Mole Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Mole Ontology within the Kireth Research Semantic Library. The mole is the SI base unit of amount of substance, symbol mol. It formalises unit identity, amount-of-substance quantity, amount dimension, the Avogadro-constant definition, elementary entities, molar quantities, chemical measurement, calibration, uncertainty, traceability and provenance.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = Mole
 ENTITY_CLASS = SIBaseUnitOfAmountOfSubstanceFramework
 PRIMARY_CONTEXT = SIBaseUnits
 DEFINITION = "The mole, symbol mol, is the SI base unit of amount of substance. One mole contains exactly 6.02214076×10^23 specified elementary entities, corresponding to the fixed numerical value of the Avogadro constant N_A expressed in mol^-1."
 SYMBOLIC_FORMS = ["N_A=6.02214076e23 mol^-1 exactly","N=n*N_A","n=N/N_A","Q_amount=value*mol"]
 SEMANTIC_ROLE = "Machine-readable semantics for the mole, amount of substance, elementary-entity specification, Avogadro constant, molar quantities, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE = [
 Mole,SIBaseUnit,SIUnit,BaseUnit,MeasurementUnit,Unit,
 InternationalSystemOfUnits,SI,AmountOfSubstance,PhysicalQuantity,Quantity,
 QuantityKind,BaseQuantity,SIBaseQuantity,QuantityValue,Dimension,
 BaseDimension,AmountOfSubstanceDimension,DimensionalSignature,UnitSymbol,
 UnitDefinition,MoleDefinition,DefiningConstant,AvogadroConstant,ExactValue,
 ElementaryEntity,SpecifiedEntity,Atom,Molecule,Ion,ElectronRelationship,
 ParticleRelationship,FormulaUnitRelationship,EntityCount,StoichiometricAmount,
 Substance,ChemicalSpeciesRelationship,MolarQuantity,MolarMass,
 MolarVolumeRelationship,MolarConcentration,AmountConcentration,MoleFraction,
 MassFractionRelationship,MolalityRelationship,Stoichiometry,
 ChemicalEquationRelationship,StoichiometricCoefficientRelationship,
 ExtentOfReactionRelationship,Mass,Kilogram,Gram,AtomicMassRelationship,
 RelativeAtomicMassRelationship,DaltonRelationship,UnitRealisation,
 MoleRealisation,GravimetricRealisationRelationship,CoulometricMethodRelationship,
 TitrimetryRelationship,IsotopeDilutionRelationship,IDMSrelationship,
 ChemicalMeasurement,AnalyticalChemistryRelationship,MeasurementSystem,
 Measurement,Measurand,MeasurementProcedure,MeasurementMethod,
 MeasurementModel,MeasurementResult,MeasurementUncertainty,Accuracy,
 Precision,Repeatability,Reproducibility,Calibration,
 ChemicalCalibrationRelationship,ReferenceStandard,ReferenceMaterial,
 CertifiedReferenceMaterial,CRM,PrimaryReferenceMaterialRelationship,
 StandardSolutionRelationship,MeasurementTraceability,MetrologicalTraceability,
 TraceabilityChain,Metrology,ChemicalMetrologyRelationship,
 ScientificMeasurement,SampleRelationship,SamplingRelationship,
 SamplePreparationRelationship,DilutionRelationship,DissolutionRelationship,
 Purity,ImpurityRelationship,MoistureRelationship,MatrixRelationship,
 MatrixEffectRelationship,RecoveryRelationship,BlankRelationship,
 DetectionLimitRelationship,QuantificationLimitRelationship,
 EnvironmentalCondition,TemperatureInfluence,PressureInfluence,Prefix,SIPrefix,
 Millimole,MicromoleRelationship,NanomoleRelationship,KilomoleRelationship,
 UnitConversion,ConversionFactor,ExactConversion,UnitCompatibility,
 DimensionalCompatibility,QuantityCompatibility,KatalRelationship,
 SIDerivedUnit,UnitExpression,UnitAlgebra,QuantityCalculus,
 DimensionalAnalysis,DimensionalConsistency,Verification,Validation,
 MethodValidationRelationship,ErrorAnalysis,Provenance,MoleProvenance,
 SIUnitProvenance,MeasurementProvenance,CalibrationProvenance,
 ReferenceMaterialProvenanceRelationship,StandardProvenance,
 BIPMrelationship,CGPMrelationship,CIPMrelationship,SIbrochureRelationship,
 VIMRelationship,GUMRelationship,IUPACrelationship,StandardVersion
 ]
 EXCLUDE_AS_PRIMARY = [
 MoleAsAnimalRelationship,MoleAsSkinLesionRelationship,MoleAsSpyRelationship,
 GeneralChemicalConcentrationWhenAmountOfSubstanceUnitIsSecondary,
 EntityCountWithoutAmountOfSubstanceSemantics
 ]
 DISAMBIGUATION_RULE = "When mole or symbol mol denotes the SI base unit of amount of substance, interpret the context as the mole measurement unit and require specification of relevant elementary entities."
}

