Time Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Time Ontology within the Kireth Research Semantic Library. Time is an SI base quantity with dimension T and coherent SI base unit second, symbol s. It formalises duration, intervals, temporal ordering, coordinate and proper time, clocks, time scales, measurement, uncertainty and traceability.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME="Time Ontology"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Fundamental Physical Quantities / Time"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/fundamental-physical-quantities/time-ontology.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}

IDENTITY {
 PRIMARY_ENTITY=Time
 ENTITY_CLASS=SIBasePhysicalQuantityFramework
 DEFINITION="Time is a fundamental physical quantity used to describe duration, temporal separation, ordering and evolution of physical systems. Its SI base dimension is T and its coherent SI base unit is the second, symbol s."
 SYMBOLIC_FORMS=["dim(time)=T","SI_unit(time)=s","Delta_t=t2-t1","f=1/T_period","v=dx/dt"]
 SEMANTIC_ROLE="Machine-readable semantics for time, duration, temporal intervals, clocks, time scales, dynamics, measurement, uncertainty and traceability."
}

SCOPE {
 INCLUDE=[
 Time,TimeQuantity,FundamentalPhysicalQuantity,BaseQuantity,PhysicalQuantity,
 Quantity,QuantityKind,QuantityValue,SI,InternationalSystemOfQuantities,
 BaseDimension,TimeDimension,Dimension,Second,SIBaseUnit,MeasurementUnit,Unit,
 UnitSymbol,Duration,TimeInterval,TemporalInterval,ElapsedTimeRelationship,
 Instant,TimePointRelationship,TemporalPositionRelationship,TemporalOrderingRelationship,
 BeforeRelationship,AfterRelationship,SimultaneityRelationship,Period,
 PeriodicityRelationship,CycleRelationship,OscillationRelationship,Frequency,
 HertzRelationship,AngularFrequencyRelationship,PhaseRelationship,RateRelationship,
 Velocity,Acceleration,HalfLifeRelationship,DecayConstantRelationship,
 LifetimeRelationship,TimeConstantRelationship,ResponseTimeRelationship,
 DelayRelationship,LatencyRelationship,TransitTimeRelationship,TimeOfFlightRelationship,
 CoordinateTimeRelationship,ProperTimeRelationship,ReferenceFrameRelationship,
 InertialFrameRelationship,SpecialRelativityRelationship,GeneralRelativityRelationship,
 TimeDilationRelationship,GravitationalTimeDilationRelationship,
 RelativityOfSimultaneityRelationship,SpacetimeRelationship,WorldlineRelationship,
 CausalityRelationship,ClockRelationship,PhysicalClockRelationship,
 AtomicClockRelationship,CaesiumClockRelationship,OpticalClockRelationship,
 QuartzClockRelationship,OscillatorRelationship,FrequencyStandardRelationship,
 TimeStandardRelationship,TimeScaleRelationship,AtomicTimeRelationship,
 InternationalAtomicTimeRelationship,TAIrelationship,UTCrelationship,
 UT1relationship,GPSSystemTimeRelationship,GNSSSystemTimeRelationship,
 LocalTimeRelationship,TimeZoneRelationship,CivilTimeRelationship,
 CalendarTimeRelationship,DateRelationship,LeapSecondRelationship,
 EarthRotationRelationship,EpochRelationship,ReferenceEpochRelationship,
 UnixTimeRelationship,JulianDateRelationship,SynchronisationRelationship,
 ClockSynchronisationRelationship,TimeTransferRelationship,FrequencyTransferRelationship,
 SatelliteTimeTransferRelationship,FibreTimeTransferRelationship,
 NetworkTimeRelationship,NTPrelationship,PTPrelationship,TimeMeasurement,
 DurationMeasurement,FrequencyMeasurementRelationship,PeriodMeasurementRelationship,
 ClockComparisonRelationship,StopwatchRelationship,TimerRelationship,
 FrequencyCounterRelationship,TimeIntervalCounterRelationship,MeasurementSystem,
 Measurand,Measurement,MeasurementMethod,MeasurementProcedure,MeasurementModel,
 MeasurementResult,MeasurementUncertainty,Accuracy,Precision,Resolution,
 Repeatability,Reproducibility,Stability,FrequencyStabilityRelationship,
 TimeStabilityRelationship,PhaseNoiseRelationship,AllanDeviationRelationship,
 TimeDeviationRelationship,ClockOffsetRelationship,ClockDriftRelationship,
 FrequencyOffsetRelationship,JitterRelationship,Calibration,
 TimeCalibrationRelationship,FrequencyCalibrationRelationship,
 ReferenceStandard,TimeStandard,FrequencyStandard,SecondRealisationRelationship,
 Caesium133Relationship,HyperfineTransitionRelationship,MeasurementTraceability,
 MetrologicalTraceability,TraceabilityChain,Metrology,
 TimeAndFrequencyMetrologyRelationship,TemperatureInfluence,
 MagneticFieldInfluenceRelationship,RelativisticCorrectionRelationship,
 GravitationalPotentialRelationship,HeightCorrectionRelationship,
 MotionCorrectionRelationship,SignalPropagationRelationship,CableDelayRelationship,
 AntennaDelayRelationship,ReceiverDelayRelationship,AtmosphericDelayRelationship,
 IonosphericDelayRelationship,TroposphericDelayRelationship,MultipathRelationship,
 TriggerErrorRelationship,QuantisationRelationship,SamplingRelationship,
 TimestampRelationship,TimestampUncertaintyRelationship,SIPrefix,Femtosecond,
 Picosecond,Nanosecond,Microsecond,Millisecond,MinuteRelationship,
 HourRelationship,DayRelationship,YearRelationship,UnitConversion,
 Verification,Validation,ErrorAnalysis,Provenance,TimeProvenance,
 QuantityProvenance,UnitProvenance,MeasurementProvenance,CalibrationProvenance,
 TimeScaleProvenanceRelationship,BIPMrelationship,SIbrochureRelationship,
 VIMRelationship,GUMRelationship,IERSrelationship
 ]
 EXCLUDE_AS_PRIMARY=[FrequencyWhenCyclesPerTimeIsPrimary,DateWhenCalendarRepresentationIsPrimary,TimeZoneWhenCivilOffsetRulesArePrimary,SpatialDistanceWhenLengthIsPrimary]
 DISAMBIGUATION_RULE="Interpret time as a physical base quantity with dimension T. Distinguish it from clock readings, timestamps, calendar dates, civil time zones and frequency."
}

