Becquerel Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Becquerel Ontology within the Kireth Research Semantic Library. The becquerel (Bq) is the coherent SI derived unit of radionuclide activity: 1 Bq = 1 s^-1, representing one nuclear transformation per second.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY=Becquerel
 ENTITY_CLASS=SIDerivedUnitOfRadionuclideActivityFramework
 DEFINITION="The becquerel, symbol Bq, is the coherent SI derived unit of activity of a radionuclide. One becquerel corresponds to one nuclear transformation per second."
 SYMBOLIC_FORMS=["1 Bq=1 s^-1","A=-dN/dt","A=lambda N","N(t)=N0 exp(-lambda t)","T_half=ln(2)/lambda"]
 SEMANTIC_ROLE="Machine-readable semantics for radionuclide activity, radioactive decay, nuclear transformations, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE=[
 Becquerel,BecquerelUnit,SIDerivedUnit,DerivedUnit,CoherentDerivedUnit,SI,Second,
 RadionuclideActivity,Activity,Radioactivity,Quantity,QuantityKind,ActivityDimension,
 UnitSymbol,BecquerelDefinition,UnitExpression,UnitAlgebra,DimensionalAnalysis,
 Radionuclide,Nuclide,Isotope,AtomicNucleus,NuclearTransformation,RadioactiveDecay,
 DecayConstant,HalfLife,MeanLifetimeRelationship,ExponentialDecayRelationship,
 ParentNuclideRelationship,DaughterNuclideRelationship,DecayChainRelationship,
 BranchingRatioRelationship,DecayModeRelationship,AlphaDecayRelationship,
 BetaMinusDecayRelationship,BetaPlusDecayRelationship,ElectronCaptureRelationship,
 IsomericTransitionRelationship,SpontaneousFissionRelationship,GammaEmissionRelationship,
 RadioactiveEquilibriumRelationship,BatemanEquationRelationship,SpecificActivityRelationship,
 ActivityConcentrationRelationship,SurfaceActivityRelationship,ReferenceTimeRelationship,
 DecayCorrectionRelationship,DetectionEfficiencyRelationship,CountingEfficiencyRelationship,
 DeadTimeRelationship,LiveTimeRelationship,CountingTimeRelationship,
 BackgroundCountRelationship,NetCountRelationship,CountRateRelationship,
 CountingStatisticsRelationship,PoissonStatisticsRelationship,ActivityMeasurement,
 DoseCalibratorRelationship,RadionuclideCalibratorRelationship,GammaSpectrometryRelationship,
 AlphaSpectrometryRelationship,BetaCountingRelationship,LiquidScintillationCountingRelationship,
 ScintillationDetectorRelationship,SemiconductorDetectorRelationship,HPGeDetectorRelationship,
 GeigerMuellerCounterRelationship,IonisationChamberRelationship,CoincidenceCountingRelationship,
 PrimaryStandardisationRelationship,EfficiencyCalibrationRelationship,Measurement,
 Measurand,MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,
 Repeatability,Reproducibility,DetectionLimitRelationship,MinimumDetectableActivityRelationship,
 Calibration,ActivityCalibrationRelationship,ReferenceStandard,ActivityStandardRelationship,
 RadioactiveReferenceSourceRelationship,MeasurementTraceability,MetrologicalTraceability,
 TraceabilityChain,Metrology,RadionuclideMetrologyRelationship,NuclearMetrologyRelationship,
 GeometryInfluenceRelationship,SelfAbsorptionRelationship,AttenuationRelationship,
 CoincidenceSummingRelationship,DeadTimeCorrectionRelationship,PileUpRelationship,
 BackgroundCorrectionRelationship,DecayCorrectionFactorRelationship,
 RadionuclidicPurityRelationship,SIPrefix,Kilobecquerel,Megabecquerel,
 Gigabecquerel,Terabecquerel,UnitConversion,CurieRelationship,
 DisintegrationsPerMinuteRelationship,Verification,Validation,ErrorAnalysis,
 Provenance,BecquerelProvenance,MeasurementProvenance,CalibrationProvenance,
 NuclearDataProvenanceRelationship,BIPMrelationship,SIbrochureRelationship,
 VIMRelationship,GUMRelationship
 ]
 EXCLUDE_AS_PRIMARY=[BecquerelAsPersonRelationship,HertzWhenFrequencyIsPrimary,GrayWhenAbsorbedDoseIsPrimary,SievertWhenEquivalentOrEffectiveDoseIsPrimary]
 DISAMBIGUATION_RULE="Interpret Bq as radionuclide activity. Although Bq has dimension s^-1, distinguish it from frequency in hertz and radiation dose quantities."
}

