Pascal Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Pascal Ontology within the Kireth Research Semantic Library. The pascal, symbol Pa, is the coherent SI derived unit of pressure and stress. It equals one newton per square metre, or kg m^-1 s^-2, and formalises pressure, stress, force-per-area relationships, measurement, calibration, uncertainty, traceability and provenance.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Pascal Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Measurement & Units"
 SPECIALISATION = "SI Derived Units / Pascal"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/si-derived-units/pascal-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = Pascal
 ENTITY_CLASS = SIDerivedUnitOfPressureAndStressFramework
 PRIMARY_CONTEXT = SIDerivedUnits
 DEFINITION = "The pascal, symbol Pa, is the coherent SI derived unit of pressure and stress. One pascal equals one newton per square metre and one kilogram per metre per second squared."
 SYMBOLIC_FORMS = ["1 Pa=1 N m^-2","1 Pa=1 kg m^-1 s^-2","p=F_normal/A","sigma=F_normal/A","[pressure]=M L^-1 T^-2"]
 SEMANTIC_ROLE = "Machine-readable semantics for the pascal, pressure, stress, force-area relations, dimensional structure, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE = [
 Pascal,PascalUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,MeasurementUnit,Unit,
 InternationalSystemOfUnits,SI,SIBaseUnits,Newton,Metre,Kilogram,Second,Force,Area,
 Pressure,Stress,NormalStress,ShearStressRelationship,DerivedQuantity,Quantity,QuantityKind,
 QuantityValue,Dimension,PressureDimension,DimensionalSignature,UnitSymbol,UnitDefinition,
 PascalDefinition,UnitExpression,UnitAlgebra,QuantityCalculus,DimensionalAnalysis,
 FluidPressure,HydrostaticPressure,DynamicPressureRelationship,StagnationPressureRelationship,
 AbsolutePressure,GaugePressure,DifferentialPressure,VacuumPressureRelationship,
 AtmosphericPressure,BarometricPressureRelationship,PressureHeadRelationship,Density,
 GravitationalAcceleration,PressureGradientRelationship,BulkModulusRelationship,
 YoungsModulusRelationship,StressTensorRelationship,TensileStressRelationship,
 CompressiveStressRelationship,YieldStressRelationship,AcousticPressureRelationship,
 SoundPressureRelationship,PressureMeasurement,PressureSensor,PressureTransducer,
 PressureGauge,Manometer,BarometerRelationship,PistonGaugeRelationship,
 DeadweightTesterRelationship,PressureBalanceRelationship,PiezoresistivePressureSensorRelationship,
 MeasurementSystem,Measurement,Measurand,MeasurementResult,MeasurementUncertainty,
 Accuracy,Precision,Resolution,Repeatability,Reproducibility,HysteresisRelationship,
 Drift,Stability,Calibration,PressureCalibrationRelationship,ReferenceStandard,
 PressureStandardRelationship,MeasurementTraceability,MetrologicalTraceability,
 TraceabilityChain,Metrology,PressureMetrologyRelationship,ScientificMeasurement,
 TemperatureInfluence,LocalGravityRelationship,FluidDensityInfluenceRelationship,
 HeadCorrectionRelationship,HeightCorrectionRelationship,LeakageRelationship,
 Prefix,SIPrefix,Kilopascal,Megapascal,GigapascalRelationship,HectopascalRelationship,
 UnitConversion,ConversionFactor,ExactConversion,UnitCompatibility,DimensionalCompatibility,
 QuantityCompatibility,BarRelationship,AtmosphereUnitRelationship,TorrRelationship,
 MillimetreOfMercuryRelationship,PoundsPerSquareInchRelationship,PSIRelationship,
 Verification,Validation,UnitValidation,DimensionalValidation,ConversionValidation,
 ErrorAnalysis,Provenance,PascalProvenance,SIDerivedUnitProvenance,SIUnitProvenance,
 MeasurementProvenance,CalibrationProvenance,StandardProvenance,BIPMrelationship,
 SIbrochureRelationship,VIMRelationship,GUMRelationship,StandardVersion
 ]
 EXCLUDE_AS_PRIMARY = [
 PascalAsPersonRelationship,PascalProgrammingLanguageRelationship,
 PascalTriangleRelationship,ForceWhenForceRatherThanForcePerAreaIsPrimary
 ]
 DISAMBIGUATION_RULE = "When pascal or symbol Pa denotes the coherent SI derived unit of pressure or stress, interpret the context as the measurement unit and distinguish it from Blaise Pascal, Pascal programming and unrelated uses."
}

