Volume Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Volume Ontology within the Kireth Research Semantic Library. Volume is a derived quantity representing three-dimensional spatial extent. Its dimension is L^3 and coherent SI derived unit is the cubic metre, symbol m^3.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Volume Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Mechanical Measurements / Volume"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/volume-ontology-2.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=Volume
 ENTITY_CLASS=DerivedGeometricalMeasurementQuantityFramework
 DEFINITION="Volume is a derived quantity representing three-dimensional spatial extent, capacity or occupied space. Its dimension is L^3 and coherent SI derived unit is the cubic metre, symbol m^3."
 SYMBOLIC_FORMS=["dim(volume)=L^3","SI_unit(volume)=m^3","V_cuboid=l*w*h","V_cylinder=pi*r^2*h","V_sphere=4*pi*r^3/3","V=triple_integral(dV)"]
 SEMANTIC_ROLE="Machine-readable semantics for geometric volume, capacity, displacement volume, computation, measurement, uncertainty and traceability."
}
SCOPE {
 INCLUDE=[
 Volume,DerivedQuantity,PhysicalQuantity,GeometricalQuantity,MechanicalMeasurement,
 Quantity,QuantityKind,QuantityValue,VolumeDimension,LengthDimension,
 CubicMetreRelationship,Metre,SI,Unit,UnitSymbol,ThreeDimensionalExtentRelationship,
 GeometricVolumeRelationship,EnclosedVolumeRelationship,CapacityRelationship,
 InternalVolumeRelationship,ExternalVolumeRelationship,DisplacementVolumeRelationship,
 SweptVolumeRelationship,VoidVolumeRelationship,PoreVolumeRelationship,
 BulkVolumeRelationship,SpecificVolumeRelationship,MolarVolumeRelationship,
 CuboidVolumeRelationship,CubeVolumeRelationship,PrismVolumeRelationship,
 PyramidVolumeRelationship,CylinderVolumeRelationship,ConeVolumeRelationship,
 SphereVolumeRelationship,HemisphereVolumeRelationship,EllipsoidVolumeRelationship,
 TorusVolumeRelationship,FrustumVolumeRelationship,CompositeVolumeRelationship,
 IrregularVolumeRelationship,PolyhedronVolumeRelationship,TetrahedronVolumeRelationship,
 MeshVolumeRelationship,ParametricVolumeRelationship,CoordinateGeometryRelationship,
 CartesianCoordinateRelationship,CylindricalCoordinateRelationship,
 SphericalCoordinateRelationship,JacobianRelationship,JacobianDeterminantRelationship,
 DifferentialVolumeElementRelationship,TripleIntegralRelationship,
 MultipleIntegralRelationship,CalculusRelationship,VectorCalculusRelationship,
 Area,Length,Distance,Width,Height,Depth,Radius,Diameter,SurfaceAreaRelationship,
 ComputationalGeometryRelationship,TetrahedralisationRelationship,MeshRelationship,
 FiniteElementRelationship,VoxelRelationship,VoxelVolumeRelationship,
 PointCloudRelationship,ThreeDimensionalReconstructionRelationship,
 GeographicVolumeRelationship,TerrainVolumeRelationship,CutAndFillRelationship,
 EarthworkVolumeRelationship,ReservoirVolumeRelationship,SurveyVolumeRelationship,
 DigitalElevationModelRelationship,GeodesyRelationship,GISrelationship,
 MapProjectionRelationship,DatumRelationship,DensityRelationship,Mass,
 Pressure,TemperatureRelationship,CompressibilityRelationship,