CORE_CONCEPTS {
 Becquerel="Coherent SI derived unit of radionuclide activity, symbol Bq."
 RadionuclideActivity="Expected rate of spontaneous nuclear transformations in a radioactive sample."
 ActivityDimension="Inverse-time dimension T^-1."
 DecayConstant="Probability-rate parameter governing radioactive decay."
 HalfLife="Time required for activity or expected undecayed nuclei to fall to one half under exponential decay."
 Radionuclide="Nuclide with an unstable nuclear state capable of spontaneous transformation."
}

RELATIONS {
 Becquerel--is_type_of-->SIDerivedUnit
 Becquerel--is_coherent_derived_unit_of-->RadionuclideActivity
 Becquerel--has_symbol-->Bq
 Becquerel--has_expression-->reciprocal_second
 RadionuclideActivity--has_dimension-->ActivityDimension
 RadionuclideActivity--relates_to-->NuclearTransformationRate
 Activity--equals_under_decay_model-->DecayConstantTimesNumberOfNuclei
 HalfLife--relates_to-->DecayConstant
 DecayChainRelationship--contains-->MultipleNuclearTransformations
 ActivityMeasurement--depends_on-->DetectionEfficiencyAndCountingModel
 MeasurementTraceability--links-->ActivityMeasurementToSI
}

OPERATORS {
 BECQUEREL(value):=radionuclide_activity_quantity(value,Becquerel)
 DIM(Becquerel):=inverse_time_dimension
 ACTIVITY(decay_constant,nuclei):=decay_constant*nuclei
 DECAY_CONSTANT(half_life):=ln(2)/half_life
 HALF_LIFE(decay_constant):=ln(2)/decay_constant
 REMAINING_NUCLEI(N0,decay_constant,time):=N0*exp(-decay_constant*time)
 ACTIVITY_AT_TIME(A0,decay_constant,time):=A0*exp(-decay_constant*time)
 DECAY_CORRECT(A0,decay_constant,time):=A0*exp(-decay_constant*time)
 PREFIX_BECQUEREL(prefix):=decimal_scaled_unit(Becquerel,prefix)
 TRACE_ACTIVITY(result):=traceability_chain_to_SI_becquerel(result)
}

AXIOMS {
 A1="The becquerel is the coherent SI derived unit of radionuclide activity."
 A2="One becquerel corresponds to one nuclear transformation per second."
 A3="The coherent SI expression is s^-1."
 A4="The canonical symbol is Bq."
 A5="Activity and frequency have the same dimensional form but different quantity semantics."
 A6="For simple exponential decay, activity is proportional to undecayed nuclei."
 A7="Half-life and decay constant are related through ln(2)."
 A8="Activity values can require explicit reference-time semantics."
 A9="Activity measurement traceability requires documented standards, nuclear data and calibration."
}

REASONING {
 R1=identify(activity,value,unit,radionuclide,decay_mode,reference_time,geometry,method)
 R2=resolve_becquerel_Bq_hertz_curie_or_person_ambiguity)
 R3=distinguish_activity_count_rate_frequency_absorbed_dose_equivalent_dose)
 R4=verify_inverse_time_dimension_with_activity_semantics)
 R5=expand_becquerel_to_reciprocal_second)
 R6=identify_decay_constant_half_life_branching_decay_chain_reference_time)
 R7=choose_exponential_decay_Bateman_chain_counting_efficiency_or_spectrometry_model)
 R8=identify_activity_measurement_method)
 R9=evaluate_counting_efficiency_geometry_decay_data_dead_time_background_attenuation_and_uncertainty)
 R10=record_radionuclide_data_reference_time_standard_calibration_traceability_and_provenance)
}

