityGradientRelationship,VorticityRelationship,
 StrainRateRelationship,DifferentialCalculusRelationship,DerivativeRelationship,
 TimeDerivativeRelationship,VectorCalculusRelationship,IntegrationRelationship,
 KinematicEquationRelationship,ConstantAccelerationRelationship,
 ProjectileMotionRelationship,FreeFallRelationship,GravityRelationship,
 KilometrePerHourRelationship,MilePerHourRelationship,FootPerSecondRelationship,
 KnotRelationship,CentimetrePerSecondRelationship,MillimetrePerSecondRelationship,
 UnitConversion,VelocityMeasurement,DirectVelocityMeasurementRelationship,
 IndirectVelocityMeasurementRelationship,TachometerRelationship,
 SpeedometerRelationship,EncoderRelationship,LinearEncoderRelationship,
 RotaryEncoderRelationship,DopplerRelationship,DopplerShiftRelationship,
 LaserDopplerVelocimetryRelationship,ParticleImageVelocimetryRelationship,
 ParticleTrackingVelocimetryRelationship,AnemometerRelationship,
 PitotTubeRelationship,UltrasonicVelocityRelationship,DopplerRadarRelationship,
 DopplerLidarRelationship,SonarVelocityRelationship,
 AcousticDopplerVelocimeterRelationship,GNSSVelocityRelationship,
 GPSVelocityRelationship,InertialNavigationRelationship,IMURelationship,
 AccelerometerRelationship,OpticalFlowRelationship,ComputerVisionRelationship,
 MotionCaptureRelationship,HighSpeedImagingRelationship,TimeOfFlightRelationship,
 MeasurementSystem,Measurand,Measurement,MeasurementMethod,MeasurementProcedure,
 MeasurementModel,MeasurementEquation,MeasurementResult,MeasurementUncertainty,
 Accuracy,Precision,Resolution,Repeatability,Reproducibility,Sensitivity,
 Linearity,RangeRelationship,DynamicRangeRelationship,BandwidthRelationship,
 FrequencyResponseRelationship,SamplingRelationship,SamplingRateRelationship,
 AliasingRelationship,QuantisationRelationship,FilteringRelationship,
 Calibration,VelocityCalibrationRelationship,SpeedCalibrationRelationship,
 TachometerCalibrationRelationship,EncoderCalibrationRelationship,
 DopplerCalibrationRelationship,ReferenceStandard,VelocityStandardRelationship,
 LengthStandardRelationship,TimeStandardRelationship,FrequencyStandardRelationship,
 MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,Metrology,
 MechanicalMetrologyRelationship,KinematicMetrologyRelationship,
 DynamicMetrologyRelationship,TemperatureInfluence,PressureInfluenceRelationship,
 AirDensityRelationship,FluidDensityRelationship,RefractiveIndexRelationship,
 SpeedOfSoundRelationship,AlignmentRelationship,AngularAlignmentRelationship,
 CosineErrorRelationship,SensorLoadingRelationship,SlipRelationship,
 WheelSlipRelationship,DopplerAngleRelationship,BeamAlignmentRelationship,
 TimingErrorRelationship,ClockErrorRelationship,PositionUncertaintyRelationship,
 DistanceUncertaintyRelationship,TimeUncertaintyRelationship,
 SamplingUncertaintyRelationship,DifferentiationNoiseRelationship,
 NoiseRelationship,BiasRelationship,DriftRelationship,ScaleFactorRelationship,
 UncertaintyPropagation,Verification,Validation,KinematicValidationRelationship,
 VelocityValidationRelationship,ErrorAnalysis,Provenance,VelocityProvenance,
 ReferenceFrameProvenanceRelationship,CoordinateSystemProvenanceRelationship,
 MeasurementProvenance,CalibrationProvenance
 ]
 EXCLUDE_AS_PRIMARY=[SpeedWhenMagnitudeWithoutDirectionIsPrimary,AccelerationWhenRateOfVelocityChangeIsPrimary,DisplacementWhenPositionChangeRatherThanRateIsPrimary,AngularVelocityWhenRotationalRateIsPrimary]
 DISAMBIGUATION_RULE="Interpret velocity as a vector rate of change of position with respect to time in a specified reference frame. Distinguish velocity from scalar speed, acceleration, displacement and angular velocity."