CORE_CONCEPTS {
 Pascal = "Coherent SI derived unit of pressure and stress, symbol Pa."
 Pressure = "Normal force distributed over area in pressure contexts."
 Stress = "Internal force per unit area within a material or continuum."
 PressureDimension = "Derived physical dimension M L^-1 T^-2."
 AbsolutePressure = "Pressure referenced to a perfect vacuum."
 GaugePressure = "Pressure referenced to ambient or another stated reference."
 DifferentialPressure = "Difference between two pressure values."
 PressureMeasurement = "Measurement process assigning a pressure value to a measurand."
}

RELATIONS {
 Pascal --is_type_of--> SIDerivedUnit
 Pascal --is_coherent_derived_unit_of--> Pressure
 Pascal --is_coherent_derived_unit_of--> Stress
 Pascal --has_symbol--> Pa
 Pascal --has_expression--> newton_per_square_metre
 Pascal --has_base_expression--> kilogram_per_metre_second_squared
 Pressure --has_dimension--> PressureDimension
 Stress --has_dimension--> PressureDimension
 Pressure --relates_to--> NormalForcePerArea
 HydrostaticPressure --depends_on--> DensityGravityAndDepth
 AbsolutePressure --references--> Vacuum
 GaugePressure --references--> AmbientPressure
 DifferentialPressure --is_difference_between--> TwoPressures
 Kilopascal --is_decimal_multiple_of--> Pascal
 Megapascal --is_decimal_multiple_of--> Pascal
 PressureCalibrationRelationship --uses--> ReferenceStandard
 MeasurementTraceability --links--> PressureMeasurementToSI
}

OPERATORS {
 PASCAL(value) := pressure_or_stress_quantity(value,Pascal)
 DIM(Pascal) := PressureDimension
 PRESSURE(normal_force,area) := normal_force/area
 NORMAL_STRESS(normal_force,area) := normal_force/area
 HYDROSTATIC_PRESSURE(density,gravity,depth) := density*gravity*depth
 GAUGE_PRESSURE(absolute,ambient) := absolute-ambient
 ABSOLUTE_PRESSURE(gauge,ambient) := gauge+ambient
 DIFFERENTIAL_PRESSURE(p1,p2) := p1-p2
 PREFIX_PASCAL(prefix) := decimal_scaled_unit(Pascal,prefix)
 CONVERT_PRESSURE(value,source,target) := compatible_pressure_conversion(value,source,target)
 TRACE_PRESSURE(result) := traceability_chain_to_SI_pascal(result)
}

AXIOMS {
 A1 = "The pascal is the coherent SI derived unit of pressure and stress."
 A2 = "One pascal equals one newton per square metre."
 A3 = "One pascal is equivalent to kg m^-1 s^-2."
 A4 = "The canonical symbol is Pa, with uppercase P and lowercase a."
 A5 = "Pressure and mechanical stress share the same dimensions and SI unit but are distinct quantity concepts."
 A6 = "Absolute, gauge and differential pressure require explicit reference semantics."
 A7 = "Hydrostatic pressure depends on fluid density, gravitational acceleration and vertical depth."
 A8 = "Pressure measurement traceability requires documented calibration and reference conditions."
 A9 = "Dimensional equality alone does not determine whether a pascal-valued quantity is pressure, stress or another compatible quantity."
}

REASONING {
 R1_CONTEXT = identify(pressure_or_stress_quantity,value,unit,reference_type,medium,measurement_method_and_intended_use)
 R2_IDENTITY = resolve_pascal_prefixed_pascal_nonSI_pressure_unit_or_symbol_Pa_ambiguity)
 R3_QUANTITY = distinguish_pressure_normal_stress_or_other_dimensionally_equivalent_quantity)
 R4_DIMENSION = verify_dimension_M_L_minus_1_T_minus_2)
 R5_DERIVATION = expand_pascal_to_N_m_minus_2_and_kg_m_minus_1_s_minus_2)
 R6_REFERENCE = classify_absolute_gauge_differential_or_other_pressure_reference)
 R7_SCALE = if_prefixed_apply_exact_decimal_scaling)
 R8_MEASUREMENT = identify_pressure_balance_manometer_transducer_gauge_or_other_method)
 R9_UNCERTAINTY = evaluate_reference_gravity_head_temperature_density_hysteresis_drift_resolution_and_repeatability)
 R10_PROVENANCE = record_unit_expression_quantity_kind_reference_type_method_standard_calibration_and_traceability)
}

CONSTRAINTS {
 C1 = "The symbol Pa is case-sensitive."
 C2 = "Pressure and stress share the pascal but retain distinct quantity semantics."
 C3 = "Gauge pressure cannot be interpreted without its reference pressure."
 C4 = "Differential pressure requires identification of both pressure points or sides."
 C5 = "Hydrostatic corrections depend on density, gravity and height differences."
 C6 = "Pressure-balance realisation can require local-gravity and effective-area corrections."
 C7 = "Gas pressure measurements can depend on gas species, temperature and instrument regime."
 C8 = "Instrument resolution alone does not determine total pressure uncertainty."
 C9 = "Traceability to the pascal requires a documented pressure-realisation or calibration chain."
 C10 = "Dimensional correctness alone does not prove that a quantity is pressure or stress."
}