CORE_CONCEPTS {
 Mole = "SI base unit of amount of substance, symbol mol."
 AmountOfSubstance = "Quantity proportional to the number of specified elementary entities in a sample."
 AmountOfSubstanceDimension = "SI base dimension for amount of substance, represented by N."
 AvogadroConstant = "Defining constant N_A with exact SI value 6.02214076×10^23 mol^-1."
 ElementaryEntity = "Specified entity counted by amount of substance, such as an atom, molecule, ion or other particle."
 MolarQuantity = "Quantity divided by amount of substance."
 MoleRealisation = "Practical determination or preparation of an amount of substance consistent with SI."
}

RELATIONS {
 Mole --is_type_of--> SIBaseUnit
 Mole --is_SI_base_unit_of--> AmountOfSubstance
 AmountOfSubstance --has_dimension--> AmountOfSubstanceDimension
 Mole --has_symbol--> mol
 Mole --is_defined_via--> AvogadroConstant
 AvogadroConstant --has_exact_value--> 6.02214076e23_per_mol
 AmountOfSubstance --counts--> SpecifiedElementaryEntities
 EntityCount --equals--> AmountOfSubstance_times_AvogadroConstant
 MolarQuantity --is_quantity_per--> AmountOfSubstance
 MoleRealisation --implements--> MoleDefinition
 ChemicalCalibrationRelationship --uses--> ReferenceMaterial
 MeasurementTraceability --links--> ChemicalMeasurementToSI
 Provenance --records--> MoleDefinitionRealisationAndMeasurementHistory
}

OPERATORS {
 MOLE(value,entity) := amount_of_substance(value,Mole,entity)
 DIM(Mole) := AmountOfSubstanceDimension
 ENTITY_COUNT(n) := n*AvogadroConstant
 AMOUNT_FROM_COUNT(N_entities) := N_entities/AvogadroConstant
 MOLAR(quantity,n) := quantity/n
 AMOUNT_CONCENTRATION(n,volume) := n/volume
 PREFIX_MOLE(prefix) := decimal_scaled_unit(Mole,prefix)
 CONVERT_AMOUNT(value,source,target) := compatible_amount_conversion(value,source,target)
 TRACE_AMOUNT(result) := traceability_chain_to_SI_mole(result)
}

AXIOMS {
 A1 = "The mole is the SI base unit of amount of substance."
 A2 = "The canonical symbol of the mole is mol."
 A3 = "Amount of substance has the SI base dimension N."
 A4 = "The Avogadro constant has the exact SI value 6.02214076×10^23 mol^-1."
 A5 = "One mole contains exactly 6.02214076×10^23 specified elementary entities."
 A6 = "Elementary entities must be specified whenever their identity is material."
 A7 = "Amount of substance and mass are distinct quantities linked through molar mass."
 A8 = "Molar concentration and amount of substance are distinct quantities."
 A9 = "Mole reasoning requires explicit entity identity, amount, definition, chemical context, uncertainty and traceability semantics."
}

REASONING {
 R1_CONTEXT = identify(amount_of_substance,value,unit,elementary_entity,sample_composition_and_intended_use)
 R2_IDENTITY = resolve_mole_prefixed_mole_entity_count_or_related_chemical_quantity)
 R3_ENTITY = identify_and_validate_specified_atoms_molecules_ions_electrons_or_other_entities)
 R4_DIMENSION = verify_quantity_kind_amount_of_substance_and_dimension_N)
 R5_DEFINITION = identify_Avogadro_constant_exact_definition_relationship)
 R6_RELATIONS = resolve_entity_count_molar_mass_concentration_fraction_and_stoichiometric_relationships)
 R7_MEASUREMENT = identify_gravimetric_coulometric_titrimetric_IDMS_or_other_traceable_method)
 R8_SAMPLE = evaluate_purity_impurities_matrix_sampling_preparation_recovery_and_blank_effects)
 R9_UNCERTAINTY = propagate_reference_material_calibration_sampling_method_purity_repeatability_and_correction_components)
 R10_PROVENANCE = record_definition_version_entity_specification_method_reference_materials_conditions_and_traceability)
}

CONSTRAINTS {
 C1 = "The symbol mol must be distinguished from unrelated abbreviations."
 C2 = "A mole statement is incomplete when elementary entities are materially ambiguous."
 C3 = "Amount of substance must not be conflated with mass."
 C4 = "Molar mass links mass and amount but is a distinct derived quantity."
 C5 = "Molar concentration depends on volume and can depend on temperature and pressure."
 C6 = "Chemical measurement uncertainty can include sampling, purity, recovery, matrix and calibration contributions."
 C7 = "Reference-material values require appropriate matrix, analyte and intended-use compatibility."
 C8 = "Instrument resolution alone does not determine total chemical-measurement uncertainty."
 C9 = "Traceability to the mole requires a documented measurement model and reference chain."
 C10 = "Historical carbon-12 wording must not be treated as the current defining basis of the mole."
}

