ISO 15926-7 Proto-templates

latest update: 2013-11-14     

ISO 15926-7 sub 4.3 defines Proto-templates:

Proto-templates are a very basic form of templates. They provide a layer of abstraction immediately above the relational entity types of ISO 15926-2 by hiding the reified relationships of ISO 15926-2. Each proto-template is constructed of two FOL axioms. The first axiom provides a short form for the relational entity type. The proto-template predicate is called a proto-triple.

Annex C gives the following list:


Proto-templates for relational entity types

ApprovalTriple(x, y, z) ↔ Approval(x) ˄ hasApproved(x, y) ˄ hasApprover(x, z)

ApprovalTemplate(y, z) ↔ ∃u(ApprovalTriple(u, y, z))

 

BoundaryOfNumberSpaceTriple(x, y, z) ↔ BoundaryOfNumberSpace(x) ˄ hasSubclass(x, y) ˄ hasSuperclass(x, z)

BoundaryOfNumberSpaceTemplate(y, z) ↔ ∃u(BoundaryOfNumberSpaceTriple(u, y, z))

 

BoundaryOfPropertySpaceTriple(x, y, z) ↔ BoundaryOfPropertySpace(x) ˄ hasSubclass(x, y) ˄ hasSuperclass(x, z)

BoundaryOfPropertySpaceTemplate(y, z) ↔ ∃u(BoundaryOfPropertySpaceTriple(u, y, z))

 

CauseOfEventTriple(x, y, z) ↔ CauseOfEvent(x) ˄ hasCaused(x, y) ˄ hasCauser(x, z)

CauseOfEventTemplate(y, z) ↔ ∃u(CauseOfEventTriple(u, y, z))

 

ClassOfApprovalTriple(x, y, z) ↔ ClassOfApproval(x) ˄ hasClassOfApproved(x, y) ˄ hasClassOfApprover(x, z)

ClassOfApprovalTemplate(y, z) ↔ ∃u(ClassOfApprovalTriple(u, y, z))

 

ClassOfCauseOfBeginningOfClassOfIndividualTriple(x, y, z) ↔ ClassOfCauseOfBeginningOfClassOfIndividual(x) ˄ hasClassOfBegun(x, y) ˄ hasClassOfCauser(x, z)

ClassOfCauseOfBeginningOfClassOfIndividualTemplate(y, z) ↔ ∃u(ClassOfCauseOfBeginningOfClassOfIndividualTriple(u, y, z))

 

ClassOfCauseOfEndingOfClassOfIndividualTriple(x, y, z) ↔ ClassOfCauseOfEndingOfClassOfIndividual(x) ˄ hasClassOfCauser(x, y) ˄ hasClassOfEnded(x, z)

ClassOfCauseOfEndingOfClassOfIndividualTemplate(y, z) ↔ ∃u(ClassOfCauseOfEndingOfClassOfIndividualTriple(u, y, z))

 

ClassOfClassOfCompositionTriple(x, y, z) ↔ ClassOfClassOfComposition(x) ˄ hasClassOfClassOfPart(x, y) ˄ hasClassOfClassOfWhole(x, z)

ClassOfClassOfCompositionTemplate(y, z) ↔ ∃u(ClassOfClassOfCompositionTriple(u, y, z))

 

ClassOfClassOfRepresentationTriple(x, y, z) ↔ ClassOfClassOfRepresentation(x) ˄ hasClassOfPattern(x, y) ˄ hasClassOfRepresented(x, z)

ClassOfClassOfRepresentationTemplate(y, z) ↔ ∃u(ClassOfClassOfRepresentationTriple(u, y, z))

 

ClassOfClassOfRepresentationTranslationTriple(x, y, z) ↔ ClassOfClassOfRepresentationTranslation(x) ˄ hasClassOfFirst(x, y) ˄ hasClassOfSecond(x, z)

ClassOfClassOfRepresentationTranslationTemplate(y, z) ↔ ∃u(ClassOfClassOfRepresentationTranslationTriple(u, y, z))

 

ClassOfClassOfResponsibilityForRepresentationTriple(x, y, z) ↔ ClassOfClassOfResponsibilityForRepresentation(x)˄hasClassOfClassOfControlled(x, y)˄hasController(x, z)

ClassOfClassOfResponsibilityForRepresentationTemplate(y, z) ↔ ∃u(ClassOfClassOfResponsibilityForRepresentationTriple(u, y, z))

 

ClassOfClassOfUsageOfRepresentationTriple(x, y, z) ↔ ClassOfClassOfUsageOfRepresentation(x) ˄ hasClassOfClassOfUsed(x, y) ˄ hasUser(x, z)

ClassOfClassOfUsageOfRepresentationTemplate(y, z) ↔ ∃u(ClassOfClassOfUsageOfRepresentationTriple(u, y, z))

 

ClassOfClassificationTriple(x, y, z) ↔ ClassOfClassification(x) ˄ hasClassOfClassified(x, y) ˄ hasClassOfClassifier(x, z)

