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Transformation of UML connectors

In this section are specified transformation rules for UML association, generalisation and dependency connectors. Transformation rules overview for UML connectors provides an overview of the section coverage.

Table 1. Transformation rules overview for UML connectors
UML element	Rules in core ontology layer	Rules in data shape layer	Rules in reasoning layer
Association	Example R.01	Example R.02
Association domain			Example R.03
Association range		Example R.05	Example R.04
Association multiplicity		Example R.08	Example R.06, Example R.07
Association asymmetry		Example R.10	Example R.09
Association inverse			Example R.11
Dependency	Example R.01	Example R.02
Dependency domain			Example R.03
Dependency range		Example R.13	Example R.12
Dependency multiplicity		Example R.08	Example R.06, Example R.07
Class generalisation	Example R.14
Property generalisation	Example R.15
Class equivalence			Example R.16
Property equivalence			Example R.17
Disjoint classes			Example R.18
Realisation	Example R.19

Unidirectional association

A binary Association specifies a semantic relationship between two member ends represented by properties. Please note that in accordance with specification [uml2.5], the association end names are not obligatory. However, we adhere to the UML conventions , where specification of at one member ends, for unidirectional association, and two member ends, for bidirectional association, is mandatory. Moreover, provision of a connector (general) name is discouraged.

Figure 1. Visual representation of a UML unidirectional association (on the left) and an OWL property with cardinality restriction on domain class (on the right)

Example R.01. Unidirectional association — in core ontology layer

Specify object property declaration axiom for the target end of the association/dependency.

Ideally, in the implementation, this rule would be combined with the relevant rules (those for the core ontology layer) in the Transformation of UML descriptors section, to provide labels and documentation for the property at the time of its creation.

Property declaration in Turtle syntax

:relationName a owl:ObjectProperty .Turtle

Property declaration in RDF/XML syntax

<owl:ObjectProperty rdf:about = "http://base.onto.uri/relationName">
</owl:ObjectProperty>XML

Example R.02. Unidirectional association — in data shape layer

Specify PropertyShape declaration axiom for each association/dependency.

Ideally, in the implementation, this rule would be combined with the relevant rules (those for the data shape layer) in the Transformation of UML descriptors section, to provide labels and documentation for the property shape at the time of its creation.

For handling bidirectional associations refer to the Bidirectional association section.

PropertyShape declaration for associations in Turtle syntax

@prefix : <http://base.onto.uri/> .
@prefix shape: <http://base.shape.uri/> .
@prefix sh: <http://www.w3.org/ns/shacl#> .

shape:ClassName
  sh:property shape:ClassName-relationName ;
.
shape:ClassName-relationName a sh:PropertyShape ;
  sh:path :relationName ;
.Turtle

PropertyShape declaration for associations in RDF/XML syntax

<rdf:Description rdf:about = "http://base.shape.uri/ClassName">
    <sh:property rdf:resource = "http://base.shape.uri/ClassName-relationName"/>
</rdf:Description>
<sh:PropertyShape rdf:about = "http://base.shape.uri/ClassName-relationName">
    <sh:path rdf:resource = "http://base.onto.uri/relationName"/>
</sh:PropertyShape>XML

Association source

Example R.03. Association source — in reasoning layer

Specify object property domain for the target end of the association/dependency.

Domain specification in Turtle syntax

:relationName
  rdfs:domain :ClassName ;
.Turtle

Domain specification in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relationName">
    <rdfs:domain rdf:resource = "http://base.onto.uri/ClassName"/>
</rdf:Description>XML

Object property domain specification for reused relations in Turtle syntax

:relationName
  rdfs:domain [
    rdf:type owl:Class ;
    owl:unionOf (
      :ClassName1
      :ClassName2
    )
  ]
.Turtle

Object property domain specification for reused relations in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relationName">
    <rdfs:domain>
        <owl:Class>
            <owl:unionOf rdf:parseType="Collection">
                <rdf:Description rdf:about="http://base.onto.uri/ClassName1"/>
                <rdf:Description rdf:about="http://base.onto.uri/ClassName2"/>
            </owl:unionOf>
        </owl:Class>
    </rdfs:domain>
</rdf:Description>XML

Association target

Example R.04. Association target — in reasoning layer

Specify object property range for the target end of the association.

