Difference between revisions of "Mapping to RDF Graphs"

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Revision as of 15:12, 4 April 2008

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Document title:
OWL 2 Web Ontology Language
Mapping to RDF Graphs (Second Edition)
Authors:
Bernardo Cuenca Grau, Oxford University
Boris Motik, Oxford University
Contributors:
Ian Horrocks, Oxford University
Bijan Parsia, The University of Manchester
Abstract:
The OWL 2 Web Ontology Language, informally OWL 2, is an ontology language for the Semantic Web with formally defined meaning. OWL 2 ontologies provide classes, properties, individuals, and data values and are stored as Semantic Web documents. OWL 2 ontologies can be used along with information written in RDF, and OWL 2 ontologies themselves are primarily exchanged as RDF documents. The OWL 2 Document Overview describes the overall state of OWL 2, and should be read before other OWL 2 documents.
This document provides a mapping from the functional-style syntax of OWL 2 to the RDF exchange syntax for OWL 2, and vice versa.
Status:
This document is an evolution of the OWL 1.1 Web Ontology Language: Mapping to RDF Graphs document that forms part of the OWL 1.1 Web Ontology Language W3C Member Submission.

Copyright © 2006-2007 by the Authors. This document is available under the W3C Document License. See the W3C Intellectual Rights Notice and Legal Disclaimers for additional information.

1 Introduction

Editor's Note: See Issue-66 (mapping inconsistencies).

This document provides mappings between the functional-style syntax of OWL 2 DL as given in the OWL 2 Specification [OWL 2 Specification] and RDF triples. Using this mapping, every OWL 2 DL ontology (in functional-style syntax) can be mapped into RDF triples and back without any change in the formal meaning of an ontology. More precisely, let O be any OWL 2 DL ontology in functional-style syntax, let RDF(O) the set of RDF triples obtained by transforming O into RDF triples as specified in Section 2, and let O' be the OWL 2 DL ontology in functional-style syntax obtained by applying the reverse-transformation from Section 3 to RDF(O); then, O and O' are logically equivalent (i.e., they have exactly the same set of models).

The RDF syntax of OWL 2 DL is backwards-compatible with OWL DL; that is, every OWL DL ontology in RDF is a valid OWL 2 ontology.

The syntax for triples used in this document is the one used in the RDF Semantics document [RDF Semantics]. Full URIs are abbreviated using the same namespaces as in the OWL 2 Specification [OWL 2 Specification].

Editor's Note: The actual namespaces used in the specification are subject to discussion and might change in future.

The following notation is used throughout this document:

  • !x denotes a URI reference;
  • _:x denotes a blank node;
  • x denotes a blank or a URI reference;
  • ct denotes an RDF literal; and
  • T(SEQ y1 ... yn) denotes the encoding of an RDF list as shown in Table 1.
Table 1. Transformation of Sequences to Triples
Sequence S Transformation T(S) Main Node of T(S)
SEQ rdf:nil
SEQ y1 ... yn _:x rdf:type rdf:List
_:x rdf:first T(y1)
_:x rdf:rest T(SEQ y2 ... yn)
_:x

2 Mapping from Functional-Style Syntax to RDF Graphs

Editor's Note: See Issue-2 (allDisjoint-RDF), Issue-68 (nonmonotonic mapping) and Issue-81 (reification, negative assertions).

As explained in the OWL 2 Specification [OWL 2 Specification], OWL 2 syntax is fully typed -- that is, from the syntax, one can immediately see what is the intended usage of some symbol.

This typing is made explicit here as follows. The type of a symbol S in an ontology O (in functional-style syntax), written Type(S,O), is defined as the smallest set such that

  • if the parse tree of O contains S under a objectPropertyURI node, then owl:ObjectPropertyType(S,O);
  • if the parse tree of O contains S under a dataPropertyURI node, then owl:DatatypePropertyType(S,O);
  • if the parse tree of O contains S under a annotationPropertyURI node, then owl:AnnotationPropertyType(S,O);
  • if the parse tree of O contains S under a owlClassURI node, then owl:ClassType(S,O);
  • if the parse tree of O contains S under a datatypeURI node, then rdfs:DatatypeType(S,O); and
  • if the parse tree of O contains S under a individualURI node, then owl2:IndividualType(S,O).