SEMANTIC_EQUIVALENCE {
 "PascalUnit" <=> "Pascal"
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
 "PSI" <=> "PoundsPerSquareInch"
}

VALIDATION {
 V1 = "Unit identity is pascal and canonical symbol is Pa."
 V2 = "Quantity kind is pressure, stress or another explicitly identified compatible quantity."
 V3 = "Derived dimension is M L^-1 T^-2."
 V4 = "Coherent SI expressions are N m^-2 and kg m^-1 s^-2."
 V5 = "Absolute, gauge and differential reference semantics are explicit where relevant."
 V6 = "Pressure and stress semantics remain distinct despite equal units and dimensions."
 V7 = "Prefixed pascal units use correct decimal scaling."
 V8 = "Conversions to non-SI pressure units use declared conversion definitions."
 V9 = "Measurement uncertainty includes relevant gravity, head, temperature, sensor and calibration effects."
 V10 = "Pressure calibration and traceability evidence are retained."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 PASCAL_DEFINITION = 0.99
 PRESSURE_REASONING = 0.99
 STRESS_REASONING = 0.98
 DIMENSION_REASONING = 0.99
 PRESSURE_REFERENCE_REASONING = 0.99
 PRESSURE_MEASUREMENT_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when quantity kind, pressure reference, medium, head correction, measurement method, calibration status or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,PascalReasoning,SIDerivedUnitReasoning,
 PressureReasoning,StressReasoning,ForceAreaReasoning,HydrostaticPressureReasoning,
 PressureReferenceReasoning,PressureMeasurementReasoning,PressureMetrologyReasoning,
 CalibrationReasoning,DimensionalReasoning,UncertaintyReasoning,TraceabilityReasoning,
 KnowledgeGraphConstruction,RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "pascal" -> Pascal
  "Pa" -> Pascal
  "kPa" -> Kilopascal
  "MPa" -> Megapascal
  "hPa" -> Hectopascal
  "psi" -> PoundsPerSquareInch
 }
}

EXECUTION_RULES {
 E1 = "If pascal or symbol Pa denotes the SI derived unit of pressure or stress, activate PascalOntology."
 E2 = "Confirm quantity kind rather than relying only on dimensional form."
 E3 = "Map the pascal coherently to N m^-2 and kg m^-1 s^-2."
 E4 = "Distinguish pressure from mechanical stress and other dimensionally equivalent quantities."
 E5 = "Classify absolute, gauge or differential pressure reference semantics where relevant."
 E6 = "Apply SI prefixes as exact decimal scale transformations."
 E7 = "For hydrostatic or pressure-balance contexts, evaluate density, gravity and head corrections."
 E8 = "For measurement contexts, evaluate sensor behaviour, environment, calibration and uncertainty."
 E9 = "Record pressure-reference, calibration and traceability provenance."
}