ClassOfClassificationTemplate(y, z) ↔ ∃u(ClassOfClassificationTriple(u, y, z))

 

ClassOfCompositionOfIndividualTriple(x, y, z) ↔ ClassOfCompositionOfIndividual(x) ˄ hasClassOfPart(x, y) ˄ hasClassOfWhole(x, z)

ClassOfCompositionOfIndividualTemplate(y, z) ↔ ∃u(ClassOfCompositionOfIndividualTriple(u, y, z))

 

ClassOfConnectionOfIndividualTriple(x, y, z) ↔ ClassOfConnectionOfIndividual(x) ˄ hasClassOfSide1(x, y) ˄ hasClassOfSide2(x, z)

ClassOfConnectionOfIndividualTemplate(y, z) ↔ ∃u(ClassOfConnectionOfIndividualTriple(u, y, z))

 

ClassOfDimensionForShapeTriple(x, y, z) ↔ ClassOfDimensionForShape(x) ˄ hasClassOfDimension(x, y) ˄ hasClassOfShape(x, z)

ClassOfDimensionForShapeTemplate(y, z) ↔ ∃u(ClassOfDimensionForShapeTriple(u, y, z))

 

ClassOfFunctionalMappingTriple(x, y, z) ↔ ClassOfFunctionalMapping(x) ˄ hasCodomain(x, y) ˄ hasDomain(x, z)

ClassOfFunctionalMappingTemplate(y, z) ↔ ∃u(ClassOfFunctionalMappingTriple(u, y, z))

 

ClassOfIndirectPropertyTriple(x, y, z) ↔ ClassOfIndirectProperty(x) ˄ hasClassOfPossessor(x, y) ˄ hasPropertySpace(x, z)

ClassOfIndirectPropertyTemplate(y, z) ↔ ∃u(ClassOfIndirectPropertyTriple(u, y, z))

 

ClassOfIndividualUsedInConnectionTriple(x, y, z) ↔ ClassOfIndividualUsedInConnection(x) ˄ hasClassOfConnection(x, y) ˄ hasClassOfUsage(x, z)

ClassOfIndividualUsedInConnectionTemplate(y, z) ↔ ∃u(ClassOfIndividualUsedInConnectionTriple(u, y, z))

 

ClassOfIntendedRoleAndDomainTriple(x, y, z) ↔ ClassOfIntendedRoleAndDomain(x) ˄ hasClassOfPlayer(x, y) ˄ hasPlayed(x, z)

ClassOfIntendedRoleAndDomainTemplate(y, z) ↔ ∃u(ClassOfIntendedRoleAndDomainTriple(u, y, z))

 

ClassOfInvolvementByReferenceTriple(x, y, z) ↔ ClassOfInvolvementByReference(x) ˄ hasClassOfInvolved(x, y) ˄ hasClassOfInvolver(x, z)

ClassOfInvolvementByReferenceTemplate(y, z) ↔ ∃u(ClassOfInvolvementByReferenceTriple(u, y, z))

 

ClassOfNamespaceTriple(x, y, z) ↔ ClassOfNamespace(x) ˄ hasClassOfClassOfWhole(x, y) ˄ hasClassOfPart(x, z)

ClassOfNamespaceTemplate(y, z) ↔ ∃u(ClassOfNamespaceTriple(u, y, z))

 

ClassOfParticipationTriple(x, y, z) ↔ ClassOfParticipation(x) ˄ hasClassOfPart(x, y) ˄ hasClassOfWhole(x, z)

ClassOfParticipationTemplate(y, z) ↔ ∃u(ClassOfParticipationTriple(u, y, z))

 

ClassOfPossibleRoleAndDomainTriple(x, y, z) ↔ ClassOfPossibleRoleAndDomain(x) ˄ hasClassOfPlayer(x, y) ˄ hasPlayed(x, z)

ClassOfPossibleRoleAndDomainTemplate(y, z) ↔ ∃u(ClassOfPossibleRoleAndDomainTriple(u, y, z))

 

ClassOfRecognitionTriple(x, y, z) ↔ ClassOfRecognition(x) ˄ hasClassOfRecognized(x, y) ˄ hasClassOfRecognizing(x, z)

ClassOfRecognitionTemplate(y, z) ↔ ∃u(ClassOfRecognitionTriple(u, y, z))

 

ClassOfRelationshipWithSignatureTriple(x, y, z) ↔ ClassOfRelationshipWithSignature(x) ˄ hasClassOfEnd1(x, y) ˄ hasClassOfEnd2(x, z)

ClassOfRelationshipWithSignatureTemplate(y, z) ↔ ∃u(ClassOfRelationshipWithSignatureTriple(u, y, z))

 

ClassOfRelativeLocationTriple(x, y, z) ↔ ClassOfRelativeLocation(x) ˄ hasClassOfLocated(x, y) ˄ hasClassOfLocator(x, z)

ClassOfRelativeLocationTemplate(y, z) ↔ ∃u(ClassOfRelativeLocationTriple(u, y, z))

 