The above definition refers to a parse tree only for the axioms from O, and not from the axioms from some ontology that O imports.

A symbol S is punned in an ontology O if Type(S,O) contains more than one element.

The following three conditions are defined to help the mapping:

  • OnlyOP(S) is true if and only if owl:ObjectPropertyType(S,O) and owl:DatatypeProperty and owl:AnnotationProperty are not in Type(S,O);
  • OnlyDP(S) is true if and only if owl:DatatypePropertyType(S,O) and owl:ObjectProperty and owl:AnnotationProperty are not in Type(S,O);
  • OnlyAP(S) is true if and only if owl:AnnotationPropertyType(S,O) and owl:ObjectProperty and owl:DatatypeProperty are not in Type(S,O).

The following shortcuts are used in the mapping of OWL 2 ontologies into RDF triples:

  • RESTRICTION[op] expands to owl:Restriction if OnlyOP(op) = true, and to owl2:ObjectRestriction otherwise;
  • RESTRICTION[dp] expands to owl:Restriction if OnlyDP(dp) = true, and to owl2:DataRestriction otherwise;
  • SUBPROPERTYOF[op1,...,opn] expands to rdfs:subPropertyOf if OnlyOP(opi) = true for each 1 ≤ i ≤ n, and to owl2:subObjectPropertyOf otherwise;
  • SUBPROPERTYOF[dp1,dp2] expands to rdfs:subPropertyOf if OnlyDP(dp1) = true and OnlyDP(dp2) = true, and to owl2:subDataPropertyOf otherwise;
  • EQUIVALENTPROPERTY[op1,...,opn] expands to owl:equivalentProperty if OnlyOP(opi) = true for each 1 ≤ i ≤ n, and to owl2:equivalentObjectProperty otherwise;
  • EQUIVALENTPROPERTY[dp1,...,dpn] expands to owl:equivalentProperty if OnlyDP(dpi) = true for each 1 ≤ i ≤ n, and to owl2:equivalentDataProperty otherwise;
  • FUNCTIONALPROPERTY[op] expands to owl:FunctionalProperty if OnlyOP(op) = true, and to owl2:FunctionalObjectProperty otherwise;
  • FUNCTIONALPROPERTY[dp] expands to owl:FunctionalProperty if OnlyDP(dp) = true, and to owl2:FunctionalDataProperty otherwise;
  • DOMAIN[op] expands to rdfs:domain if OnlyOP(op) = true, and to owl2:objectPropertyDomain otherwise;
  • DOMAIN[dp] expands to rdfs:domain if OnlyDP(dp) = true, and to owl2:dataPropertyDomain otherwise;
  • RANGE[op] expands to rdfs:range if OnlyOP(op) = true, and to owl2:objectPropertyRange otherwise; and
  • RANGE[dp] expands to rdfs:range if OnlyDP(dp) = true, and to owl2:dataPropertyRange otherwise.

Table 2 presents the operator T that maps an OWL 2 ontology in functional-style syntax into a set of RDF triples. This table does not consider axioms with annotations: the mapping of such axioms is described in Section 2.1. In the mapping of DatatypeRestriction construct, faceti can be one of the facets listed in the OWL 2 Specification section on Data Range Expressions, and xsd:faceti is a URI resource whose namespace is xsd: and whose fragment is the facet name. In the mapping, each _:x is a fresh blank node for different applications of the mapping rules.