CORE_CONCEPTS {
 Time="Fundamental physical quantity describing duration, temporal separation and evolution."
 TimeDimension="Base physical dimension T."
 Second="Coherent SI base unit of time, symbol s."
 Duration="Magnitude of a time interval between events or instants."
 Instant="Temporal position within a specified time scale or coordinate system."
 Period="Duration associated with one cycle of a periodic phenomenon."
 Frequency="Number of cycles or events per unit time, dimension T^-1."
 ProperTimeRelationship="Time measured along a timelike worldline by an ideal clock."
 CoordinateTimeRelationship="Time coordinate assigned within a specified reference system."
}

BASE_QUANTITY {
 QUANTITY=Time
 DIMENSION=T
 SI_BASE_UNIT=Second
 UNIT_SYMBOL=s
 STATUS="SI base quantity"
}

RELATIONS {
 Time--is_type_of-->FundamentalPhysicalQuantity
 Time--is_base_quantity_in-->InternationalSystemOfQuantities
 Time--has_dimension-->TimeDimension
 Time--has_SI_base_unit-->Second
 Second--has_symbol-->s
 Duration--has_dimension-->TimeDimension
 Period--has_dimension-->TimeDimension
 Frequency--has_dimension-->T_inverse
 Frequency--is_reciprocal_of-->Period
 Velocity--depends_on-->LengthAndTime
 Acceleration--depends_on-->LengthAndTimeSquared
 ProperTimeRelationship--depends_on-->WorldlineAndSpacetimeMetric
 CoordinateTimeRelationship--depends_on-->ReferenceSystem
 AtomicClockRelationship--realises_or_maintains-->TimeOrFrequencyReference
 MeasurementTraceability--links-->TimeMeasurementToSI
}

