OML formalization of VIM4 Committee Draft 11 January 2021

Commit Snapshot, 10 January 2022

This version:: https://opencaesar.github.io/metrology-vocabularies/bipm.org/jcgm/vim4
Editor:: Jet Propulsion Laboratory
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1. Namespace

http://bipm.org/jcgm/vim4 [vim4]

2. Imports

http://purl.org/dc/elements/1.1 [dc]
http://www.w3.org/2000/01/rdf-schema [rdfs]
http://www.w3.org/2002/07/owl [owl]
http://www.w3.org/2001/XMLSchema [xsd]
http://iso.org/iso-1087-1 [iso-1087-1]

3. Aspects

3.1. GeneralProperty

Supertypes	IdentifiedElement
Subtypes	GeneralNominalProperty GeneralQuantity

3.2. GeneralQuantity

General quantity in [VIM4 CD: 1.1] corresponds precisely to kind-of-quantity in [OonP: S.13.3.1].

property whose instances can be compared by ratio or only by order

Supertypes	GeneralProperty
Subtypes	GeneralOrdinalQuantity GeneralUnitaryQuantity
Relations with target	IndividualQuantity ← Instantiates → GeneralQuantity

3.3. HasCoherence

Subtypes	SystemHasDerivedUnit SystemOfUnits
Properties	isCoherent

3.4. IdentifiedElement

Subtypes	GeneralProperty IndividualProperty Measurement MeasurementMethod MeasurementModel MeasurementPrinciple MeasurementProcedure MeasurementScale Multiple SystemOfQuantities SystemOfUnits
Properties	id
Keys	id

3.5. IndividualProperty

Supertypes	IdentifiedElement
Subtypes	IndividualNominalProperty IndividualQuantity
Relations with target	MeasurementScale ← Includes → IndividualProperty

3.6. IndividualQuantity

instance of a general quantity

Supertypes	IndividualProperty
Subtypes	IndividualOrdinalQuantity IndividualUnitaryQuantity
Relations with source	IndividualQuantity ← Characterizes → Object IndividualQuantity ← Instantiates → GeneralQuantity
Relations with target	MeasurementModel ← HasInput → IndividualQuantity QuantityValue ← IsAttributedTo → IndividualQuantity MeasurementModel ← IsInfluencedBy → IndividualQuantity MeasurementModel ← Measures → IndividualQuantity MeasurementModel ← UsesCorrection → IndividualQuantity

3.7. Object

Relations with target	IndividualQuantity ← Characterizes → Object

3.8. QuantityValue

Subtypes	OrdinalQuantityValue UnitaryQuantityValue
Properties	isReferenceValue isTrueValue
Relations with source	QuantityValue ← IsAttributedTo → IndividualQuantity
Relations with target	MeasurementModel ← YieldsMeasuredValue → QuantityValue

3.9. RationalExponent

Subtypes	HasPowerOfUnitFactor HasPowerOfUnitaryQuantityFactor HasQuantityDimension
Properties	exponent (must have exactly 1)

4. Concepts

4.1. GeneralNominalProperty

Supertypes	GeneralProperty

4.2. GeneralOrdinalQuantity

general quantity whose instances can be compared by order but not by ratio

Supertypes	GeneralQuantity

4.3. GeneralUnitaryQuantity

general quantity whose instances can be compared by ratio

Supertypes	GeneralQuantity
Relations with source	GeneralUnitaryQuantity ← Specializes → GeneralUnitaryQuantity
Relations with target	GeneralUnitaryQuantity ← Specializes → GeneralUnitaryQuantity SystemOfQuantities ← SystemHasBaseUnitaryQuantity → GeneralUnitaryQuantity SystemOfQuantities ← SystemHasDerivedUnitaryQuantity → GeneralUnitaryQuantity SystemOfQuantities ← SystemHasUnitaryQuantity → GeneralUnitaryQuantity

4.4. IndividualNominalProperty

Supertypes	IndividualProperty

4.5. IndividualOrdinalQuantity

instance of a general ordinal quantity

Supertypes	IndividualQuantity
Subtypes	InherentOrdinalQuantity OrdinalQuantityValue
Relations with source	IndividualOrdinalQuantity ← Instantiates → GeneralOrdinalQuantity

4.6. IndividualUnitaryQuantity

instance of a general unitary quantity

Supertypes	IndividualQuantity
Subtypes	InherentUnitaryQuantity MeasurementUnit UnitaryQuantityValue
Relations with source	IndividualUnitaryQuantity ← Instantiates → GeneralUnitaryQuantity