Table 2. Transformation to Triples
Functional-Style Syntax S Transformation T(S) Main Node of T(S)
Ontology(ontologyURI
Import(oID1) ... Import(oIDk)
Annotation(apID1 ct1) ... Annotation(apIDn ctn)
axiom1 ... axiomm)
ontologyURI rdf:type owl:Ontology
ontologyURI owl:imports oIDi 1 ≤ i ≤ k
ontologyURI T(apIDi) T(cti) 1 ≤ i ≤ n
T(axiomi) 1 ≤ i ≤ m
ontologyURI
Ontology(
Import(oID1) ... Import(oIDk)
Annotation(apID1 ct1) ... Annotation(apIDn ctn)
axiom1 ... axiomm)
_:x rdf:type owl:Ontology
_:x owl:imports oIDi 1 ≤ i ≤ k
_:x T(apIDi) T(cti) 1 ≤ i ≤ n
T(axiomi) 1 ≤ i ≤ m
_:x
datatypeURI datatypeURI rdf:type rdfs:Datatype datatypeURI
owlClassURI owlClassURI rdf:type owl:Class owlClassURI
objectPropertyURI objectPropertyURI rdf:type owl:ObjectProperty objectPropertyURI
dataPropertyURI dataPropertyURI rdf:type owl:DatatypeProperty dataPropertyURI
annotationPropertyURI annotationPropertyURI rdf:type owl:AnnotationProperty annotationPropertyURI
individualURI individualURI
constant constant
DataComplementOf(dr) _:x rdf:type rdfs:Datatype
_:x owl:complementOf T(dr)
_:x
DataOneOf(ct1 ... ctn) _:x rdf:type rdfs:Datatype
_:x owl:oneOf T(SEQ ct1 ... ctn)
_:x
DatatypeRestriction(dt facet1 ct1 ... facetn ctn) _:x rdf:type rdfs:Datatype
_:x owl2:onDatatype T(dt)
_:x owl2:withRestrictions T(SEQ _:x1 ... _:xn)
_:xi xsd:faceti cti 1 ≤ i ≤ n
_:x
InverseObjectProperty(op) _:x owl2:inverseObjectPropertyExpression T(op) _:x
ObjectUnionOf(c1 ... cn) _:x rdf:type owl:Class
_:x owl:unionOf T(SEQ c1 ... cn)
_:x
ObjectIntersectionOf(c1 ... cn) _:x rdf:type owl:Class
_:x owl:intersectionOf T(SEQ c1 ... cn)
_:x
ObjectComplementOf(c) _:x rdf:type owl:Class
_:x owl:complementOf T(c)
_:x
ObjectOneOf(iID1 ... iIDn) _:x rdf:type owl:Class
_:x owl:oneOf T(SEQ iID1 ... iIDn)
_:x
ObjectSomeValuesFrom(op c) _:x rdf:type RESTRICTION[op]
_:x owl:onProperty T(op)
_:x owl:someValuesFrom T(c)
_:x
ObjectAllValuesFrom(op c) _:x rdf:type RESTRICTION[op]
_:x owl:onProperty T(op)
_:x owl:allValuesFrom T(c)
_:x
ObjectExistsSelf(op) _:x rdf:type owl2:SelfRestriction
_:x owl:onProperty T(op)
_:x
ObjectHasValue(op iID) _:x rdf:type RESTRICTION[op]
_:x owl:onProperty T(op)
_:x owl:hasValue T(iID)
_:x
ObjectMinCardinality(n op c) _:x rdf:type RESTRICTION[op]
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(op)
_:x owl2:onClass T(c)
_:x
ObjectMaxCardinality(n op c) _:x rdf:type RESTRICTION[op]
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(op)
_:x owl2:onClass T(c)
_:x
ObjectExactCardinality(n op c) _:x rdf:type RESTRICTION[op]
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(op)
_:x owl2:onClass T(c)
_:x
ObjectMinCardinality(n op) _:x rdf:type RESTRICTION[op]
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(op)
_:x