ClassOfRepresentationOfThingTriple(x, y, z) ↔ ClassOfRepresentationOfThing(x) ˄ hasPattern(x, y) ˄ hasRepresented(x, z)

ClassOfRepresentationOfThingTemplate(y, z) ↔ ∃u(ClassOfRepresentationOfThingTriple(u, y, z))

 

ClassOfRepresentationTranslationTriple(x, y, z) ↔ ClassOfRepresentationTranslation(x) ˄ hasClassOfFirst(x, y) ˄ hasClassOfSecond(x, z)

ClassOfRepresentationTranslationTemplate(y, z) ↔ ∃u(ClassOfRepresentationTranslationTriple(u, y, z))

 

ClassOfResponsibilityForRepresentationTriple(x, y, z) ↔ ClassOfResponsibilityForRepresentation(x) ˄ hasClassOfControlled(x, y) ˄ hasController(x, z)

ClassOfResponsibilityForRepresentationTemplate(y, z) ↔ ∃u(ClassOfResponsibilityForRepresentationTriple(u, y, z))

 

ClassOfScaleConversionTriple(x, y, z) ↔ ClassOfScaleConversion(x) ˄ hasCodomain(x, y) ˄ hasDomain(x, z)

ClassOfScaleConversionTemplate(y, z) ↔ ∃u(ClassOfScaleConversionTriple(u, y, z))

 

ClassOfSpecializationTriple(x, y, z) ↔ ClassOfSpecialization(x) ˄ hasClassOfSubclass(x, y) ˄ hasClassOfSuperclass(x, z)

ClassOfSpecializationTemplate(y, z) ↔ ∃u(ClassOfSpecializationTriple(u, y, z))

 

ClassOfTemporalSequenceTriple(x, y, z) ↔ ClassOfTemporalSequence(x) ˄ hasClassOfPredecessor(x, y) ˄ hasClassOfSuccessor(x, z)

ClassOfTemporalSequenceTemplate(y, z) ↔ ∃u(ClassOfTemporalSequenceTriple(u, y, z))

 

ClassOfUsageOfRepresentationTriple(x, y, z) ↔ ClassOfUsageOfRepresentation(x) ˄ hasClassOfUsed(x, y) ˄ hasUser(x, z)

ClassOfUsageOfRepresentationTemplate(y, z) ↔ ∃u(ClassOfUsageOfRepresentationTriple(u, y, z))

 

ClassificationTriple(x, y, z) ↔ Classification(x) ˄ hasClassified(x, y) ˄ hasClassifier(x, z)

ClassificationTemplate(y, z) ↔ ∃u(ClassificationTriple(u, y, z))

 

ComparisonOfPropertyTriple(x, y, z) ↔ ComparisonOfProperty(x) ˄ hasGreaterElement(x, y) ˄ hasLesserElement(x, z)

ComparisonOfPropertyTemplate(y, z) ↔ ∃u(ComparisonOfPropertyTriple(u, y, z))

 

CompositionOfIndividualTriple(x, y, z) ↔ CompositionOfIndividual(x) ˄ hasPart(x, y) ˄ hasWhole(x, z)

CompositionOfIndividualTemplate(y, z) ↔ ∃u(CompositionOfIndividualTriple(u, y, z))

 

ConnectionOfIndividualTriple(x, y, z) ↔ ConnectionOfIndividual(x) ˄ hasSide1(x, y) ˄ hasSide2(x, z)

ConnectionOfIndividualTemplate(y, z) ↔ ∃u(ConnectionOfIndividualTriple(u, y, z))

 

DifferenceOfSetOfClassTriple(x, y, z) ↔ DifferenceOfSetOfClass(x) ˄ hasInput(x, y) ˄ hasResult(x, z)

DifferenceOfSetOfClassTemplate(y, z) ↔ ∃u(DifferenceOfSetOfClassTriple(u, y, z))

 

DimensionOfIndividualTriple(x, y, z) ↔ DimensionOfIndividual(x) ˄ hasIndividual(x, y) ˄ hasIndividualDimension(x, z)

DimensionOfIndividualTemplate(y, z) ↔ ∃u(DimensionOfIndividualTriple(u, y, z))

 

DimensionOfShapeTriple(x, y, z) ↔ DimensionOfShape(x) ˄ hasDimension(x, y) ˄ hasShape(x, z)

DimensionOfShapeTemplate(y, z) ↔ ∃u(DimensionOfShapeTriple(u, y, z))

 

FunctionalMappingTriple(x, y, z) ↔ FunctionalMapping(x) ˄ hasInput(x, y) ˄ hasResult(x, z)

FunctionalMappingTemplate(y, z) ↔ ∃u(FunctionalMappingTriple(u, y, z))

 

IndirectPropertyTriple(x, y, z) ↔ IndirectProperty(x) ˄ hasPossessor(x, y) ˄ hasProperty(x, z)

IndirectPropertyTemplate(y, z) ↔ ∃u(IndirectPropertyTriple(u, y, z))

 