4.7. InherentOrdinalQuantity

Supertypes	IndividualOrdinalQuantity
Relations with source	InherentOrdinalQuantity ← Characterizes → Object (cardinality restricted to exactly 1)

4.8. InherentUnitaryQuantity

Supertypes	IndividualUnitaryQuantity
Relations with source	InherentUnitaryQuantity ← Characterizes → Object (cardinality restricted to exactly 1)

4.9. Measurement

Supertypes	IdentifiedElement
Relations with target	MeasurementProcedure ← Describes → Measurement

4.10. MeasurementMethod

Supertypes	IdentifiedElement
Relations with target	MeasurementProcedure ← UsesOperationsOf → MeasurementMethod

4.11. MeasurementModel

Supertypes	IdentifiedElement
Relations with source	MeasurementModel ← HasInput → IndividualQuantity MeasurementModel ← IsInfluencedBy → IndividualQuantity MeasurementModel ← Measures → IndividualQuantity MeasurementModel ← UsesCorrection → IndividualQuantity MeasurementModel ← YieldsMeasuredValue → QuantityValue MeasurementModel ← YieldsMeasurementUncertainty → MeasurementUncertainty
Relations with target	MeasurementProcedure ← IsBasedOn → MeasurementModel

4.12. MeasurementPrinciple

Supertypes	IdentifiedElement
Relations with target	MeasurementProcedure ← Per → MeasurementPrinciple

4.13. MeasurementProcedure

Supertypes	IdentifiedElement
Relations with source	MeasurementProcedure ← Describes → Measurement MeasurementProcedure ← IsBasedOn → MeasurementModel MeasurementProcedure ← Per → MeasurementPrinciple MeasurementProcedure ← UsesOperationsOf → MeasurementMethod

4.14. MeasurementScale

Supertypes	IdentifiedElement
Subtypes	OrdinalScale ReferenceSet UnitaryScale
Relations with source	MeasurementScale ← Includes → IndividualProperty

4.15. MeasurementUncertainty

Relations with target	MeasurementModel ← YieldsMeasurementUncertainty → MeasurementUncertainty

4.16. MeasurementUnit

Supertypes	IndividualUnitaryQuantity
Subtypes	PrefixedMeasurementUnit UnprefixedMeasurementUnit
Relations with source	MeasurementUnit ← HasMultiple → Multiple MeasurementUnit ← IsMultipleOf → MeasurementUnit
Relations with target	UnitaryQuantityValue ← HasUnit → MeasurementUnit MeasurementUnit ← IsMultipleOf → MeasurementUnit SystemOfUnits ← SystemHasBaseUnit → MeasurementUnit SystemOfUnits ← SystemHasDerivedUnit → MeasurementUnit SystemOfUnits ← SystemHasUnit → MeasurementUnit

4.17. Multiple

Supertypes	IdentifiedElement
Relations with target	MeasurementUnit ← HasMultiple → Multiple

4.18. OrdinalQuantityValue

Supertypes	IndividualOrdinalQuantity QuantityValue
Relations with source	OrdinalQuantityValue ← IsAttributedTo → InherentOrdinalQuantity

4.19. OrdinalScale

Supertypes	MeasurementScale
Relations with source	OrdinalScale ← Includes → OrdinalQuantityValue

4.20. PrefixedMeasurementUnit

Supertypes	MeasurementUnit
Relations with source	PrefixedMeasurementUnit ← HasMultiple → Multiple (cardinality restricted to exactly 1) PrefixedMeasurementUnit ← IsMultipleOf → MeasurementUnit (cardinality restricted to exactly 1)

4.21. ReferenceSet

Supertypes	MeasurementScale
Relations with source	ReferenceSet ← Includes → IndividualNominalProperty

4.22. SystemOfQuantities

system of quantities in [VIM4 CD: 1.3, Note 2] corresponds precisely to system of unitary kinds-ef-quantity in [OonP: S.13.7].

set of quantities together with a set of non-contradictory equations relating those quantities.

Supertypes	IdentifiedElement
Relations with source	SystemOfQuantities ← SystemHasBaseUnitaryQuantity → GeneralUnitaryQuantity SystemOfQuantities ← SystemHasDerivedUnitaryQuantity → GeneralUnitaryQuantity SystemOfQuantities ← SystemHasUnitaryQuantity → GeneralUnitaryQuantity
Relations with target	SystemOfUnits ← Given → SystemOfQuantities

4.23. SystemOfUnits

set of base units and derived units, together with their multiples and submultiples, defined in accordance with given rules, for a given system of quantities.