CONSTRAINTS {
 C1="Bq is case-sensitive."
 C2="The dimensional identity s^-1 does not make becquerel interchangeable with hertz."
 C3="Activity is not detector count rate; efficiency and response must be considered."
 C4="Activity is not absorbed, equivalent or effective dose."
 C5="Activity requires a reference time when decay over the interval is significant."
 C6="Decay correction requires appropriate half-life or decay-constant data."
 C7="Decay chains can require coupled Bateman models."
 C8="Count rates can require background, dead-time, pile-up, attenuation and coincidence corrections."
 C9="Instrument resolution alone does not determine total activity uncertainty."
 C10="Traceability requires a documented activity standard or validated primary measurement chain."
}

SEMANTIC_EQUIVALENCE {
 "BecquerelUnit"<=>"Becquerel"
 "RadionuclideActivity"<=>"Activity"
 "Radioactivity"<=>"RadionuclideActivity"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}

VALIDATION {
 V1="Unit identity is becquerel and symbol is Bq."
 V2="Quantity kind is radionuclide activity."
 V3="Coherent SI expression is s^-1."
 V4="Activity and frequency remain semantically distinct."
 V5="Activity and detector count rate remain distinct unless response is resolved."
 V6="Reference-time and decay-correction semantics are represented where required."
 V7="Half-life, decay constant, branching and decay-chain data match the radionuclide state."
 V8="SI prefixes use correct decimal scaling."
 V9="Measurement uncertainty includes counting, efficiency, geometry, decay-data, background and calibration effects."
 V10="Activity calibration and traceability evidence are retained."
}

CONFIDENCE {
 BASE_CONFIDENCE=0.99
 BECQUEREL_DEFINITION=0.99
 ACTIVITY_REASONING=0.99
 DECAY_REASONING=0.99
 DECAY_CHAIN_REASONING=0.98
 MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when radionuclide identity, nuclear state, half-life, branching data, reference time, geometry, efficiency, calibration or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,BecquerelReasoning,SIDerivedUnitReasoning,RadionuclideActivityReasoning,RadioactiveDecayReasoning,HalfLifeReasoning,DecayConstantReasoning,DecayChainReasoning,NuclearTransformationReasoning,ActivityMeasurementReasoning,RadionuclideMetrologyReasoning,CountingStatisticsReasoning,CalibrationReasoning,DimensionalReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "becquerel"->Becquerel
  "Bq"->Becquerel
  "kBq"->Kilobecquerel
  "MBq"->Megabecquerel
  "GBq"->Gigabecquerel
  "TBq"->Terabecquerel
 }
}

EXECUTION_RULES {
 E1="Activate BecquerelOntology when Bq denotes the SI unit of radionuclide activity."
 E2="Confirm activity semantics rather than relying only on inverse-time dimensions."
 E3="Map becquerel to s^-1 while preserving radionuclide-activity meaning."
 E4="Distinguish activity from frequency, count rate and radiation dose."
 E5="Preserve radionuclide identity, nuclear state, decay mode and reference time."
 E6="Apply exponential or decay-chain models according to the decay system."
 E7="Apply SI prefixes as exact decimal transformations."
 E8="Evaluate efficiency, geometry, counting statistics, decay corrections, background, dead time, calibration and uncertainty."
 E9="Record nuclear data, reference time, standard, calibration and traceability provenance."
}