IndividualUsedInConnectionTriple(x, y, z) ↔ IndividualUsedInConnection(x)˄hasConnection(x, y)˄hasUsage(x, z)

IndividualUsedInConnectionTemplate(y, z) ↔ ∃u(IndividualUsedInConnectionTriple(u, y, z))

 

IntendedRoleAndDomainTriple(x, y, z) ↔ IntendedRoleAndDomain(x) ˄ hasPlayed(x, y) ˄ hasPlayer(x, z)

IntendedRoleAndDomainTemplate(y, z) ↔ ∃u(IntendedRoleAndDomainTriple(u, y, z))

 

IntersectionOfSetOfClassTriple(x, y, z) ↔ IntersectionOfSetOfClass(x) ˄ hasInput(x, y) ˄ hasResult(x, z)

IntersectionOfSetOfClassTemplate(y, z) ↔ ∃u(IntersectionOfSetOfClassTriple(u, y, z))

 

InvolvementByReferenceTriple(x, y, z) ↔ InvolvementByReference(x) ˄ hasInvolved(x, y) ˄ hasInvolver(x, z)

InvolvementByReferenceTemplate(y, z) ↔ ∃u(InvolvementByReferenceTriple(u, y, z))

 

LifecycleStageTriple(x, y, z) ↔ LifecycleStage(x) ˄ hasInterest(x, y) ˄ hasInterested(x, z)

LifecycleStageTemplate(y, z) ↔ ∃u(LifecycleStageTriple(u, y, z))

 

LowerBoundOfNumberRangeTriple(x, y, z) ↔ LowerBoundOfNumberRange(x) ˄ hasClassified(x, y) ˄ hasClassifier(x, z)

LowerBoundOfNumberRangeTemplate(y, z) ↔ ∃u(LowerBoundOfNumberRangeTriple(u, y, z))

 

LowerBoundOfPropertyRangeTriple(x, y, z) ↔ LowerBoundOfPropertyRange(x) ˄ hasClassified(x, y) ˄ hasClassifier(x, z)

LowerBoundOfPropertyRangeTemplate(y, z) ↔ ∃u(LowerBoundOfPropertyRangeTriple(u, y, z))

 

OtherRelationshipTriple(x, y, z) ↔ OtherRelationship(x) ˄ hasEnd1(x, y) ˄ hasEnd2(x, z)

OtherRelationshipTemplate(y, z) ↔ ∃u(OtherRelationshipTriple(u, y, z))

 

PossibleRoleAndDomainTriple(x, y, z) ↔ PossibleRoleAndDomain(x) ˄ hasPlayed(x, y) ˄ hasPlayer(x, z)

PossibleRoleAndDomainTemplate(y, z) ↔ ∃u(PossibleRoleAndDomainTriple(u, y, z))

 

PropertyForShapeDimensionTriple(x, y, z) ↔ PropertyForShapeDimension(x) ˄ hasProperty(x, y) ˄ hasShapeDimension(x, z)

PropertyForShapeDimensionTemplate(y, z) ↔ ∃u(PropertyForShapeDimensionTriple(u, y, z))

 

PropertyQuantificationTriple(x, y, z) ↔ PropertyQuantification(x) ˄ hasInput(x, y) ˄ hasResult(x, z)

PropertyQuantificationTemplate(y, z) ↔ ∃u(PropertyQuantificationTriple(u, y, z))

 

PropertySpaceForClassOfShapeDimensionTriple(x, y, z) ↔ PropertySpaceForClassOfShapeDimension(x) ˄ hasClassOfShapeDimension(x, y) ˄ hasPropertySpace(x, z)

PropertySpaceForClassOfShapeDimensionTemplate(y, z) ↔ ∃u(PropertySpaceForClassOfShapeDimensionTriple(u, y, z))

 

RecognitionTriple(x, y, z) ↔ Recognition(x) ˄ hasRecognized(x, y) ˄ hasRecognizing(x, z)

RecognitionTemplate(y, z) ↔ ∃u(RecognitionTriple(u, y, z))

 

RelativeLocationTriple(x, y, z) ↔ RelativeLocation(x) ˄ hasLocated(x, y) ˄ hasLocator(x, z)

RelativeLocationTemplate(y, z) ↔ ∃u(RelativeLocationTriple(u, y, z))

 

RepresentationOfThingTriple(x, y, z) ↔ RepresentationOfThing(x) ˄ hasRepresented(x, y) ˄ hasSign(x, z)

RepresentationOfThingTemplate(y, z) ↔ ∃u(RepresentationOfThingTriple(u, y, z))

 

ResponsibilityForRepresentationTriple(x, y, z) ↔ ResponsibilityForRepresentation(x) ˄ hasControlled(x, y) ˄ hasController(x, z)

ResponsibilityForRepresentationTemplate(y, z) ↔ ∃u(ResponsibilityForRepresentationTriple(u, y, z))

 

ScaleTriple(x, y, z) ↔ Scale(x) ˄ hasCodomain(x, y) ˄ hasDomain(x, z)