ObjectMaxCardinality(n op) _:x rdf:type RESTRICTION[op]
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(op)
_:x
ObjectExactCardinality(n op) _:x rdf:type RESTRICTION[op]
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(op)
_:x
DataSomeValuesFrom(dp dr) _:x rdf:type RESTRICTION[dp]
_:x owl:onProperty T(dp)
_:x owl:someValuesFrom T(dr)
_:x
DataSomeValuesFrom(dp1 ... dpn dr) _:x rdf:type RESTRICTION[dp]
_:x owl:onProperty T(SEQ dp1 ... dpn)
_:x owl:someValuesFrom T(dr)
_:x
DataAllValuesFrom(dp dr) _:x rdf:type RESTRICTION[dp]
_:x owl:onProperty T(dp)
_:x owl:allValuesFrom T(dr)
_:x
DataAllValuesFrom(dp1 ... dpn dr) _:x rdf:type RESTRICTION[dp]
_:x owl:onProperty T(SEQ dp1 ... dpn)
_:x owl:allValuesFrom T(dr)
_:x
DataHasValue(dp ct) _:x rdf:type RESTRICTION[dp]
_:x owl:onProperty T(dp)
_:x owl:hasValue T(ct)
_:x
DataMinCardinality(n dp dr) _:x rdf:type RESTRICTION[dp]
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(dp)
_:x owl2:onDataRange T(dr)
_:x
DataMaxCardinality(n dp dr) _:x rdf:type RESTRICTION[dp]
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(dp)
_:x owl2:onDataRange T(dr)
_:x
DataExactCardinality(n dp dr) _:x rdf:type RESTRICTION[dp]
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(dp)
_:x owl2:onDataRange T(dr)
_:x
DataMinCardinality(n dp) _:x rdf:type RESTRICTION[dp]
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(dp)
_:x
DataMaxCardinality(n dp) _:x rdf:type RESTRICTION[dp]
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(dp)
_:x
DataExactCardinality(n dp) _:x rdf:type RESTRICTION[dp]
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty T(dp)
_:x
EntityAnnotation(Datatype(dID)
Annotation(apID1 ct1) ... Annotation(apIDn ctn))
T(dID) T(apIDi) T(cti) 1 ≤ i ≤ n
EntityAnnotation(OWLClass(cID)
Annotation(apID1 ct1) ... Annotation(apIDn ctn))
T(cID) T(apIDi) T(cti) 1 ≤ i ≤ n
EntityAnnotation(ObjectProperty(opID)
Annotation(apID1 ct1) ... Annotation(apIDn ctn))
T(opID) T(apIDi) T(cti) 1 ≤ i ≤ n
EntityAnnotation(DataProperty(dpID)
Annotation(apID1 ct1) ... Annotation(apIDn ctn))
T(dpID) T(apIDi) T(cti) 1 ≤ i ≤ n
EntityAnnotation(AnnotationProperty(apID)
Annotation(apID1 ct1) ... Annotation(apIDn ctn))
T(apID) T(apIDi) T(cti) 1 ≤ i ≤ n
EntityAnnotation(Individual(iID)
Annotation(apID1 ct1) ... Annotation(apIDn ctn))
T(iID) T(apIDi) T(cti) 1 ≤ i ≤ n
SubClassOf(c1 c2) T(c1) rdfs:subClassOf T(c2)
EquivalentClasses(c1 ... cn) T(ci) owl:equivalentClass T(ci+1) 1 ≤ i ≤ n-1
DisjointClasses(c1 c2) T(c1) owl:disjointWith T(c2)
DisjointClasses(c1 ... cn), n ≠ 2 _:x rdf:type owl2:AllDisjointClasses
_:x owl2:members T(SEQ c1 ... cn)
DisjointUnion(cID c1 ... cn) T(cID) owl2:disjointUnionOf T(SEQ c1 ... cn)
SubObjectPropertyOf(op1 op2) T(op1) SUBPROPERTYOF[op1,op2] T(op2)
SubObjectPropertyOf(