RECURSION {
 ENTRY=Becquerel
 EXPAND(Becquerel)->[
 SIDerivedUnits,Second,RadionuclideActivity,ActivityDimension,Radionuclide,Nuclide,
 AtomicNucleus,NuclearTransformation,RadioactiveDecay,DecayConstant,HalfLife,
 ExponentialDecayRelationship,ParentNuclideRelationship,DaughterNuclideRelationship,
 DecayChainRelationship,BranchingRatioRelationship,DecayModeRelationship,
 AlphaDecayRelationship,BetaMinusDecayRelationship,BetaPlusDecayRelationship,
 ElectronCaptureRelationship,GammaEmissionRelationship,RadioactiveEquilibriumRelationship,
 BatemanEquationRelationship,SpecificActivityRelationship,ActivityConcentrationRelationship,
 ReferenceTimeRelationship,DecayCorrectionRelationship,DetectionEfficiencyRelationship,
 CountRateRelationship,CountingStatisticsRelationship,ActivityMeasurement,
 DoseCalibratorRelationship,GammaSpectrometryRelationship,LiquidScintillationCountingRelationship,
 HPGeDetectorRelationship,GeigerMuellerCounterRelationship,IonisationChamberRelationship,
 CoincidenceCountingRelationship,MeasurementUncertainty,Calibration,
 ActivityStandardRelationship,RadioactiveReferenceSourceRelationship,
 MeasurementTraceability,Metrology,RadionuclideMetrologyRelationship,
 DeadTimeCorrectionRelationship,BackgroundCorrectionRelationship,
 SelfAbsorptionRelationship,CoincidenceSummingRelationship,RadionuclidicPurityRelationship,
 Kilobecquerel,Megabecquerel,Gigabecquerel,Terabecquerel,CurieRelationship,
 UnitConversion,Verification,Validation,BecquerelProvenance
 ]
 STOP_CONDITION="Stop when becquerel identity, activity, decay model, reference time, uncertainty and provenance are resolved."
}

ROUTING {
 PARENT_ONTOLOGY="SI Derived Units"
 RELATED_ONTOLOGIES=["SI Derived Units","Second Ontology","Hertz Ontology","Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Reference Standard Ontology","Measurement Uncertainty Ontology","Physics Ontology","Nuclear Physics Ontology","Probability & Statistics Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Becquerel -> Second for reciprocal-second expression",
 "Becquerel -> Hertz to preserve activity-versus-frequency distinction",
 "Becquerel -> Nuclear Physics for radionuclides, transformations and decay chains",
 "Becquerel -> Probability & Statistics for counting statistics",
 "Becquerel -> Measurement and Metrology for calibration and traceability"
 ]
}

UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible radionuclide, decay or measurement relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve becquerel-versus-activity distinction.","Preserve activity-versus-frequency distinction.","Preserve activity-versus-count-rate distinction.","Preserve activity-versus-dose distinction.","Preserve reference-time semantics.","Preserve radionuclide-state and nuclear-data provenance.","Preserve machine-readable becquerel semantics."]
}

OUTPUT {
 CANONICAL_DEFINITION="The becquerel, symbol Bq, is the coherent SI derived unit of radionuclide activity and corresponds to one nuclear transformation per second."
 QUANTITY_SUMMARY="Radionuclide activity is an inverse-time quantity describing the expected rate of spontaneous nuclear transformations."
 DECAY_SUMMARY="For simple exponential decay, activity is related to decay constant, number of nuclei and half-life."
 REFERENCE_TIME_SUMMARY="Activity values can require an explicit reference time and decay correction."
 MEASUREMENT_SUMMARY="Activity can be measured using activity meters, spectrometry, scintillation, ionisation and coincidence methods."
 UNCERTAINTY_SUMMARY="Precision activity measurement can require counting, efficiency, geometry, decay-data, background, dead-time, attenuation and calibration corrections."
}

FLOW {
 INPUT
 -> detect_becquerel_context
 -> identify_activity_value_unit_radionuclide_decay_mode_reference_time_geometry_and_method
 -> resolve_becquerel_Bq_hertz_curie_or_person_ambiguity
 -> distinguish_activity_count_rate_frequency_absorbed_dose_equivalent_dose
 -> verify_inverse_time_dimension_with_activity_semantics
 -> expand_becquerel_to_reciprocal_second
 -> identify_decay_constant_half_life_branching_decay_chain_and_reference_time
 -> choose_decay_counting_spectrometry_or_standardisation_model
 -> identify_activity_measurement_method
 -> evaluate_measurement_uncertainty
 -> record_nuclear_data_reference_time_standard_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-SI-DERIVED-UNITS-BECQUEREL-ONTOLOGY-V1"
}

}

END_FLOW