}

CORE_CONCEPTS {
 Velocity="Vector rate of change of position with respect to time."
 InstantaneousVelocityRelationship="Time derivative of position at an instant."
 AverageVelocityRelationship="Displacement divided by elapsed time over an interval."
 Speed="Magnitude of the velocity vector."
 RelativeVelocityRelationship="Velocity of one object or frame relative to another."
 ReferenceFrame="Frame relative to which position and velocity are defined."
 VelocityMeasurement="Measurement process assigning a velocity vector or component value."
}
QUANTITY_MODEL {
 QUANTITY=Velocity
 DIMENSION=L_T_inverse
 COHERENT_SI_UNIT=MetrePerSecond
 UNIT_SYMBOL=m/s
 VECTOR_STATUS="vector"
 DERIVATION="Length/Time"
 STATUS="SI derived quantity"
}
RELATIONS {
 Velocity--is_type_of-->VectorQuantity
 Velocity--is_type_of-->KinematicQuantity
 Velocity--is_derived_from-->PositionAndTime
 Velocity--has_dimension-->L_T_inverse
 Velocity--has_coherent_SI_unit-->MetrePerSecondRelationship
 InstantaneousVelocityRelationship--is_defined_by-->TimeDerivativeOfPosition
 AverageVelocityRelationship--is_defined_by-->DisplacementOverElapsedTime
 Speed--is_magnitude_of-->Velocity
 RelativeVelocityRelationship--depends_on-->ReferenceFramesAndObjectVelocities
 Acceleration--is_time_derivative_of-->Velocity
 VelocityFieldRelationship--maps-->PositionAndTimeToVelocity
 MeasurementTraceability--links-->VelocityMeasurementToLengthAndTimeReferences
}
OPERATORS {
 VELOCITY(value,unit,direction):=velocity_vector_quantity(value,unit,direction)
 DIM(Velocity):=L*T^-1
 INSTANTANEOUS_VELOCITY(position,time):=derivative(position,time)
 AVERAGE_VELOCITY(displacement,elapsed_time):=displacement/elapsed_time
 SPEED(velocity):=norm(velocity)
 RELATIVE_VELOCITY(v_object,v_reference):=v_object-v_reference
 POSITION_FROM_VELOCITY(v,t):=integral(v,t)
 ACCELERATION_FROM_VELOCITY(v,t):=derivative(v,t)
 COMPONENT(vector,axis):=project(vector,axis)
 CONVERT_VELOCITY(value,source,target):=compatible_velocity_conversion(value,source,target)
 PROPAGATE_VELOCITY_UNCERTAINTY(model,inputs):=uncertainty_propagation(model,inputs)
}

AXIOMS {
 A1="Velocity is a vector quantity."
 A2="Velocity has dimension L T^-1."
 A3="The coherent SI derived unit of velocity is metre per second, symbol m/s."
 A4="Velocity is defined relative to a reference frame."
 A5="Instantaneous velocity is the time derivative of position."
 A6="Average velocity is displacement divided by elapsed time."
 A7="Speed is the magnitude of velocity and is scalar."
 A8="Velocity and acceleration are distinct quantity kinds."
 A9="Coordinate components of velocity depend on the chosen coordinate system or basis."
 A10="Traceable velocity measurement requires traceable spatial and temporal or frequency references."
}
REASONING {
 R1=identify(velocity_value,unit,direction,object,trajectory,position,time_interval,coordinate_system,reference_frame,measurement_method)
 R2=distinguish_velocity_speed_acceleration_displacement_angular_velocity_or_propagation_speed)
 R3=verify_dimension_L_T_inverse)
 R4=resolve_metre_per_second_kilometre_per_hour_mile_per_hour_knot_or_other_velocity_unit)
 R5=identify_instantaneous_average_relative_radial_tangential_component_field_or_flow_velocity)
 R6=resolve_coordinate_system_reference_frame_basis_direction_and_sign_convention)
 R7=choose_position_derivative_displacement_over_time_Doppler_encoder_GNSS_imaging_flow_or_other_measurement_model)
 R8=apply_alignment_timing_scale_slip_environmental_Doppler_angle_and_reference_frame_corrections)
 R9=evaluate_position_time_sampling_differentiation_alignment_sensor_calibration_and_model_uncertainty)
 R10=record_object_trajectory_coordinate_system_reference_frame_method_calibration_traceability_and_provenance)
}
CONSTRAINTS {
 C1="Velocity must not be conflated with scalar speed."