OPERATORS {
 TIME(value,unit):=time_quantity(value,unit)
 DIM(Time):=T
 INTERVAL(t1,t2):=t2-t1
 FREQUENCY(period):=1/period
 PERIOD(frequency):=1/frequency
 RATE(change,time_interval):=change/time_interval
 VELOCITY(displacement,time_interval):=displacement/time_interval
 DECAY_CONSTANT(half_life):=ln(2)/half_life
 CLOCK_OFFSET(clock_time,reference_time):=clock_time-reference_time
 PREFIX_SECOND(prefix):=decimal_scaled_unit(Second,prefix)
 CONVERT_TIME(value,source,target):=compatible_time_conversion(value,source,target)
 TRACE_TIME(result):=traceability_chain_to_SI_second(result)
}

AXIOMS {
 A1="Time is an SI base quantity."
 A2="The base dimension of time is T."
 A3="The coherent SI base unit of time is the second, symbol s."
 A4="Time is distinct from its numerical value, unit, timestamp and calendar representation."
 A5="A duration or time interval has time dimension T."
 A6="Frequency has inverse-time dimension T^-1 and is distinct from time."
 A7="Period and frequency are reciprocal only for appropriately defined periodic phenomena."
 A8="Relativistic time comparisons require specified worldlines, reference frames or coordinate systems."
 A9="Clock readings require an identified time scale or reference to be globally interpretable."
 A10="High-accuracy time and frequency metrology requires calibration, uncertainty, synchronisation and traceability."
}

REASONING {
 R1=identify(time_quantity,value,unit,event_or_interval,clock,time_scale,reference_frame,measurement_method)
 R2=distinguish_time_duration_instant_period_frequency_timestamp_date_time_zone_or_related_entity)
 R3=verify_base_dimension_T)
 R4=resolve_second_prefixed_second_nonSI_time_unit_and_conversion)
 R5=identify_interval_ordering_periodic_clock_time_scale_coordinate_time_or_proper_time_context)
 R6=identify_reference_epoch_time_scale_reference_frame_worldline_or_clock_reference)
 R7=apply_relativistic_corrections_when_precision_motion_or_gravitational_potential_requires_them)
 R8=identify_atomic_clock_counter_timer_time_interval_time_transfer_or_other_method)
 R9=evaluate_clock_offset_stability_jitter_propagation_delay_environment_relativistic_corrections_and_calibration)
 R10=record_quantity_unit_time_scale_epoch_reference_frame_method_standard_calibration_traceability_and_provenance)
}

CONSTRAINTS {
 C1="Time must not be conflated with frequency."
 C2="A clock reading is an observation or representation of time, not the base quantity itself."
 C3="A timestamp requires an identified time scale, epoch and representation."
 C4="Calendar date and civil time are conventional representations and are not identical to physical duration."
 C5="UTC, TAI, UT1 and GNSS time scales must not be treated as interchangeable."
 C6="Minute, hour and day conversions require applicable conventional definitions."
 C7="Relativistic precision timing requires motion and gravitational-potential effects to be considered."
 C8="Signal-transfer timing can require propagation, equipment and atmospheric delay corrections."
 C9="Instrument resolution alone does not determine total time uncertainty."
 C10="Traceability to the second requires a documented time or frequency realisation and calibration chain."
}

SEMANTIC_EQUIVALENCE {
 "TimeQuantity"<=>"Time"
 "TemporalDuration"<=>"Duration"
 "SIUnitOfTime"<=>"Second"
 "InternationalSystemOfUnits"<=>"SI"
 "MetrologicalTraceability"<=>"MeasurementTraceability"
}

VALIDATION {
 V1="Quantity identity is time or an explicitly compatible time quantity."
 V2="Base dimension is T."
 V3="Coherent SI base unit is second with symbol s."
 V4="Time, duration, instant, frequency, timestamp and date semantics remain distinct."
 V5="Period-frequency reciprocal relationships are applied only where appropriate."
 V6="Time-scale and epoch information are explicit for timestamps and clock comparisons."
 V7="Reference-frame and relativistic assumptions are explicit where significant."
 V8="Unit conversion preserves time quantity kind and scale."
 V9="Measurement uncertainty includes clock, transfer, environment, model and calibration effects."
 V10="Time and frequency calibration and traceability evidence are retained."
}