ScaleTemplate(y, z) ↔ ∃u(ScaleTriple(u, y, z))

 

SpecializationTriple(x, y, z) ↔ Specialization(x) ˄ hasSubclass(x, y) ˄ hasSuperclass(x, z)

SpecializationTemplate(y, z) ↔ ∃u(SpecializationTriple(u, y, z))

 

SpecializationByRoleTriple(x, y, z) ↔ SpecializationByRole(x) ˄ hasSubclass(x, y) ˄ hasSuperclass(x, z)

SpecializationByRoleTemplate(y, z) ↔ ∃u(SpecializationByRoleTriple(u, y, z))

 

SpecializationOfIndividualDimensionFromPropertyTriple(x, y, z) ↔ SpecializationOfIndividualDimensionFromProperty(x) ˄ hasSubclass(x, y) ˄ hasSuperclass(x, z)

SpecializationOfIndividualDimensionFromPropertyTemplate(y, z) ↔ ∃u(SpecializationOfIndividualDimensionFromPropertyTriple(u, y, z))

 

TemporalSequenceTriple(x, y, z) ↔ TemporalSequence(x) ˄ hasPredecessor(x, y) ˄ hasSuccessor(x, z)

TemporalSequenceTemplate(y, z) ↔ ∃u(TemporalSequenceTriple(u, y, z))

 

UnionOfSetOfClassTriple(x, y, z) ↔ UnionOfSetOfClass(x) ˄ hasInput(x, y) ˄ hasResult(x, z)

UnionOfSetOfClassTemplate(y, z) ↔ ∃u(UnionOfSetOfClassTriple(u, y, z))

 

UpperBoundOfNumberRangeTriple(x, y, z) ↔ UpperBoundOfNumberRange(x) ˄ hasClassified(x, y) ˄ hasClassifier(x, z)

UpperBoundOfNumberRangeTemplate(y, z) ↔ ∃u(UpperBoundOfNumberRangeTriple(u, y, z))

 

UpperBoundOfPropertyRangeTriple(x, y, z) ↔ UpperBoundOfPropertyRange(x) ˄ hasClassified(x, y) ˄ hasClassifier(x, z)

UpperBoundOfPropertyRangeTemplate(y, z) ↔ ∃u(UpperBoundOfPropertyRangeTriple(u, y, z))

 

UsageOfRepresentationTriple(x, y, z) ↔ UsageOfRepresentation(x) ˄ hasUsed(x, y) ˄ hasUser(x, z)

UsageOfRepresentationTemplate(y, z) ↔ ∃u(UsageOfRepresentationTriple(u, y, z))

 

Proto-templates for subtypes of relational entity types

ArrangementOfIndividualTriple(x, y, z) ↔ ArrangementOfIndividual(x) ˄ CompositionOfIndividualTriple(x, y, z)

ArrangementOfIndividualTemplate(y, z) ↔ ∃u(ArrangementOfIndividualTriple(u, y, z))

 

AssemblyOfIndividualTriple(x, y, z) ↔ AssemblyOfIndividual(x) ˄ ArrangementOfIndividualTriple(x, y, z)

AssemblyOfIndividualTemplate(y, z) ↔ ∃u(AssemblyOfIndividualTriple(u, y, z))

 

BeginningTriple(x, y, z) ↔ Beginning(x) ˄ TemporalBoundingTriple(x, y, z)

BeginningTemplate(y, z) ↔ ∃u(BeginningTriple(u, y, z))

 

ClassOfArrangementOfIndividualTriple(x, y, z) ↔ ClassOfArrangementOfIndividual(x) ˄ ClassOfCompositionOfIndividualTriple(x, y, z)

ClassOfArrangementOfIndividualTemplate(y, z) ↔ ∃u(ClassOfArrangementOfIndividualTriple(u, y, z))

 

ClassOfAssemblyOfIndividualTriple(x, y, z) ↔ ClassOfAssemblyOfIndividual(x) ˄ ClassOfArrangementOfIndividualTriple(x, y, z)

ClassOfAssemblyOfIndividualTemplate(y, z) ↔ ∃u(ClassOfAssemblyOfIndividualTriple(u, y, z))

 

ClassOfClassOfDefinitionTriple(x, y, z) ↔ ClassOfClassOfDefinition(x) ˄ ClassOfClassOfRepresentationTriple(x, y, z)

ClassOfClassOfDefinitionTemplate(y, z) ↔ ∃u(ClassOfClassOfDefinitionTriple(u, y, z))

 

ClassOfClassOfDescriptionTriple(x, y, z) ↔ ClassOfClassOfDescription(x)˄ClassOfClassOfRepresentationTriple(x, y, z)

ClassOfClassOfDescriptionTemplate(y, z) ↔ ∃u(ClassOfClassOfDescriptionTriple(u, y, z))

 

ClassOfClassOfIdentificationTriple(x, y, z) ↔ ClassOfClassOfIdentification(x) ˄ ClassOfClassOfRepresentationTriple(x, y, z)