 BulkModulusRelationship,ThermalExpansionRelationship,FluidRelationship,
 LiquidRelationship,GasRelationship,SolidRelationship,EquationOfStateRelationship,
 IdealGasLawRelationship,VolumetricFlowRateRelationship,VolumeMeasurement,
 DirectVolumeMeasurementRelationship,IndirectVolumeMeasurementRelationship,
 DimensionalVolumeMeasurementRelationship,DisplacementMethodRelationship,
 FluidDisplacementRelationship,ArchimedesPrincipleRelationship,
 VolumetricGlasswareRelationship,VolumetricFlaskRelationship,
 MeasuringCylinderRelationship,BuretteRelationship,PipetteRelationship,
 PycnometerRelationship,TankGaugingRelationship,LevelMeasurementRelationship,
 CoordinateMeasurementRelationship,LaserScannerRelationship,LidarRelationship,
 PhotogrammetryRelationship,ComputedTomographyRelationship,
 ThreeDimensionalImagingRelationship,SurveyingRelationship,TotalStationRelationship,
 GNSSRelationship,MeasurementSystem,Measurand,Measurement,MeasurementMethod,
 MeasurementModel,MeasurementResult,MeasurementUncertainty,Accuracy,Precision,
 Resolution,Repeatability,Reproducibility,Calibration,VolumeCalibrationRelationship,
 DimensionalCalibrationRelationship,VolumetricCalibrationRelationship,
 CapacityCalibrationRelationship,ReferenceStandard,VolumeStandardRelationship,
 CapacityStandardRelationship,LengthStandardRelationship,
 GravimetricVolumeStandardRelationship,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,Metrology,DimensionalMetrologyRelationship,
 VolumeMetrologyRelationship,TemperatureInfluence,PressureInfluenceRelationship,
 CompressibilityCorrectionRelationship,AirBuoyancyRelationship,
 DensityCorrectionRelationship,MeniscusRelationship,EvaporationRelationship,
 LeakageRelationship,BoundaryDefinitionRelationship,SegmentationUncertaintyRelationship,
 CoordinateUncertaintyRelationship,SurfaceReconstructionRelationship,
 MeshResolutionRelationship,DiscretisationErrorRelationship,
 NumericalIntegrationRelationship,UncertaintyPropagation,Verification,Validation,
 VolumeValidationRelationship,ErrorAnalysis,Provenance,VolumeProvenance,
 MeasurementProvenance,CalibrationProvenance
 ]
 EXCLUDE_AS_PRIMARY=[AreaWhenTwoDimensionalExtentIsPrimary,LengthWhenOneDimensionalExtentIsPrimary,MassWhenMatterQuantityIsPrimary,VolumetricFlowRateWhenVolumePerTimeIsPrimary,SpecificVolumeWhenVolumePerMassIsPrimary]
 DISAMBIGUATION_RULE="Interpret volume as three-dimensional spatial extent with dimension L^3. Distinguish geometric volume from capacity, volumetric flow rate, specific volume, molar volume and colloquial sound volume."
}
CORE_CONCEPTS {
 Volume="Derived quantity representing three-dimensional spatial extent or occupied space."
 VolumeDimension="Derived physical dimension L^3."
 CubicMetreRelationship="Coherent SI derived unit of volume, symbol m^3."
 GeometricVolumeRelationship="Three-dimensional measure of a defined geometric body or region."
 CapacityRelationship="Maximum or specified internal volume a container can hold."
 DisplacementVolumeRelationship="Volume inferred from displacement of a fluid or other medium."
 VolumeMeasurement="Measurement or computation assigning a volume value to a defined body, region or capacity."