subObjectPropertyChain(op1 ... opn) op)
_:x SUBPROPERTYOF[op1,...,opn,op] T(op)
_:x owl2: propertyChain T(SEQ op1 ... opn)
EquivalentObjectProperties(op1 ... opn) T(opi) EQUIVALENTPROPERTY[op1,...,opn] T(opi+1) 1 ≤ i ≤ n-1
DisjointObjectProperties(op1 op2) T(op1) owl2:disjointObjectProperties T(op2)
DisjointObjectProperties(op1 ... opn), n ≠ 2 _:x rdf:type owl2:AllDisjointProperties
_:x owl2:members T(SEQ op1 ... opn)
ObjectPropertyDomain(op c) T(op) DOMAIN[op] T(c)
ObjectPropertyRange(op c) T(op) RANGE[op] T(c)
InverseObjectProperties(op1 op2) T(op1) owl:inverseOf T(op2)
TransitiveObjectProperty(op) T(op) rdf:type owl:TransitiveProperty
FunctionalObjectProperty(op) T(op) rdf:type FUNCTIONALPROPERTY[op]
InverseFunctionalObjectProperty(op) T(op) rdf:type owl:InverseFunctionalProperty
ReflexiveObjectProperty(op) T(op) rdf:type owl2:ReflexiveProperty
IrreflexiveObjectProperty(op) T(op) rdf:type owl2:IrreflexiveProperty
SymmetricObjectProperty(op) T(op) rdf:type owl:SymmetricProperty
AsymmetricObjectProperty(op) T(op) rdf:type owl2:AsymmetricProperty
SubDataPropertyOf(dp1 dp2) T(dp1) SUBPROPERTYOF[dp1,dp2] T(dp2)
EquivalentDataProperties(dp1 ... dpn) T(dpi) EQUIVALENTPROPERTY[dp1,...,dpn] T(dpi+1) 1 ≤ i ≤ n-1
DisjointDataProperties(dp1 dp2) T(dp1) owl2:disjointDataProperties T(dp2)
DisjointDataProperties(dp1 ... dpn), n ≠ 2 _:x rdf:type owl2:AllDisjointProperties
_:x owl2:members T(SEQ dp1 ... dpn)
DataPropertyDomain(dp c) T(dp) DOMAIN[dp] T(c)
DataPropertyRange(dp dr) T(op) RANGE[dp] T(dr)
FunctionalDataProperty(dp) T(dp) rdf:type FUNCTIONALPROPERTY[dp]
SameIndividual(iID1 ... iIDn) T(iIDi) owl:sameAs T(iIDi+1) 1 ≤ i ≤ n-1
DifferentIndividuals(iID1 iID2) T(iID1) owl:differentFrom T(iID2)
DifferentIndividuals(iID1 ... iIDn) _:x rdf:type owl:AllDifferent
_:x owl:distinctMembers T(SEQ iID1 ... iIDn)
ClassAssertion(iID c) T(iID) rdf:type T(c)
ObjectPropertyAssertion(op iID1 iID2) T(iID1) T(op) T(iID2)
NegativeObjectPropertyAssertion(op iID1 iID2) _:x rdf:type owl2:NegativeObjectPropertyAssertion
_:x rdf:subject T(iID1)
_:x rdf:predicate T(op)
_:x rdf:object T(iID2)
DataPropertyAssertion(dp iID ct) T(iID) T(dp) T(ct)
NegativeDataPropertyAssertion(op iID ct) _:x rdf:type owl2:NegativeDataPropertyAssertion
_:x rdf:subject T(iID)
_:x rdf:predicate T(dp)
_:x rdf:object T(ct)
Declaration(Datatype(dID)) T(dID) owl2:declaredAs rdfs:Datatype
Declaration(OWLClass(cID)) T(cID) owl2:declaredAs owl:Class
Declaration(ObjectProperty(opID)) T(opID) owl2:declaredAs owl:ObjectProperty
Declaration(DataProperty(dpID)) T(dpID) owl2:declaredAs owl:DatatypeProperty
Declaration(AnnotationProperty(apID)) T(dpID) owl2:declaredAs owl:AnnotationProperty
Declaration(Individual(iID)) T(iID) owl2:declaredAs owl2:Individual