Range specification in Turtle syntax

:relationName
  rdfs:range :ClassName ;
.Turtle

Range specification in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relationName">
    <rdfs:range rdf:resource = "http://base.onto.uri/ClassName"/>
</rdf:Description>XML

Object property range specification for reused relations in Turtle syntax

:relationName
  rdfs:range [
    rdf:type owl:Class ;
    owl:unionOf (
      :OtherClass1
      :OtherClass2
    )
  ]
.Turtle

Object property range specification for reused relations in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relationName">
    <rdfs:range>
        <owl:Class>
            <owl:unionOf rdf:parseType="Collection">
                <rdf:Description rdf:about="http://base.onto.uri/OtherClass1"/>
                <rdf:Description rdf:about="http://base.onto.uri/OtherClass2"/>
            </owl:unionOf>
        </owl:Class>
    </rdfs:range>
</rdf:Description>XML

Example R.05. Association range shape — in data shape layer

Within the SHACL PropertyShape corresponding to an association relation linked to a given source UML Class, specify property constraints indicating the range class.

Property class constraint in Turtle syntax

@prefix : <http://base.onto.uri/> .
@prefix shape: <http://base.shape.uri/> .
@prefix sh: <http://www.w3.org/ns/shacl#> .

shape:ClassName-relationName
  sh:class :OtherClass ;
.Turtle

Property class constraint in RDF/XML syntax

<rdf:Description rdf:about = "http://base.shape.uri/ClassName-relationName">
    <sh:class rdf:resource = "http://base.onto.uri/OtherClass"/>
</rdf:Description>XML

Association multiplicity

Example R.06. Association multiplicity — in reasoning layer

For the association/dependency target multiplicity, where min and max are different than ``*'' (any) and multiplicity is not [1..1], specify a subclass axiom where the source class specialises an anonymous restriction of properties formulated according to cases provided by rule:attribute-rc-multiplicity.

Min cardinality restriction in Turtle syntax

:ClassName
  rdfs:subClassOf [ a owl:Restriction ;
    owl:minCardinality "1"^^xsd:integer;
    owl:onProperty :relationName ;
  ] ;
.Turtle

Min cardinality restriction in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/ClassName">
    <rdfs:subClassOf>
        <owl:Restriction>
            <owl:onProperty rdf:resource = "http://base.onto.uri/relationName"/>
            <owl:minCardinality rdf:datatype="http://www.w3.org...#integer" >1</owl:cardinality>
        </owl:Restriction>
    </rdfs:subClassOf>
</rdf:Description>XML

Example R.07. Association multiplicity "one" — in reasoning layer

If the association/dependency multiplicity is exactly one, i.e. [1..1], specify a functional property axiom like in rule:attribute-rc-multiplicity-one.

Declaring a functional property in Turtle syntax

:relationName a owl:FunctionalProperty .Turtle

Declaring a functional property in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relationName">
    <rdf:type rdf:resource = "http://...owl#FunctionalProperty"/>
</rdf:Description>XML

Example R.08. Association multiplicity — in data shape layer

Within the SHACL PropertyShape corresponding to an association/dependency relation linked to a given source UML Class, specify property constraints indicating minimum and maximum cardinality, according to cases provided by rule:attribute-ds-multiplicity.