SEMANTIC_EQUIVALENCE {
 "InternationalSystemOfUnits" <=> "SI"
 "MetrologicalTraceability" <=> "MeasurementTraceability"
 "CertifiedReferenceMaterial" <=> "CRM"
 "IsotopeDilutionMassSpectrometry" <=> "IDMS"
}

VALIDATION {
 V1 = "Unit identity is mole and canonical symbol is mol."
 V2 = "Quantity kind is amount of substance."
 V3 = "Base dimension is N."
 V4 = "Modern definition uses the exact SI numerical value of the Avogadro constant."
 V5 = "Elementary entities are explicitly specified where material."
 V6 = "Entity-count relations preserve N_entities = n*N_A."
 V7 = "Mass, molar mass, amount and concentration semantics remain distinct."
 V8 = "Sample preparation, purity, matrix and recovery effects are documented where material."
 V9 = "Measurement uncertainty and traceability evidence are retained."
 V10 = "Definition, method, reference-material and calibration relationships are traceable to documented standards and versions."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 MOLE_DEFINITION = 0.99
 AMOUNT_OF_SUBSTANCE_REASONING = 0.99
 ENTITY_SPECIFICATION_REASONING = 0.99
 DIMENSION_REASONING = 0.99
 AVOGADRO_CONSTANT_REASONING = 0.99
 CHEMICAL_MEASUREMENT_REASONING = 0.98
 TRACEABILITY_REASONING = 0.99
 POLICY = "Reduce confidence when elementary entity, sample composition, measurement model, reference material, purity, method or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
 SemanticSearch,OntologyGrounding,MoleReasoning,SIBaseUnitReasoning,
 AmountOfSubstanceReasoning,ElementaryEntityReasoning,AvogadroConstantReasoning,
 EntityCountReasoning,MolarQuantityReasoning,StoichiometryReasoning,
 ChemicalMeasurementReasoning,ChemicalMetrologyReasoning,
 ReferenceMaterialReasoning,CalibrationReasoning,UncertaintyReasoning,
 TraceabilityReasoning,KnowledgeGraphConstruction,RetrievalAugmentation,
 RecursiveInference
 ]
 NORMALISE {
  "mole" -> Mole
  "mol" -> Mole
  "SI" -> InternationalSystemOfUnits
  "CRM" -> CertifiedReferenceMaterial
  "IDMS" -> IsotopeDilutionMassSpectrometry
 }
}

EXECUTION_RULES {
 E1 = "If mole or symbol mol denotes the SI base unit of amount of substance, activate MoleOntology."
 E2 = "Confirm quantity kind amount of substance and base dimension N."
 E3 = "Identify the specified elementary entity whenever scientifically material."
 E4 = "Use the modern Avogadro-constant defining relationship when formal definition semantics are required."
 E5 = "Preserve exact entity-count relation N_entities = n*N_A."
 E6 = "Distinguish amount of substance from mass, molar mass, concentration and fraction."
 E7 = "Evaluate sampling, purity, matrix, recovery and reference-material effects where material."
 E8 = "Distinguish mole definition from practical chemical measurement and calibration."
 E9 = "Preserve uncertainty and record definition versions, entity specification, methods, references and provenance."
}