}
QUANTITY_MODEL {
 QUANTITY=Volume
 DIMENSION=L_cubed
 COHERENT_SI_UNIT=CubicMetre
 UNIT_SYMBOL=m^3
 DERIVATION="Length*Length*Length"
 STATUS="SI derived quantity"
}
RELATIONS {
 Volume--is_type_of-->DerivedQuantity
 Volume--is_derived_from-->LengthCubed
 Volume--has_dimension-->L_cubed
 Volume--has_coherent_SI_unit-->CubicMetreRelationship
 CapacityRelationship--has_quantity_kind-->Volume
 SpecificVolumeRelationship--relates_to-->VolumeAndMass
 MolarVolumeRelationship--relates_to-->VolumeAndAmountOfSubstance
 DensityRelationship--relates_to-->MassAndVolume
 VolumetricFlowRateRelationship--relates_to-->VolumeAndTime
 VolumeMeasurement--targets-->VolumeMeasurand
 MeasurementTraceability--links-->VolumeMeasurementToSI
}
OPERATORS {
 VOLUME(value,unit):=volume_quantity(value,unit)
 DIM(Volume):=L^3
 CUBOID_VOLUME(length,width,height):=length*width*height
 PRISM_VOLUME(base_area,height):=base_area*height
 CYLINDER_VOLUME(radius,height):=pi*radius^2*height
 CONE_VOLUME(radius,height):=pi*radius^2*height/3
 SPHERE_VOLUME(radius):=4*pi*radius^3/3
 ELLIPSOID_VOLUME(a,b,c):=4*pi*a*b*c/3
 PYRAMID_VOLUME(base_area,height):=base_area*height/3
 GENERAL_VOLUME(region):=triple_integral(1,dV)
 DISPLACEMENT_VOLUME(final_level,initial_level):=final_level-initial_level
 VOLUME_FROM_MASS_DENSITY(mass,density):=mass/density
 CONVERT_VOLUME(value,source,target):=compatible_volume_conversion(value,source,target)
 PROPAGATE_VOLUME_UNCERTAINTY(model,inputs):=uncertainty_propagation(model,inputs)
}
AXIOMS {
 A1="Volume is a derived quantity with dimension L^3."
 A2="The coherent SI derived unit of volume is the cubic metre, symbol m^3."
 A3="Volume is distinct from length and area."
 A4="Geometric volume requires a defined three-dimensional region, body, boundary or model."
 A5="Capacity has quantity kind volume but represents an internal holding capability."
 A6="Specific volume, molar volume and volumetric flow rate are distinct quantity kinds."
 A7="Coordinate-based volume calculations depend on coordinate-system and Jacobian semantics."
 A8="Fluid volume can depend materially on temperature, pressure and compressibility."
 A9="Volume uncertainty depends on uncertainties in dimensions, boundaries, coordinates, density or models."
 A10="Traceable volume measurement requires documented dimensional, gravimetric or volumetric reference chains."
}
REASONING {
 R1=identify(volume_value,unit,body,region,boundary,geometry,material,state,coordinate_system,measurement_method)
 R2=distinguish_geometric_volume_capacity_displacement_volume_specific_volume_molar_volume_flow_rate_or_sound_volume)
 R3=verify_dimension_L_cubed)
 R4=resolve_cubic_metre_prefixed_cubic_units_litre_and_nonSI_volume_units)
 R5=identify_cuboid_prism_cylinder_cone_sphere_polyhedron_parametric_mesh_voxel_or_irregular_geometry)
 R6=resolve_coordinates_boundary_surface_parameterisation_mesh_or_reconstruction)
 R7=choose_dimensional_displacement_gravimetric_volumetric_coordinate_imaging_survey_or_computational_method)
 R8=apply_temperature_pressure_density_buoyancy_meniscus_leakage_scale_and_reconstruction_corrections)
 R9=evaluate_dimension_boundary_coordinate_density_environment_sampling_mesh_calibration_and_model_uncertainty)
 R10=record_body_region_geometry_material_state_coordinate_system_method_calibration_traceability_and_provenance)
}
CONSTRAINTS {
 C1="Volume must not be conflated with area or length."
 C2="Cubic-unit conversions require cubed linear conversion factors."
 C3="Capacity and geometric external volume must remain distinct where material."
 C4="Specific volume and molar volume must not be interpreted as ordinary volume."
 C5="Volumetric flow rate is volume per time and is a distinct quantity kind."
 C6="Fluid-volume measurements can require temperature, pressure, density and meniscus corrections."
 C7="Irregular-body displacement requires complete immersion or an explicit partial-displacement model."