 C2="Velocity must not be conflated with acceleration."
 C3="Velocity must not be conflated with displacement."
 C4="A velocity vector requires direction or components in a specified basis."
 C5="Reference frame must be explicit when relative motion can change the result."
 C6="Average velocity must use displacement, not total path distance."
 C7="Differentiating noisy position data can amplify measurement noise."
 C8="Doppler velocity measurements require correct propagation and angle semantics."
 C9="Sampling rate and bandwidth must be sufficient for the velocity dynamics."
 C10="Traceability requires documented spatial, temporal, frequency and calibration references."
}

SEMANTIC_EQUIVALENCE {
 "LinearVelocity"<=>"VelocityInTranslationalContext"
 "VelocityMagnitude"<=>"Speed"
 "AverageVelocity"<=>"DisplacementPerElapsedTime"
 "SIUnitOfVelocity"<=>"MetrePerSecond"
 "MeterPerSecond"<=>"MetrePerSecond"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}
VALIDATION {
 V1="Velocity object or field, direction and reference frame are identified where required."
 V2="Velocity dimension is L T^-1."
 V3="Coherent SI derived unit is metre per second with symbol m/s."
 V4="Velocity and speed semantics remain distinct."
 V5="Velocity, displacement and acceleration semantics remain distinct."
 V6="Coordinate system, basis and reference frame are retained where material."
 V7="Average velocity uses displacement and elapsed time."
 V8="Unit conversions preserve velocity quantity kind and vector direction."
 V9="Uncertainty includes position, timing, sampling, alignment, sensor and calibration effects."
 V10="Velocity measurement, calibration, traceability and provenance are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 VELOCITY_DEFINITION=0.99
 DIMENSION_REASONING=0.99
 VECTOR_REASONING=0.99
 REFERENCE_FRAME_REASONING=0.98
 KINEMATIC_REASONING=0.99
 VELOCITY_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when direction, coordinate system, reference frame, time basis, measurement model, calibration or uncertainty are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,VelocityReasoning,MechanicalMeasurementReasoning,KinematicsReasoning,VectorReasoning,ReferenceFrameReasoning,RelativeMotionReasoning,SpeedReasoning,AccelerationReasoning,TrajectoryReasoning,VelocityFieldReasoning,FlowVelocityReasoning,DopplerReasoning,DimensionalReasoning,MetrePerSecondReasoning,UnitConversionReasoning,VelocityMeasurementReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,VerificationValidation,KnowledgeGraphConstruction,RecursiveInference]
}

EXECUTION_RULES {
 E1="Activate VelocityOntology when reasoning concerns vector rate of change of position with time."
 E2="Identify object or field, direction, coordinate system, reference frame and time basis."
 E3="Distinguish velocity from speed, displacement, acceleration and angular velocity."
 E4="Map velocity to dimension L T^-1 and coherent SI derived unit metre per second."
 E5="Choose instantaneous, average, relative, component, field or flow velocity semantics."
 E6="Apply compatible unit conversions and reference-frame transformations."
 E7="Evaluate timing, sampling, differentiation, alignment, Doppler geometry, sensor response and calibration."
 E8="Route speed, acceleration, displacement and angular velocity when primary."
 E9="Record trajectory, coordinate system, reference frame, method, calibration, uncertainty and provenance."