Min cardinality constraint in Turtle syntax

@prefix shape: <http://base.shape.uri/> .
@prefix sh: <http://www.w3.org/ns/shacl#> .

shape:ClassName-relationName
  sh:minCount 1 ;
.Turtle

Min cardinality constraint in RDF/XML syntax

<rdf:Description rdf:about = "http://base.shape.uri/ClassName-relationName">
    <sh:minCount rdf:datatype="http://www.w3.org...#integer"
      >1</sh:minCount>
</rdf:Description>XML

Recursive association

In case of recursive associations, that are from one class to itself, (depicted in Visual representation of a UML recursive association (on the left) and OWL recursive properties with cardinality restrictions on domain class (on the right)), the transformation rules must be applied as in the case of regular unidirectional association, which are from Example R.01 to Example R.07. In addition, the association must be marked as asymmetric expressed in Example R.10 and Example R.09.

Figure 2. Visual representation of a UML recursive association (on the left) and OWL recursive properties with cardinality restrictions on domain class (on the right)

Example R.09. Association asymmetry — in reasoning layer

Specify an asymmetric object property axiom for each end of a recursive association.

Declaring an asymmetric property in Turtle syntax

:relatesTo a owl:AsymmetricProperty .Turtle

Declaring an asymmetric property in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relatesTo">
    <rdf:type rdf:resource = "http://...owl#AsymmetricProperty"/>
</rdf:Description>XML

Example R.10. Association asymmetry — in data shape layer

Within the SHACL Node Shape corresponding to the UML Class, specify SPARQL constraint selecting instances connected by the object property in a reciprocal manner.

Adding details to a NodeShape for an asymmetric property in Turtle syntax

@prefix : <http://base.onto.uri/> .
@prefix shape: <http://base.shape.uri/> .
@prefix sh: <http://www.w3.org/ns/shacl#> .

shape:ClassName
  sh:sparql [
    sh:select """
      SELECT ?this ?that
      WHERE {
        ?this :relatesTo ?that .
        ?that :relatesTo ?this .
      }
    """ ;
  ] ;
.Turtle

Adding details to a NodeShape for an asymmetric property in RDF/XML syntax

<rdf:Description rdf:about = "http://base.shape.uri/ClassName">
    <sh:sparql rdf:parseType="Resource">
        <sh:select>
          SELECT ?this ?that
          WHERE {
            ?this :relatesTo ?that .
            ?that :relatesTo ?this .}
        </sh:select>
    </sh:sparql>
</rdf:Description>XML

Bidirectional association

The bidirectional associations should be treated, both on source and target ends, like two unidirectional associations (see Visual representation of a UML bidirectional association (on the left) and OWL properties with cardinality restrictions on domain class (on the right)). The transformation rules from Example R.01 and Example R.02, and all the other rules for unidirectional associations shown in Transformation rules overview for UML connectors must be applied to both ends. In addition to those rules, the inverse relation axiom must be specified.

Figure 3. Visual representation of a UML bidirectional association (on the left) and OWL properties with cardinality restrictions on domain class (on the right)

Example R.11. Association inverse — in reasoning layer

Specify an inverse object property axiom between the source and target ends of the bidirectional association.

Declaring an inverse property in Turtle syntax

:relatesTo owl:inverseOf :isRelatedTo .Turtle

Declaring an inverse property in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relatesTo">
    <owl:inverseOf rdf:resource = "http://base.onto.uri/isRelatedTo"/>
</rdf:Description>XML

Unidirectional dependency

In general the UML dependency connectors should be transformed by the rules specified for UML association connectors (see Transformation rules overview for UML connectors).

The following two rules, concerning the transformation of dependency targets, are different from the rules for the transformation of association targets.

Example R.12. Dependency target — in reasoning layer

Specify object property range for the target end of the dependency.

Range specification in Turtle syntax

:relationName
  rdfs:range skos:Concept ;
.Turtle

Range specification in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/relationName">
    <rdfs:range rdf:resource = ".../02/skos/core#Concept"/>
</rdf:Description>XML

In OWL we want to state only that the range of a Dependency connector is a skos:Concept, without committing to a specific list. We do this additional restriction in the data shape.