ClassOfClassOfIdentificationTemplate(y, z) ↔ ∃u(ClassOfClassOfIdentificationTriple(u, y, z))

 

ClassOfClassOfRelationshipWithSignatureTriple(x, y, z) ↔ ClassOfClassOfRelationshipWithSignature(x) ˄ ClassOfRelationshipWithSignatureTriple(x, y, z)

ClassOfClassOfRelationshipWithSignatureTemplate(y, z) ↔ ∃u(ClassOfClassOfRelationshipWithSignatureTriple(u, y, z))

 

ClassOfContainmentOfIndividualTriple(x, y, z) ↔ ClassOfContainmentOfIndividual(x) ˄ ClassOfRelativeLocationTriple(x, y, z)

ClassOfContainmentOfIndividualTemplate(y, z) ↔ ∃u(ClassOfContainmentOfIndividualTriple(u, y, z))

 

ClassOfDefinitionTriple(x, y, z) ↔ ClassOfDefinition(x) ˄ ClassOfRepresentationOfThingTriple(x, y, z)

ClassOfDefinitionTemplate(y, z) ↔ ∃u(ClassOfDefinitionTriple(u, y, z))

 

ClassOfDescriptionTriple(x, y, z) ↔ ClassOfDescription(x) ˄ ClassOfRepresentationOfThingTriple(x, y, z)

ClassOfDescriptionTemplate(y, z) ↔ ∃u(ClassOfDescriptionTriple(u, y, z))

 

ClassOfDirectConnectionTriple(x, y, z) ↔ ClassOfDirectConnection(x) ˄ ClassOfConnectionOfIndividualTriple(x, y, z)

ClassOfDirectConnectionTemplate(y, z) ↔ ∃u(ClassOfDirectConnectionTriple(u, y, z))

 

ClassOfFeatureWholePartTriple(x, y, z) ↔ ClassOfFeatureWholePart(x)˄ClassOfArrangementOfIndividualTriple(x, y, z)

ClassOfFeatureWholePartTemplate(y, z) ↔ ∃u(ClassOfFeatureWholePartTriple(u, y, z))

 

ClassOfIdentificationTriple(x, y, z) ↔ ClassOfIdentification(x) ˄ ClassOfRepresentationOfThingTriple(x, y, z)

ClassOfIdentificationTemplate(y, z) ↔ ∃u(ClassOfIdentificationTriple(u, y, z))

 

ClassOfIndirectConnectionTriple(x, y, z) ↔ ClassOfIndirectConnection(x) ˄ ClassOfConnectionOfIndividualTriple(x, y, z)

ClassOfIndirectConnectionTemplate(y, z) ↔ ∃u(ClassOfIndirectConnectionTriple(u, y, z))

 

ClassOfIsomorphicFunctionalMappingTriple(x, y, z) ↔ ClassOfIsomorphicFunctionalMapping(x) ˄ ClassOfFunctionalMappingTriple(x, y, z)

ClassOfIsomorphicFunctionalMappingTemplate(y, z) ↔ ∃u(ClassOfIsomorphicFunctionalMappingTriple(u, y, z))

 

ClassOfLeftNamespaceTriple(x, y, z) ↔ ClassOfLeftNamespace(x) ˄ ClassOfNamespaceTriple(x, y, z)

ClassOfLeftNamespaceTemplate(y, z) ↔ ∃u(ClassOfLeftNamespaceTriple(u, y, z))

 

ClassOfRightNamespaceTriple(x, y, z) ↔ ClassOfRightNamespace(x) ˄ ClassOfNamespaceTriple(x, y, z)

ClassOfRightNamespaceTemplate(y, z) ↔ ∃u(ClassOfRightNamespaceTriple(u, y, z))

 

ClassOfTemporalWholePartTriple(x, y, z) ↔ ClassOfTemporalWholePart(x) ˄ ClassOfCompositionOfIndividualTriple(x, y, z)

ClassOfTemporalWholePartTemplate(y, z) ↔ ∃u(ClassOfTemporalWholePartTriple(u, y, z))

 

ContainmentOfIndividualTriple(x, y, z) ↔ ContainmentOfIndividual(x) ˄ RelativeLocationTriple(x, y, z)

ContainmentOfIndividualTemplate(y, z) ↔ ∃u(ContainmentOfIndividualTriple(u, y, z))

 

CoordinateSystemTriple(x, y, z) ↔ CoordinateSystem(x) ˄ MultidimensionalScaleTriple(x, y, z)

CoordinateSystemTemplate(y, z) ↔ ∃u(CoordinateSystemTriple(u, y, z))

 

DefinitionTriple(x, y, z) ↔ Definition(x) ˄ RepresentationOfThingTriple(x, y, z)

DefinitionTemplate(y, z) ↔ ∃u(DefinitionTriple(u, y, z))

 

DescriptionTriple(x, y, z) ↔ Description(x) ˄ RepresentationOfThingTriple(x, y, z)

DescriptionTemplate(y, z) ↔ ∃u(DescriptionTriple(u, y, z))