RECURSION {
 ENTRY = Mole
 EXPAND(Mole) -> [
 SIBaseUnits,SIBaseUnit,SIUnits,InternationalSystemOfUnits,SI,
 AmountOfSubstance,PhysicalQuantity,Quantity,QuantityKind,QuantityValue,
 AmountOfSubstanceDimension,Dimension,BaseDimension,DimensionalSignature,
 Unit,MeasurementUnit,UnitSymbol,MoleDefinition,DefiningConstant,
 AvogadroConstant,ElementaryEntity,SpecifiedEntity,Atom,Molecule,Ion,
 EntityCount,StoichiometricAmount,Substance,ChemicalSpeciesRelationship,
 MolarQuantity,MolarMass,MolarConcentration,AmountConcentration,MoleFraction,
 Stoichiometry,ExtentOfReactionRelationship,Mass,Kilogram,Gram,
 UnitRealisation,MoleRealisation,GravimetricRealisationRelationship,
 CoulometricMethodRelationship,TitrimetryRelationship,IDMSrelationship,
 ChemicalMeasurement,MeasurementSystem,Measurement,Measurand,
 MeasurementResult,MeasurementUncertainty,Calibration,ReferenceStandard,
 ReferenceMaterial,CertifiedReferenceMaterial,CRM,MeasurementTraceability,
 Metrology,ChemicalMetrologyRelationship,SampleRelationship,
 SamplingRelationship,SamplePreparationRelationship,Purity,
 MatrixRelationship,RecoveryRelationship,BlankRelationship,SIPrefix,
 Millimole,MicromoleRelationship,NanomoleRelationship,UnitConversion,
 KatalRelationship,SIDerivedUnit,DimensionalAnalysis,Verification,
 Validation,MoleProvenance
 ]
 EXPAND(MoleFamilies) -> [
 MoleIdentitySymbolQuantityAndDimension,
 AvogadroConstantDefinitionAndEntityCountSemantics,
 ElementaryEntitiesAtomsMoleculesIonsAndParticles,
 MassMolarMassConcentrationFractionAndStoichiometry,
 ChemicalMeasurementMethodsAndAmountRealisation,
 ReferenceMaterialsSamplingPurityMatrixAndRecovery,
 UncertaintyCalibrationAndTraceability,
 ValidationStandardsVersionsAndProvenance
 ]
 STOP_CONDITION = "Stop when mole identity, amount quantity, entity specification, dimension, definition, chemical relationships, measurement, uncertainty and provenance are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "SI Base Units"
 RELATED_ONTOLOGIES = [
 "SI Base Units","SI Units Ontology","Measurement & Units Ontologies",
 "Foundations of Measurement","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","Chemistry Ontology",
 "Probability & Statistics Ontologies","Verification & Validation"
 ]
 ROUTE_RULES = [
 "Mole -> SI Base Units for parent base-unit semantics",
 "Mole -> SI Units Ontology for system-wide SI semantics",
 "Mole -> Quantity and Physical Quantity ontologies for amount-of-substance semantics",
 "Mole -> Dimension Ontology for base dimension N",
 "Mole -> Unit Ontology for unit identity, prefixes and conversion",
 "Mole -> Measurement and Scientific Measurement for chemical measurement",
 "Mole -> Metrology and Reference Standard for chemical calibration and traceability",
 "Mole -> Chemistry Ontology for species, stoichiometry and composition semantics",
 "Mole -> Measurement Uncertainty for uncertainty evaluation",
 "Mole -> Verification & Validation for quantity, method and consistency checks"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible mole realisation, chemical measurement or reasoning relationships"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
 "Preserve mole-versus-amount-of-substance distinction.",
 "Preserve amount-of-substance-versus-entity-count distinction.",
 "Preserve amount-versus-mass distinction.",
 "Preserve amount-versus-concentration distinction.",
 "Preserve unit-versus-quantity distinction.",
 "Preserve mole-definition-versus-practical-measurement distinction.",
 "Preserve historical-carbon-12-versus-current-definition distinction.",
 "Preserve machine-readable mole semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "The mole, symbol mol, is the SI base unit of amount of substance; one mole contains exactly 6.02214076×10^23 specified elementary entities."
 QUANTITY_SUMMARY = "The mole expresses amount of substance, whose SI base dimension is N."
 DEFINITION_SUMMARY = "The exact Avogadro constant N_A = 6.02214076×10^23 mol^-1 establishes the relation between amount of substance and entity count."
 ENTITY_SUMMARY = "Atoms, molecules, ions, electrons or other elementary entities must be specified when their identity is material."
 CHEMICAL_SUMMARY = "Amount of substance connects to molar mass, concentration, composition and stoichiometric relationships while remaining a distinct quantity."
 UNCERTAINTY_SUMMARY = "Chemical amount measurements can require uncertainty contributions from sampling, purity, matrix effects, recovery, reference materials, calibration and repeatability."
 VALIDATION_SUMMARY = "Mole semantics should preserve unit identity, amount quantity, entity specification, dimension, definition, chemical relationships, uncertainty and provenance."
}

FLOW {
 INPUT
 -> detect_mole_context
 -> identify_amount_of_substance_value_unit_elementary_entity_sample_composition_and_intended_use
 -> resolve_mole_prefixed_mole_entity_count_or_related_chemical_quantity
 -> identify_and_validate_specified_elementary_entities
 -> verify_quantity_kind_amount_of_substance_and_dimension_N
 -> identify_Avogadro_constant_exact_definition_relationship
 -> resolve_entity_count_molar_mass_concentration_fraction_and_stoichiometric_relationships
 -> identify_traceable_chemical_measurement_method
 -> evaluate_purity_impurities_matrix_sampling_preparation_recovery_and_blank_effects
 -> propagate_reference_material_calibration_sampling_method_purity_repeatability_and_correction_uncertainty
 -> record_definition_version_entity_specification_method_reference_materials_conditions_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-BASE-UNITS-MOLE-ONTOLOGY-V1"
}

}

END_FLOW