Example R.13. Dependency range shape — in data shape layer

Within the SHACL PropertyShape corresponding to a dependency relation linked to a given source UML Class, constraint the range of the dependency.

Specify the suitable constraint based on the constraint level set for the UML Enumeration (as defined in rule:enumeration-constraint-level):

permissive: set skos:Concept as the expected type of an enumeration item
restrictive: refer to a NodeShape for an enumeration item that further restricts allowed values (see the transformation rule for enumeration item).

Permissive shape in Turtle syntax

@prefix : <http://base.onto.uri/> .
@prefix shape: <http://base.shape.uri/> .
@prefix sh: <http://www.w3.org/ns/shacl#> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

shape:ClassName-relationName a sh:PropertyShape ;
    sh:path :relationName;
    sh:class skos:Concept .Turtle

Permissive shape in RDF/XML syntax

<rdf:Description rdf:about = "http://base.shape.uri/ClassName-relationName">
  <rdf:type rdf:resource = "http://...shacl#PropertyShape"/>
  <sh:path rdf:resource = "http://base.onto.uri/relationName"/>
  <sh:class rdf:resource = "http://...skos/core#Concept"/>
</rdf:Description>XML

Restrictive shape in Turtle syntax

@prefix : <http://base.onto.uri/> .
@prefix shape: <http://base.shape.uri/> .
@prefix sh: <http://www.w3.org/ns/shacl#> .

shape:ClassName-relationName a sh:PropertyShape ;
    sh:path :relationName;
    sh:node shape:EnumName-itemShape .Turtle

Restrictive shape in RDF/XML syntax

<rdf:Description rdf:about = "http://base.shape.uri/ClassName-relationName">
  <rdf:type rdf:resource = "http://...shacl#PropertyShape"/>
  <sh:path rdf:resource = "http://base.onto.uri/relationName"/>
  <sh:node rdf:resource = "http://base.shape.uri/EnumName-itemShape"/>
</rdf:Description>XML

Class generalisation

Generalisation [uml2.5] defines specialization relationship between Classifiers. In case of UML Classes it relates a more specific Class to a more general Class.

Figure 4. Visual representation of UML generalisation (on the left) and OWL subclass relation (on the right)

UML generalisation set [uml2.5] groups generalisations; incomplete and disjoint constraints indicate that the set is not complete and its specific Classes have no common instances. The UML conventions specify that all sibling classes are by default disjoint, therefore even if no generalisation set is provided it is assumed to be implicit. Sibling classes will be declared disjoint with one another in the reasoning layer (see Example R.18).

Example R.14. Class generalisation — in core ontology layer

Specify subclass axiom for the generalisation between UML Classes.

Subclass declaration in Turtle syntax

:ClassName rdfs:subClassOf :SuperClass.
:OtherClass rdfs:subClassOf :SuperClass.Turtle

Subclass declaration in RDF/XML syntax

<owl:Class rdf:about = "http://base.onto.uri/ClassName">
    <rdfs:subClassOf rdf:resource = "http://base.onto.uri/SuperClass"/>
</owl:Class>
<owl:Class rdf:about = "http://base.onto.uri/OtherClass">
    <rdfs:subClassOf rdf:resource = "http://base.onto.uri/SuperClass"/>
</owl:Class>XML

Property generalisation

Generalisation [uml2.5] defines specialization relationship between Classifiers. In case of the UML associations it relates a more specific Association to more general Association.

Figure 5. Visual representation of UML property generalisation (on the left) and OWL sub-property relation (on the right)

Example R.15. Property generalisation — in core ontology layer

Specify a sub-property axiom representing the generalisation between named roles of UML associations. Properties on the subject and object positions correspond to the association roles belonging to the same side of the association ends. Such a sub-property axiom is specified for the target side of association ends (for unidirectional associations) or for both source and target sides of the association ends (for bidirectional associations).