Supertypes	HasCoherence IdentifiedElement
Relations with source	SystemOfUnits ← Given → SystemOfQuantities (cardinality restricted to exactly 1) SystemOfUnits ← SystemHasBaseUnit → MeasurementUnit SystemOfUnits ← SystemHasDerivedUnit → MeasurementUnit SystemOfUnits ← SystemHasUnit → MeasurementUnit

4.24. UnitaryQuantityValue

Supertypes	IndividualUnitaryQuantity QuantityValue
Properties	hasDoubleNumber
Relations with source	UnitaryQuantityValue ← HasUnit → MeasurementUnit (cardinality restricted to exactly 1) UnitaryQuantityValue ← IsAttributedTo → InherentUnitaryQuantity

4.25. UnitaryScale

Supertypes	MeasurementScale
Relations with source	UnitaryScale ← Includes → UnitaryQuantityValue

4.26. UnprefixedMeasurementUnit

Supertypes	MeasurementUnit
Relations with source	UnprefixedMeasurementUnit ← HasMultiple → Multiple (cardinality restricted to exactly 0) UnprefixedMeasurementUnit ← IsMultipleOf → MeasurementUnit (cardinality restricted to exactly 0)

5. Relation Entities

5.1. Characterizes

An InherentQuantity characterizes an Object.

Source	IndividualQuantity
Target	Object
Forward Relation	`characterizes`
Attributes	Functional

5.2. Describes

Source	MeasurementProcedure
Target	Measurement
Forward Relation	`describes`
Attributes	Functional

5.3. Given

Source	SystemOfUnits
Target	SystemOfQuantities
Forward Relation	`given`
Attributes	Functional

5.4. HasInput

Source	MeasurementModel
Target	IndividualQuantity
Forward Relation	`hasInput`
Attributes

5.5. HasMultiple

Source	MeasurementUnit
Target	Multiple
Forward Relation	`hasMultiple`
Attributes	Functional

5.6. HasPowerOfUnitFactor

Source	SystemHasDerivedUnit
Target	SystemHasUnit
Supertypes	RationalExponent
Forward Relation	`hasPowerOfUnitFactor`
Attributes

5.7. HasPowerOfUnitaryQuantityFactor

Source	SystemHasDerivedUnitaryQuantity
Target	SystemHasUnitaryQuantity
Supertypes	RationalExponent
Forward Relation	`hasPowerOfUnitaryQuantityFactor`
Attributes

5.8. HasQuantityDimension

Source	SystemHasUnitaryQuantity
Target	SystemHasBaseUnitaryQuantity
Supertypes	RationalExponent
Forward Relation	`hasQuantityDimension`
Attributes

5.9. HasUnit

Source	UnitaryQuantityValue
Target	MeasurementUnit
Forward Relation	`unit`
Attributes	Functional

5.10. Includes

Source	MeasurementScale
Target	IndividualProperty
Forward Relation	`includes`
Attributes
Properties	ordinalPosition

5.11. Instantiates

Source	IndividualQuantity
Target	GeneralQuantity
Forward Relation	`instantiates`
Attributes	Functional

5.12. IsAttributedTo

Source	QuantityValue
Target	IndividualQuantity
Forward Relation	`isAttributedTo`
Attributes	Functional

5.13. IsBasedOn

Source	MeasurementProcedure
Target	MeasurementModel
Forward Relation	`isBasedOn`
Attributes	Functional

5.14. IsInfluencedBy

Source	MeasurementModel
Target	IndividualQuantity
Forward Relation	`isInfluencedBy`
Attributes

5.15. IsMultipleOf

Source	MeasurementUnit
Target	MeasurementUnit
Forward Relation	`isMultipleOf`
Attributes	Functional

5.16. Measures

Source	MeasurementModel
Target	IndividualQuantity
Forward Relation	`measures`
Attributes	Functional

5.17. Per

Source	MeasurementProcedure
Target	MeasurementPrinciple
Forward Relation	`per`
Attributes

5.18. Specializes

Source	GeneralUnitaryQuantity
Target	GeneralUnitaryQuantity
Forward Relation	`specializes`
Attributes	Asymmetric Irreflexive

5.19. SystemHasBaseUnit

Source	SystemOfUnits
Target	MeasurementUnit
Supertypes	SystemHasUnit
Forward Relation	`systemHasBaseUnit`
Attributes

5.20. SystemHasBaseUnitaryQuantity

quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the set of base quantities can be expressed in terms of the others.