}
RECURSION {
 ENTRY=Velocity
 EXPAND(Velocity)->[
 MechanicalMeasurements,Position,Displacement,Distance,Time,Metre,Second,
 MetrePerSecondRelationship,InstantaneousVelocityRelationship,
 AverageVelocityRelationship,LinearVelocityRelationship,RelativeVelocityRelationship,
 RadialVelocityRelationship,TangentialVelocityRelationship,VelocityVectorRelationship,
 VelocityMagnitudeRelationship,Speed,Acceleration,AngularVelocityRelationship,
 CoordinateSystem,ReferenceFrame,InertialReferenceFrameRelationship,
 RelativeMotionRelationship,TrajectoryRelationship,MotionRelationship,
 ParticleKinematicsRelationship,RigidBodyKinematicsRelationship,
 VelocityFieldRelationship,FlowVelocityRelationship,FluidVelocityRelationship,
 VelocityGradientRelationship,DerivativeRelationship,VectorCalculusRelationship,
 KinematicEquationRelationship,KilometrePerHourRelationship,MilePerHourRelationship,
 KnotRelationship,UnitConversion,VelocityMeasurement,TachometerRelationship,
 EncoderRelationship,LaserDopplerVelocimetryRelationship,
 ParticleImageVelocimetryRelationship,AnemometerRelationship,
 DopplerRadarRelationship,DopplerLidarRelationship,
 AcousticDopplerVelocimeterRelationship,GNSSVelocityRelationship,
 InertialNavigationRelationship,OpticalFlowRelationship,
 MeasurementUncertainty,Calibration,VelocityStandardRelationship,
 MeasurementTraceability,KinematicMetrologyRelationship,
 SamplingRateRelationship,BandwidthRelationship,AlignmentRelationship,
 DopplerAngleRelationship,TimingErrorRelationship,DifferentiationNoiseRelationship,
 Verification,Validation,VelocityProvenance
 ]
 STOP_CONDITION="Stop when velocity identity, vector direction, reference frame, dimension, unit, measurement uncertainty and provenance are resolved."
}

ROUTING {
 PARENT_ONTOLOGY="Mechanical Measurements"
 RELATED_ONTOLOGIES=["Mechanical Measurements","Distance Ontology 2","Length Ontology 2","Time Ontology","Metre Ontology","Second Ontology","SI Derived Units","Quantity Ontology","Dimension Ontology 2","Unit Ontology","Vector Ontology","Calculus & Analysis Ontologies","Physics Ontology","Mechanics Ontology","Fluid Mechanics Ontology","Measurement Ontology","Metrology Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Velocity -> Mechanical Measurements for measurement-system semantics",
 "Velocity -> Position and Distance for spatial-change semantics",
 "Velocity -> Time and Second Ontologies for temporal semantics",
 "Velocity -> Vector Ontology for direction and component semantics",
 "Velocity -> Calculus for derivatives and integrals",
 "Velocity -> Mechanics for kinematic and reference-frame semantics",
 "Velocity -> Fluid Mechanics for velocity-field and flow semantics",
 "Velocity -> Measurement and Metrology for calibration, uncertainty and traceability"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible kinematic, vector, measurement or reference-frame relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve velocity-versus-speed distinction.","Preserve velocity-versus-acceleration distinction.","Preserve velocity-versus-displacement distinction.","Preserve vector direction and component semantics.","Preserve reference-frame semantics.","Preserve measurement uncertainty and traceability.","Preserve machine-readable velocity semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="Velocity is a vector kinematic quantity representing rate of change of position with time, with dimension L T^-1 and coherent SI derived unit metre per second, symbol m/s."
 VECTOR_SUMMARY="Velocity requires magnitude and direction or vector components in a specified basis."
 KINEMATIC_SUMMARY="Instantaneous velocity is the derivative of position; average velocity is displacement divided by elapsed time."
 REFERENCE_FRAME_SUMMARY="Velocity is reference-frame dependent and relative velocity requires explicit frame semantics."
 MEASUREMENT_SUMMARY="Velocity can be determined from position-time data, encoders, Doppler methods, GNSS, imaging, flow instrumentation and inertial systems."
}

FLOW {
 INPUT
 -> detect_velocity_context
 -> identify_value_unit_direction_object_trajectory_position_time_coordinate_system_reference_frame_and_method
 -> distinguish_velocity_speed_acceleration_displacement_angular_velocity_or_propagation_speed
 -> verify_dimension_L_T_inverse
 -> resolve_metre_per_second_or_compatible_velocity_unit
 -> identify_instantaneous_average_relative_component_field_flow_or_other_velocity_semantics
 -> resolve_coordinate_system_reference_frame_basis_direction_and_sign_convention
 -> select_velocity_measurement_or_computation_model
 -> apply_alignment_timing_scale_slip_environmental_Doppler_angle_and_reference_frame_corrections
 -> evaluate_measurement_and_model_uncertainty
 -> record_object_trajectory_coordinate_system_reference_frame_method_calibration_traceability_and_provenance
 -> 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-MECHANICAL-MEASUREMENTS-VELOCITY-ONTOLOGY-V1"
}
}
END_FLOW