 C8="Mesh, voxel and image-derived volumes require defined spatial scale, boundary and reconstruction semantics."
 C9="Resolution alone does not determine total volume uncertainty."
 C10="Traceability requires documented dimensional, gravimetric, capacity or volumetric calibration and uncertainty."
}
SEMANTIC_EQUIVALENCE {
 "SpatialVolume"<=>"VolumeInGeometricContext"
 "Capacity"<=>"InternalHoldingVolumeInContainerContext"
 "SIUnitOfVolume"<=>"CubicMetre"
 "CubicMeter"<=>"CubicMetre"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}
VALIDATION {
 V1="Measured or computed body, region or capacity is identified."
 V2="Volume dimension is L^3."
 V3="Coherent SI derived unit is cubic metre with symbol m^3."
 V4="Volume, area and length semantics remain distinct."
 V5="Geometric volume, capacity, specific volume, molar volume and flow-rate semantics are preserved."
 V6="Coordinate system, scale, material state and geometry are explicit where required."
 V7="Volume formulas match the selected geometry or measurement model."
 V8="Unit conversions correctly cube the associated length scale."
 V9="Uncertainty includes dimensional, boundary, environmental, density, reconstruction and calibration effects."
 V10="Volume measurement, calibration, traceability and provenance records are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 VOLUME_DEFINITION=0.99
 DIMENSION_REASONING=0.99
 GEOMETRY_REASONING=0.99
 FLUID_VOLUME_REASONING=0.98
 COMPUTATIONAL_VOLUME_REASONING=0.98
 VOLUME_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when body, region, boundary, geometry, material state, coordinate system, scale, method, environmental conditions, calibration or uncertainty are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,VolumeReasoning,MechanicalMeasurementReasoning,GeometryReasoning,SolidGeometryReasoning,CoordinateGeometryReasoning,CalculusReasoning,ComputationalGeometryReasoning,FluidVolumeReasoning,CapacityReasoning,SurveyVolumeReasoning,DimensionalReasoning,CubicMetreReasoning,UnitConversionReasoning,VolumeMeasurementReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,VerificationValidation,KnowledgeGraphConstruction,RecursiveInference]
}
EXECUTION_RULES {
 E1="Activate VolumeOntology when reasoning concerns three-dimensional spatial extent, occupied space or capacity."
 E2="Identify body, region, boundary, geometry, material state, coordinate system and measurement model."
 E3="Distinguish volume from area, specific volume, molar volume and volumetric flow rate."
 E4="Map volume to derived dimension L^3 and coherent SI derived unit cubic metre."
 E5="Choose geometric, integral, displacement, gravimetric, mesh, voxel, imaging or survey model."
 E6="Apply cubed unit-conversion factors and environmental or reconstruction corrections."
 E7="Evaluate dimensional, boundary, environmental, density, sampling, mesh and calibration uncertainty."
 E8="Route area, density, specific volume, molar volume and volumetric flow rate when primary."
 E9="Record body, geometry, state, coordinate system, method, calibration, uncertainty and provenance."