Source	SystemOfQuantities
Target	GeneralUnitaryQuantity
Supertypes	SystemHasUnitaryQuantity
Forward Relation	`systemHasBaseUnitaryQuantity`
Attributes
Properties	dimensionSymbol
Relations with target	SystemHasUnitaryQuantity ← HasQuantityDimension → SystemHasBaseUnitaryQuantity

5.21. SystemHasDerivedUnit

Source	SystemOfUnits
Target	MeasurementUnit
Supertypes	HasCoherence SystemHasUnit
Forward Relation	`systemHasDerivedUnit`
Attributes
Properties	isOffSystemUnit
Relations with source	SystemHasDerivedUnit ← HasPowerOfUnitFactor → SystemHasUnit

5.22. SystemHasDerivedUnitaryQuantity

quantity, in a system of quantities, defined in terms of the base quantities of that system.

Source	SystemOfQuantities
Target	GeneralUnitaryQuantity
Supertypes	SystemHasUnitaryQuantity
Forward Relation	`systemHasDerivedUnitaryQuantity`
Attributes
Properties	isDimensionless
Relations with source	SystemHasDerivedUnitaryQuantity ← HasPowerOfUnitaryQuantityFactor → SystemHasUnitaryQuantity

5.23. SystemHasUnit

Source	SystemOfUnits
Target	MeasurementUnit
Subtypes	SystemHasBaseUnit SystemHasDerivedUnit
Forward Relation	`systemHasUnit`
Attributes
Relations with target	SystemHasDerivedUnit ← HasPowerOfUnitFactor → SystemHasUnit

5.24. SystemHasUnitaryQuantity

Source	SystemOfQuantities
Target	GeneralUnitaryQuantity
Subtypes	SystemHasBaseUnitaryQuantity SystemHasDerivedUnitaryQuantity
Forward Relation	`systemHasUnitaryQuantity`
Attributes
Relations with source	SystemHasUnitaryQuantity ← HasQuantityDimension → SystemHasBaseUnitaryQuantity
Relations with target	SystemHasDerivedUnitaryQuantity ← HasPowerOfUnitaryQuantityFactor → SystemHasUnitaryQuantity

5.25. UsesCorrection

Source	MeasurementModel
Target	IndividualQuantity
Forward Relation	`usesCorrection`
Attributes

5.26. UsesOperationsOf

Source	MeasurementProcedure
Target	MeasurementMethod
Forward Relation	`usesOperationsOf`
Attributes	Functional

5.27. YieldsMeasuredValue

Source	MeasurementModel
Target	QuantityValue
Forward Relation	`yieldsMeasuredValue`
Attributes

5.28. YieldsMeasurementUncertainty

Source	MeasurementModel
Target	MeasurementUncertainty
Forward Relation	`yieldsMeasurementUncertainty`
Attributes	Functional

6. Scalar Properties

6.1. dimensionSymbol

Domain	SystemHasBaseUnitaryQuantity
Range	string
Attributes	Functional

6.2. exponent

Domain	RationalExponent
Range	rational
Attributes	Functional

6.3. hasDoubleNumber

Domain	UnitaryQuantityValue
Range	double
Attributes	Functional

6.4. id

Domain	IdentifiedElement
Range	string
Attributes	Functional

6.5. isCoherent

Domain	HasCoherence
Range	boolean
Attributes	Functional

6.6. isDimensionless

Domain	SystemHasDerivedUnitaryQuantity
Range	boolean
Attributes	Functional

6.7. isOffSystemUnit

Domain	SystemHasDerivedUnit
Range	boolean
Attributes	Functional

6.8. isReferenceValue

Domain	QuantityValue
Range	boolean
Attributes	Functional

6.9. isTrueValue

Domain	QuantityValue
Range	boolean
Attributes	Functional

6.10. ordinalPosition

Domain	Includes
Range	positiveInteger
Attributes	Functional

7. Rules

7.1. DerivationDefinedWithinTheSameSystemOfQuantities

hasPowerOfUnitaryQuantityFactor(d, f) ∧ SystemHasDerivedUnitaryQuantity(ds, d, dq) ∧ SystemHasUnitaryQuantity(fs, f, fq) -> sameAs(ds, fs)

7.2. DerivationDefinedWithinTheSameSystemOfUnits

hasPowerOfUnitFactor(d, f) ∧ SystemHasDerivedUnit(ds, d, du) ∧ SystemHasUnit(fs, f, fu) -> sameAs(ds, fs)

7.3. DimensionDefinedWithinTheSameSystemOfQuantities

hasQuantityDimension(d, b) ∧ SystemHasUnitaryQuantity(ds, d, dq) ∧ SystemHasBaseUnitaryQuantity(bs, b, bq) -> sameAs(ds, bs)

7.4. InstantiatesSpecializesTransitivity

instantiates(i, g1) ∧ specializes(g1, g2) -> instantiates(i, g2)

7.5. SpecializesTransitivity

specializes(a, b) ∧ specializes(b, c) -> specializes(a, c)