RECURSION {
 ENTRY = Pascal
 EXPAND(Pascal) -> [
 SIDerivedUnits,DerivedUnit,SIDerivedUnit,CoherentDerivedUnit,SIUnits,SIBaseUnits,
 Newton,Metre,Kilogram,Second,Force,Area,Pressure,Stress,PressureDimension,
 Quantity,QuantityKind,Dimension,DimensionalSignature,Unit,UnitSymbol,PascalDefinition,
 UnitExpression,UnitAlgebra,DimensionalAnalysis,HydrostaticPressure,AbsolutePressure,
 GaugePressure,DifferentialPressure,AtmosphericPressure,Density,GravitationalAcceleration,
 NormalStress,ShearStressRelationship,YoungsModulusRelationship,BulkModulusRelationship,
 PressureMeasurement,PressureSensor,PressureTransducer,PressureGauge,Manometer,
 PistonGaugeRelationship,DeadweightTesterRelationship,PressureBalanceRelationship,
 MeasurementSystem,Measurement,MeasurementUncertainty,Calibration,ReferenceStandard,
 PressureStandardRelationship,MeasurementTraceability,Metrology,TemperatureInfluence,
 LocalGravityRelationship,HeadCorrectionRelationship,SIPrefix,Kilopascal,Megapascal,
 HectopascalRelationship,BarRelationship,AtmosphereUnitRelationship,TorrRelationship,
 PSIRelationship,UnitConversion,Verification,Validation,PascalProvenance
 ]
 EXPAND(PascalFamilies) -> [
 PascalIdentitySymbolQuantityAndDimension,
 NewtonAreaAndBaseUnitExpansion,
 PressureStressAndContinuumSemantics,
 AbsoluteGaugeDifferentialAtmosphericAndHydrostaticPressure,
 MechanicalStressModuliAndMaterialRelationships,
 PressureMeasurementSensorsGaugesBalancesAndStandards,
 GravityHeadTemperatureSensorEffectsUncertaintyCalibrationAndTraceability,
 ValidationConversionSemanticDisambiguationAndProvenance
 ]
 STOP_CONDITION = "Stop when pascal identity, quantity kind, dimensional expression, pressure reference, measurement semantics, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Derived Units"
 RELATED_ONTOLOGIES = [
 "SI Derived Units","Derived Units Ontology","SI Base Units","SI Units Ontology",
 "Newton Ontology","Metre Ontology","Kilogram Ontology","Second Ontology",
 "Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology",
 "Measurement Ontology","Scientific Measurement Ontology 2","Metrology Ontology",
 "Reference Standard Ontology","Measurement System Ontology","Measurement Uncertainty Ontology",
 "Dimensional Analysis Ontology","Physics Ontology","Materials Science Ontology",
 "Verification & Validation"
 ]
 ROUTE_RULES = [
 "Pascal -> SI Derived Units for parent derived-unit semantics",
 "Pascal -> Derived Units Ontology for general derived-unit algebra",
 "Pascal -> Newton and Metre ontologies for N m^-2 semantics",
 "Pascal -> Kilogram, Metre and Second ontologies for base-unit expansion",
 "Pascal -> Quantity and Physical Quantity ontologies for pressure and stress semantics",
 "Pascal -> Dimension Ontology for M L^-1 T^-2 dimensional structure",
 "Pascal -> Physics and Materials Science for fluid, continuum and stress semantics",
 "Pascal -> Measurement and Scientific Measurement for pressure measurement",
 "Pascal -> Metrology and Reference Standard for calibration and traceability",
 "Pascal -> Measurement Uncertainty for uncertainty evaluation",
 "Pascal -> Verification & Validation for pressure, dimensional and semantic checks"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible pressure, stress, measurement or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
 "Preserve pascal-versus-pressure distinction.",
 "Preserve pressure-versus-stress distinction.",
 "Preserve absolute-versus-gauge-versus-differential-pressure distinction.",
 "Preserve force-versus-force-per-area distinction.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve dimensional-correctness-versus-quantity-meaning distinction.",
 "Preserve measurement-reference-versus-unit-definition distinction.",
 "Preserve machine-readable pascal semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "The pascal, symbol Pa, is the coherent SI derived unit of pressure and stress and equals N m^-2 or kg m^-1 s^-2."
 QUANTITY_SUMMARY = "Pressure and stress share dimension M L^-1 T^-2 but retain distinct quantity meanings."
 REFERENCE_SUMMARY = "Pressure values can be absolute, gauge or differential and require explicit reference semantics."
 HYDROSTATIC_SUMMARY = "Hydrostatic pressure depends on fluid density, gravitational acceleration and depth."
 MEASUREMENT_SUMMARY = "Pressure measurement can use balances, piston gauges, manometers, transducers and other traceable pressure systems."
 UNCERTAINTY_SUMMARY = "Precision pressure measurement can require uncertainty contributions from gravity, head, density, temperature, hysteresis, drift, sensor response and calibration."
 VALIDATION_SUMMARY = "Pascal semantics should preserve unit identity, quantity kind, dimensional structure, pressure reference, measurement uncertainty, traceability and provenance."
}

FLOW {
 INPUT
 -> detect_pascal_context
 -> identify_pressure_or_stress_quantity_value_unit_reference_type_medium_measurement_method_and_intended_use
 -> resolve_pascal_prefixed_pascal_nonSI_pressure_unit_or_symbol_Pa_ambiguity
 -> distinguish_pressure_normal_stress_or_other_dimensionally_equivalent_quantity
 -> verify_dimension_M_L_minus_1_T_minus_2
 -> expand_pascal_to_N_m_minus_2_and_kg_m_minus_1_s_minus_2
 -> classify_absolute_gauge_differential_or_other_pressure_reference
 -> if_prefixed_apply_exact_decimal_scaling
 -> identify_pressure_balance_manometer_transducer_gauge_or_other_method
 -> evaluate_reference_gravity_head_temperature_density_hysteresis_drift_resolution_and_repeatability
 -> record_unit_expression_quantity_kind_reference_type_method_standard_calibration_and_traceability
 -> 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-SI-DERIVED-UNITS-PASCAL-ONTOLOGY-V1"
}

}

END_FLOW