}
RECURSION {
 ENTRY=Volume
 EXPAND(Volume)->[
 MechanicalMeasurements,Length,Area,VolumeDimension,CubicMetreRelationship,Metre,
 GeometricVolumeRelationship,CapacityRelationship,DisplacementVolumeRelationship,
 SpecificVolumeRelationship,MolarVolumeRelationship,CuboidVolumeRelationship,
 PrismVolumeRelationship,PyramidVolumeRelationship,CylinderVolumeRelationship,
 ConeVolumeRelationship,SphereVolumeRelationship,EllipsoidVolumeRelationship,
 CompositeVolumeRelationship,PolyhedronVolumeRelationship,MeshVolumeRelationship,
 ParametricVolumeRelationship,CoordinateGeometryRelationship,JacobianRelationship,
 TripleIntegralRelationship,ComputationalGeometryRelationship,
 TetrahedralisationRelationship,VoxelRelationship,PointCloudRelationship,
 ThreeDimensionalReconstructionRelationship,GeographicVolumeRelationship,
 TerrainVolumeRelationship,CutAndFillRelationship,SurveyVolumeRelationship,
 DensityRelationship,Mass,Pressure,TemperatureRelationship,CompressibilityRelationship,
 EquationOfStateRelationship,VolumetricFlowRateRelationship,VolumeMeasurement,
 DisplacementMethodRelationship,ArchimedesPrincipleRelationship,
 VolumetricGlasswareRelationship,PycnometerRelationship,TankGaugingRelationship,
 LaserScannerRelationship,LidarRelationship,PhotogrammetryRelationship,
 ComputedTomographyRelationship,SurveyingRelationship,GNSSRelationship,
 MeasurementUncertainty,Calibration,VolumeStandardRelationship,
 GravimetricVolumeStandardRelationship,MeasurementTraceability,
 VolumeMetrologyRelationship,ThermalExpansionRelationship,
 AirBuoyancyRelationship,MeniscusRelationship,LeakageRelationship,
 BoundaryDefinitionRelationship,SegmentationUncertaintyRelationship,
 SurfaceReconstructionRelationship,DiscretisationErrorRelationship,
 Verification,Validation,VolumeProvenance
 ]
 STOP_CONDITION="Stop when volume identity, dimension, unit, body or region geometry, material state, measurement uncertainty and provenance are resolved."
}
ROUTING {
 PARENT_ONTOLOGY="Mechanical Measurements"
 RELATED_ONTOLOGIES=["Mechanical Measurements","Fundamental Physical Quantities","Length Ontology 2","Distance Ontology 2","Area Ontology 2","Metre Ontology","SI Derived Units","Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Geometry Ontologies","Calculus & Analysis Ontologies","Computational Mathematics Ontologies","Fluid Mechanics Ontology","Geodesy Ontology","Verification & Validation"]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 RULES=["Preserve volume-versus-area distinction.","Preserve volume-versus-capacity context.","Preserve volume-versus-specific-volume distinction.","Preserve volume-versus-flow-rate distinction.","Preserve cubic unit-conversion semantics.","Preserve material-state and environmental semantics.","Preserve measurement uncertainty and traceability.","Preserve machine-readable volume semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="Volume is a derived quantity representing three-dimensional spatial extent, with dimension L^3 and coherent SI derived unit cubic metre, symbol m^3."
 GEOMETRY_SUMMARY="Volume can describe regular solids, composite bodies, irregular regions, meshes, voxels and reconstructed three-dimensional objects."
 CALCULUS_SUMMARY="General volume can be computed using triple integrals, coordinate transformations and Jacobians."
 FLUID_SUMMARY="Fluid volume can depend on temperature, pressure, density, compressibility and measurement conditions."
 MEASUREMENT_SUMMARY="Volume can be determined using dimensional, displacement, gravimetric, volumetric, coordinate, imaging and survey methods."
}
FLOW {
 INPUT
 -> detect_volume_context
 -> identify_volume_value_unit_body_region_boundary_geometry_material_state_coordinate_system_and_method
 -> distinguish_geometric_volume_capacity_displacement_volume_specific_volume_molar_volume_flow_rate_or_sound_volume
 -> verify_dimension_L_cubed
 -> resolve_cubic_metre_prefixed_cubic_units_litre_and_nonSI_volume_units
 -> identify_geometric_integral_displacement_mesh_voxel_imaging_survey_or_fluid_model
 -> resolve_coordinates_boundary_surface_parameterisation_mesh_or_reconstruction
 -> select_volume_measurement_or_computation_method
 -> apply_temperature_pressure_density_buoyancy_meniscus_leakage_scale_and_reconstruction_corrections
 -> evaluate_measurement_and_model_uncertainty
 -> record_body_region_geometry_material_state_coordinate_system_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-VOLUME-ONTOLOGY-2-V1"
}
}
END_FLOW