CONFIDENCE {
 BASE_CONFIDENCE=0.99
 TIME_DEFINITION=0.99
 BASE_DIMENSION_REASONING=0.99
 SECOND_UNIT_REASONING=0.99
 TEMPORAL_REASONING=0.99
 TIME_SCALE_REASONING=0.98
 RELATIVITY_REASONING=0.98
 TIME_MEASUREMENT_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when time scale, epoch, reference frame, worldline, clock reference, method, calibration or traceability are underspecified."
}

AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,TimeReasoning,FundamentalQuantityReasoning,BaseQuantityReasoning,TemporalReasoning,DurationReasoning,FrequencyReasoning,DynamicsReasoning,RelativityReasoning,TimeScaleReasoning,ClockReasoning,SynchronisationReasoning,DimensionalReasoning,SecondReasoning,UnitConversionReasoning,TimeMeasurementReasoning,TimeFrequencyMetrologyReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,KnowledgeGraphConstruction,RecursiveInference]
 NORMALISE {
  "time"->Time
  "duration"->Duration
  "second"->Second
  "seconds"->Second
  "s"->Second
  "ms"->Millisecond
  "us"->Microsecond
  "ns"->Nanosecond
 }
}

EXECUTION_RULES {
 E1="Activate TimeOntology when reasoning concerns physical duration, temporal separation or time evolution."
 E2="Distinguish time from frequency, timestamp, date, time zone and clock reading."
 E3="Map time to base dimension T and SI base unit second."
 E4="Resolve time scale, epoch, reference frame and clock reference where required."
 E5="Apply compatible time-unit conversions with correct scaling and conventions."
 E6="For precision timing, evaluate synchronisation, propagation, clock stability and relativistic effects."
 E7="Preserve measurement method, calibration, uncertainty and traceability."
 E8="Route frequency, decay, rate and specialised temporal quantities when they become primary."
 E9="Record quantity, unit, time scale, reference system, measurement and provenance."
}

RECURSION {
 ENTRY=Time
 EXPAND(Time)->[
 FundamentalPhysicalQuantities,PhysicalQuantity,BaseQuantity,TimeDimension,
 Second,SIBaseUnits,Quantity,QuantityKind,QuantityValue,Unit,Dimension,
 Duration,TimeInterval,Instant,TemporalOrderingRelationship,Period,Frequency,
 HertzRelationship,RateRelationship,Velocity,Acceleration,HalfLifeRelationship,
 TimeConstantRelationship,CoordinateTimeRelationship,ProperTimeRelationship,
 ReferenceFrameRelationship,SpecialRelativityRelationship,GeneralRelativityRelationship,
 TimeDilationRelationship,SpacetimeRelationship,ClockRelationship,
 AtomicClockRelationship,CaesiumClockRelationship,OpticalClockRelationship,
 FrequencyStandardRelationship,TimeStandardRelationship,TAIrelationship,
 UTCrelationship,UT1relationship,GPSSystemTimeRelationship,EpochRelationship,
 SynchronisationRelationship,TimeTransferRelationship,NTPrelationship,
 PTPrelationship,TimeMeasurement,FrequencyMeasurementRelationship,
 TimeIntervalCounterRelationship,MeasurementUncertainty,AllanDeviationRelationship,
 ClockOffsetRelationship,ClockDriftRelationship,JitterRelationship,Calibration,
 SecondRealisationRelationship,Caesium133Relationship,MeasurementTraceability,
 TimeAndFrequencyMetrologyRelationship,RelativisticCorrectionRelationship,
 SignalPropagationRelationship,CableDelayRelationship,AtmosphericDelayRelationship,
 Femtosecond,Picosecond,Nanosecond,Microsecond,Millisecond,MinuteRelationship,
 HourRelationship,DayRelationship,UnitConversion,Verification,Validation,TimeProvenance
 ]
 EXPAND(TimeFamilies)->[
 TimeIdentityBaseQuantityDimensionAndSecond,
 DurationIntervalsInstantsOrderingAndPeriodicity,
 FrequencyRatesDerivativesDynamicsAndDecay,
 CoordinateTimeProperTimeRelativityAndSpacetime,
 AtomicClocksFrequencyStandardsAndSecondRealisation,
 TAIUTCUT1GNSSCivilTimeScalesEpochsAndCalendars,
 SynchronisationTimeTransferNetworkAndSatelliteTiming,
 MeasurementStabilityUncertaintyCalibrationTraceabilityAndProvenance
 ]
 STOP_CONDITION="Stop when time identity, dimension, unit, temporal reference, measurement uncertainty and provenance are resolved."
}