 

DirectConnectionTriple(x, y, z) ↔ DirectConnection(x) ˄ ConnectionOfIndividualTriple(x, y, z)

DirectConnectionTemplate(y, z) ↔ ∃u(DirectConnectionTriple(u, y, z))

 

EndingTriple(x, y, z) ↔ Ending(x) ˄ TemporalBoundingTriple(x, y, z)

EndingTemplate(y, z) ↔ ∃u(EndingTriple(u, y, z))

 

FeatureWholePartTriple(x, y, z) ↔ FeatureWholePart(x) ˄ ArrangementOfIndividualTriple(x, y, z)

FeatureWholePartTemplate(y, z) ↔ ∃u(FeatureWholePartTriple(u, y, z))

 

IdentificationTriple(x, y, z) ↔ Identification(x) ˄ RepresentationOfThingTriple(x, y, z)

IdentificationTemplate(y, z) ↔ ∃u(IdentificationTriple(u, y, z))

 

IndirectConnectionTriple(x, y, z) ↔ IndirectConnection(x) ˄ ConnectionOfIndividualTriple(x, y, z)

IndirectConnectionTemplate(y, z) ↔ ∃u(IndirectConnectionTriple(u, y, z))

 

LeftNamespaceTriple(x, y, z) ↔ LeftNamespace(x) ˄ NamespaceTriple(x, y, z)

LeftNamespaceTemplate(y, z) ↔ ∃u(LeftNamespaceTriple(u, y, z))

 

MultidimensionalScaleTriple(x, y, z) ↔ MultidimensionalScale(x) ˄ ScaleTriple(x, y, z)

MultidimensionalScaleTemplate(y, z) ↔ ∃u(MultidimensionalScaleTriple(u, y, z))

 

NamespaceTriple(x, y, z) ↔ Namespace(x) ˄ ClassOfArrangementOfIndividualTriple(x, y, z)

NamespaceTemplate(y, z) ↔ ∃u(NamespaceTriple(u, y, z))

 

ParticipationTriple(x, y, z) ↔ Participation(x) ˄ CompositionOfIndividualTriple(x, y, z)

ParticipationTemplate(y, z) ↔ ∃u(ParticipationTriple(u, y, z))

 

RightNamespaceTriple(x, y, z) ↔ RightNamespace(x) ˄ NamespaceTriple(x, y, z)

RightNamespaceTemplate(y, z) ↔ ∃u(RightNamespaceTriple(u, y, z))

 

SpecializationByDomainTriple(x, y, z) ↔ SpecializationByDomain(x) ˄ SpecializationTriple(x, y, z)

SpecializationByDomainTemplate(y, z) ↔ ∃u(SpecializationByDomainTriple(u, y, z))

 

TemporalBoundingTriple(x, y, z) ↔ TemporalBounding(x) ˄ CompositionOfIndividualTriple(x, y, z)

TemporalBoundingTemplate(y, z) ↔ ∃u(TemporalBoundingTriple(u, y, z))

 

TemporalWholePartTriple(x, y, z) ↔ TemporalWholePart(x) ˄ CompositionOfIndividualTriple(x, y, z)

TemporalWholePartTemplate(y, z) ↔ ∃u(TemporalWholePartTriple(u, y, z))

 