Property specialisation in Turtle syntax

:hasSister rdfs:subPropertyOf :relatesTo .
:isSisterOf rdfs:subPropertyOf :isRelatedTo .Turtle

Property specialisation in RDF/XML syntax

<owl:ObjectProperty rdf:about = "http://base.onto.uri/hasSister">
    <rdfs:subPropertyOf rdf:resource = "http://base.onto.uri/relatesTo"/>
</owl:ObjectProperty>
<owl:ObjectProperty rdf:about = "http://base.onto.uri/isSisterOf">
    <rdfs:subPropertyOf rdf:resource = "http://base.onto.uri/isRelatedTo"/>
</owl:ObjectProperty>XML

Class equivalence

Figure 6. Visual representation of UML class equivalence (on the left) and OWL class equivalence (on the right)

Example R.16. Equivalent classes — in reasoning layer

Specify equivalent class axiom for the generalisation with <<equivalent>> or <<complete>> stereotype between UML Classes.

Class equivalence in Turtle syntax

:ClassName owl:equivalentClass :SuperClass.Turtle

Class equivalence in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/ClassName">
    <owl:equivalentClass rdf:resource = "http://base.onto.uri/SuperClass"/>
</rdf:Description>XML

Property equivalence

Example R.17. Equivalent properties — in reasoning layer

Specify equivalent property axiom for the generalisation with <<equivalent>> or <<complete>> stereotype between UML properties.

Property equivalence in Turtle syntax

:hasSister owl:equivalentProperty :relatesTo .
:isSisterOf owl:equivalentProperty :isRelatedTo .Turtle

Property equivalence in RDF/XML syntax

<rdf:Description rdf:about = "http://base.onto.uri/hasSister">
  <owl:equivalentProperty rdf:resource = "http://base.onto.uri/relatesTo"/>
</rdf:Description>
<rdf:Description rdf:about = "http://base.onto.uri/isSisterOf">
  <owl:equivalentProperty rdf:resource = "http://base.onto.uri/isRelatedTo"/>
</rdf:Description>XML

Disjoint classes

Example R.18. Disjoint classes — in reasoning layer

Specify a disjoint classes axiom for all "sibling" classes, i.e. for multiple UML Classes that have generalisation connectors to the same UML Class.

For the generalisation relations depicted in Visual representation of UML generalisation (on the left) and OWL subclass relation (on the right), the generated output should have the following form.

Disjoint classes declaration in Turtle syntax

[ a owl:AllDisjointClasses ;
  owl:members  ( :ClassName :OtherClass )
] .Turtle

Disjoint classes declaration in RDF/XML syntax

<rdf:Description>
    <rdf:type rdf:resource="http://...owl#AllDisjointClasses"/>
    <owl:members rdf:parseType="Collection">
        <rdf:Description rdf:about="http://base.onto.uri/ClassName"/>
        <rdf:Description rdf:about="http://base.onto.uri/OtherClass"/>
    </owl:members>
</rdf:Description>XML

Realisation relations

Realisation defines a relationship between an Object element and a UML Class or Enumeration element. At the moment we only provide transformation rules for UML Realization connectors that connect to UML Classes.

Example R.19. Class realisation — in core ontology layer

Declare an individual with a specified class as its type, for a UML Realization connector between a UML Object and a UML Class.

Individual declaration in Turtle syntax

:ObjectName a owl:NamedIndividual, :ClassName .Turtle

Individual declaration in RDF/XML syntax

<owl:NamedIndividual rdf:about="http://base.onto.uri/ObjectName">
    <rdf:type rdf:resource="http://base.onto.uri/ClassName"/>
</owl:NamedIndividual>XML

Transformation of UML connectors

Unidirectional association

Association source

Association target

Association multiplicity

Recursive association

Bidirectional association

Unidirectional dependency

Class generalisation

Property generalisation

Class equivalence

Property equivalence

Disjoint classes

Realisation relations

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