ROUTING {
 PARENT_ONTOLOGY="Fundamental Physical Quantities"
 RELATED_ONTOLOGIES=["Fundamental Physical Quantities","SI Base Units","Second Ontology","Hertz Ontology","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology","Measurement Ontology","Metrology Ontology","Reference Standard Ontology","Measurement Uncertainty Ontology","Physics Ontology","Relativity Ontology","Astronomy Ontology","Verification & Validation"]
 ROUTE_RULES=[
 "Time -> Fundamental Physical Quantities for base-quantity semantics",
 "Time -> Second Ontology for SI base-unit definition and realisation",
 "Time -> Hertz Ontology for frequency and reciprocal-time relationships",
 "Time -> Quantity and Dimension ontologies for quantity-kind and dimension semantics",
 "Time -> Relativity for coordinate time, proper time and time dilation",
 "Time -> Astronomy for Earth-rotation and astronomical time-scale relationships",
 "Time -> Measurement and Metrology for clock measurement, calibration and traceability"
 ]
}

UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible temporal, timing, relativistic or measurement relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve time-versus-unit distinction.","Preserve time-versus-frequency distinction.","Preserve duration-versus-instant distinction.","Preserve physical-time-versus-clock-reading distinction.","Preserve physical-time-versus-calendar-representation distinction.","Preserve time-scale distinctions.","Preserve relativistic reference semantics.","Preserve machine-readable time semantics."]
}

OUTPUT {
 CANONICAL_DEFINITION="Time is a fundamental physical quantity with base dimension T and coherent SI base unit second, symbol s."
 TEMPORAL_SUMMARY="Time describes duration, temporal separation, ordering and physical evolution."
 FREQUENCY_SUMMARY="Frequency is an inverse-time quantity and period is a time quantity; they are reciprocal for defined periodic phenomena."
 RELATIVITY_SUMMARY="Coordinate time and proper time require explicit reference-system and worldline semantics in relativistic contexts."
 TIMESCALE_SUMMARY="TAI, UTC, UT1 and GNSS time scales have distinct definitions and must retain their reference semantics."
 MEASUREMENT_SUMMARY="Time can be measured and disseminated using atomic clocks, counters, time-transfer systems and synchronised networks."
 UNCERTAINTY_SUMMARY="Precision timing can require clock-stability, propagation-delay, environmental, synchronisation, relativistic and calibration uncertainty contributions."
}

FLOW {
 INPUT
 -> detect_time_context
 -> identify_time_quantity_value_unit_event_interval_clock_time_scale_reference_frame_and_method
 -> distinguish_time_duration_instant_period_frequency_timestamp_date_time_zone_or_related_entity
 -> verify_base_dimension_T
 -> resolve_second_prefixed_second_nonSI_time_unit_and_conversion
 -> identify_interval_ordering_periodic_clock_time_scale_coordinate_time_or_proper_time_context
 -> identify_reference_epoch_time_scale_reference_frame_worldline_or_clock_reference
 -> apply_relativistic_corrections_when_required
 -> identify_time_measurement_or_transfer_method
 -> evaluate_clock_transfer_environment_model_and_calibration_uncertainty
 -> record_quantity_unit_time_scale_epoch_reference_frame_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-FUNDAMENTAL-PHYSICAL-QUANTITIES-TIME-ONTOLOGY-V1"
}

}

END_FLOW