EntityTriples

entityTriple(x, y, z) ↔ (

ApprovalTriple(x, y, z) ∨

ArrangementOfIndividualTriple(x, y, z) ∨

AssemblyOfIndividualTriple(x, y, z) ∨

BeginningTriple(x, y, z) ∨

BoundaryOfNumberSpaceTriple(x, y, z) ∨

BoundaryOfPropertySpaceTriple(x, y, z) ∨

CauseOfEventTriple(x, y, z) ∨

ClassificationTriple(x, y, z) ∨

ClassOfApprovalTriple(x, y, z) ∨

ClassOfArrangementOfIndividualTriple(x, y, z) ∨

ClassOfAssemblyOfIndividualTriple(x, y, z) ∨

ClassOfCauseOfBeginningOfClassOfIndividualTriple(x, y, z) ∨

ClassOfCauseOfEndingOfClassOfIndividualTriple(x, y, z) ∨

ClassOfClassificationTriple(x, y, z) ∨

ClassOfClassOfCompositionTriple(x, y, z) ∨

ClassOfClassOfDefinitionTriple(x, y, z) ∨

ClassOfClassOfDescriptionTriple(x, y, z) ∨

ClassOfClassOfIdentificationTriple(x, y, z) ∨

ClassOfClassOfRelationshipWithSignatureTriple(x, y, z) ∨

ClassOfClassOfRepresentationTranslationTriple(x, y, z) ∨

ClassOfClassOfRepresentationTriple(x, y, z) ∨

ClassOfClassOfResponsibilityForRepresentationTriple(x, y, z) ∨

ClassOfClassOfUsageOfRepresentationTriple(x, y, z) ∨

ClassOfCompositionOfIndividualTriple(x, y, z) ∨

ClassOfConnectionOfIndividualTriple(x, y, z) ∨

ClassOfContainmentOfIndividualTriple(x, y, z) ∨

ClassOfDefinitionTriple(x, y, z) ∨

ClassOfDescriptionTriple(x, y, z) ∨

ClassOfDimensionForShapeTriple(x, y, z) ∨

ClassOfDirectConnectionTriple(x, y, z) ∨

ClassOfFeatureWholePartTriple(x, y, z) ∨

ClassOfFunctionalMappingTriple(x, y, z) ∨

ClassOfIdentificationTriple(x, y, z) ∨

ClassOfIndirectConnectionTriple(x, y, z) V

ClassOfIndirectPropertyTriple(x, y, z) ∨

ClassOfIndividualUsedInConnectionTriple(x, y, z) ∨

ClassOfIntendedRoleAndDomainTriple(x, y, z) ∨

ClassOfInvolvementByReferenceTriple(x, y, z) ∨

ClassOfIsomorphicFunctionalMappingTriple(x, y, z) ∨

ClassOfLeftNamespaceTriple(x, y, z) ∨

ClassOfNamespaceTriple(x, y, z) ∨

ClassOfParticipationTriple(x, y, z) ∨

ClassOfPossibleRoleAndDomainTriple(x, y, z) ∨

ClassOfRecognitionTriple(x, y, z) ∨

ClassOfRelationshipWithSignatureTriple(x, y, z) ∨

ClassOfRelativeLocationTriple(x, y, z) ∨

ClassOfRepresentationOfThingTriple(x, y, z) ∨

ClassOfRepresentationTranslationTriple(x, y, z) ∨

ClassOfResponsibilityForRepresentationTriple(x, y, z) ∨

ClassOfRightNamespaceTriple(x, y, z) ∨

ClassOfScaleConversionTriple(x, y, z) ∨

ClassOfSpecializationTriple(x, y, z) ∨

ClassOfTemporalSequenceTriple(x, y, z) v

ClassOfTemporalWholePartTriple(x, y, z) ∨

ClassOfUsageOfRepresentationTriple(x, y, z) ∨

ComparisonOfPropertyTriple(x, y, z) ∨

CompositionOfIndividualTriple(x, y, z) ∨

ConnectionOfIndividualTriple(x, y, z) ∨

ContainmentOfIndividualTriple(x, y, z) ∨

CoordinateSystemTriple(x, y, z) ∨

DefinitionTriple(x, y, z) ∨

DescriptionTriple(x, y, z) ∨

DifferenceOfSetOfClassTriple(x, y, z) ∨

DimensionOfIndividualTriple(x, y, z) ∨

DimensionOfShapeTriple(x, y, z) ∨

DirectConnectionTriple(x, y, z) ∨

EndingTriple(x, y, z) ∨

FeatureWholePartTriple(x, y, z) ∨

FunctionalMappingTriple(x, y, z) ∨

IdentificationTriple(x, y, z) ∨

IndirectConnectionTriple(x, y, z) ∨

IndirectPropertyTriple(x, y, z) ∨

IndividualUsedInConnectionTriple(x, y, z) ∨

IntendedRoleAndDomainTriple(x, y, z) ∨

IntersectionOfSetOfClassTriple(x, y, z) ∨

InvolvementByReferenceTriple(x, y, z) ∨

LeftNamespaceTriple(x, y, z) ∨

LifecycleStageTriple(x, y, z) ∨

LowerBoundOfNumberRangeTriple(x, y, z) ∨

LowerBoundOfPropertyRangeTriple(x, y, z) ∨

MultidimensionalScaleTriple(x, y, z) ∨

NamespaceTriple(x, y, z) ∨

OtherRelationshipTriple(x, y, z) ∨

ParticipationTriple(x, y, z) ∨

PossibleRoleAndDomainTriple(x, y, z) ∨

PropertyForShapeDimensionTriple(x, y, z) ∨

PropertyQuantificationTriple(x, y, z) ∨

PropertySpaceForClassOfShapeDimensionTriple(x, y, z) ∨

RecognitionTriple(x, y, z) V RelativeLocationTriple(x, y, z) ∨

RepresentationOfThingTriple(x, y, z) ∨

ResponsibilityForRepresentationTriple(x, y, z) ∨

RightNamespaceTriple(x, y, z) ∨

ScaleTriple(x, y, z) ∨

SpecializationByDomainTriple(x, y, z) ∨

SpecializationByRoleTriple(x, y, z) ∨

SpecializationOfIndividualDimensionFromPropertyTriple(x, y, z) ∨

SpecializationTriple(x, y, z) ∨

TemporalBoundingTriple(x, y, z) ∨

TemporalSequenceTriple(x, y, z) ∨

TemporalWholePartTriple(x, y, z) ∨

UnionOfSetOfClassTriple(x, y, z) ∨

UpperBoundOfNumberRangeTriple(x, y, z) ∨

UpperBoundOfPropertyRangeTriple(x, y, z) ∨

UsageOfRepresentationTriple(x, y, z))