2.1 Annotated Axioms

Editor's Note: See Issue-12 (multi-triple annotations) and Issue-67 (reification).

If an axiom ax contains embedded annotations Annotation(apIDi cti), 1 ≤ i ≤ n, its serialization into RDF depends on the type of the axiom. In the following discussion, let ax' be the axiom that is equivalent to ax but that contains no annotations. Note that the Label and Comment annotations are just abbreviations, so they are serialized into RDF by expanding the abbreviation and then applying the serialization presented here.

2.1.1 Axioms that Generate Single Triples

If ax' is translated into a single RDF triple s p o, then the axiom ax is translated into RDF as follows:

_:x rdf:type owl2:Axiom
_:x T(apIDi) T(cti) 1 ≤ i ≤ n
_:x rdf:subject s
_:x rdf:predicate p
_:x rdf:object o

This is the case of the following axiom types: SubClassOf, DisjointUnion, DisjointClasses for two classes, SubObjectPropertyOf (with or without property chains on the subproperty), ObjectPropertyDomain, ObjectPropertyRange, InverseObjectProperties, TransitiveObjectProperty, FunctionalObjectProperty, InverseFunctionalObjectProperty, ReflexiveObjectProperty, IrreflexiveObjectProperty, SymmetricObjectProperty, AsymmetricObjectProperty, SubDataPropertyOf, DataPropertyDomain, DataPropertyRange, FunctionalDataProperty, ClassAssertion, ObjectPropertyAssertion, DataPropertyAssertion, Declaration, and DifferentIndividuals for two individuals.

2.1.2 Axioms that are Translated to Multiple Triples

If the axiom ax' is of type EquivalentClasses, EquivalentObjectProperties, DisjointObjectProperties, EquivalentDataProperties, DisjointDataProperties, SameIndividual, or EntityAnnotation its translation into RDF can be broken up into several RDF triples (because RDF can only represent binary relations). In this case, each of the RDF triples obtained by the translation of ax' is transformed as described in previous section, and the annotations are repeated for each of the blank nodes _:x obtained in the translation.

2.1.3 Axioms Represented by Blank Nodes

If the axiom ax' is of type NegativeObjectPropertyAssertion, NegativeDataPropertyAssertion, DisjointClasses for more than two classes, or DifferentIndividuals for more than two individuals, then its translation already requires introducing a blank node _:x. In such cases, ax is translated by first translating ax' into _:x as shown in Table 2, and then attaching the annotations of ax to _:x.

For example, a negative object property assertion

NegativeObjectPropertyAssertion( Annotation( apID1 ct1 ) op iID1 iID2)

is translated into the following RDF triples:

_:x rdf:type owl2:NegativeObjectPropertyAssertion
_:x rdf:subject T(iID1)
_:x rdf:predicate T(op)
_:x rdf:object T(iID2)
_:x T(apID1) T(ct1)

3 Mapping from RDF Graphs to Functional-Style Syntax

This section specifies how to map a set of RDF triples G into an OWL 2 ontology in functional-style syntax O, if possible. The function Type(x) assigns a set of types to each resource node x in G (in this and all other definitions, the graph G is implicitly understood and is not specified explicitly) and is defined as the smallest set satisfying the conditions from Table 3.

Table 3. Types of Nodes in a Graph
If G contains a triple of this form... ...then Type(x) must contain this URI.
x rdf:type owl:Class owl:Class
x rdf:type owl:Restriction owl:Class
x rdf:type owl2:ObjectRestriction owl:Class
x rdf:type owl2:DataRestriction owl:Class
x rdf:type rdfs:Datatype rdfs:Datatype
x rdf:type owl:DataRange rdfs:Datatype
x rdf:type owl:ObjectProperty owl:ObjectProperty
x rdf:type owl:TransitiveProperty owl:ObjectProperty
x rdf:type owl:SymmetricProperty owl:ObjectProperty
x rdf:type owl2:AsymmetricProperty owl:ObjectProperty
x rdf:type owl2:ReflexiveProperty owl:ObjectProperty
x rdf:type owl2:IrreflexiveProperty owl:ObjectProperty
x rdf:type owl2:FunctionalObjectProperty owl:ObjectProperty
x rdf:type owl:DatatypeProperty owl:DatatypeProperty
x rdf:type owl2:FunctionalDataProperty owl:DatatypeProperty
x rdf:type owl:AnnotationProperty owl:AnnotationProperty
x rdf:type owl2:Individual owl2:Individual

For purposes of backward compatability, owl:DataRange should be treated the same as rdfs:Datatype in this mapping. However, this treatment is likely to be removed in the future.

For a resource node x, the functions OnlyOP(x) and OnlyDP(x) are defined as follows:

  • OnlyOP(x) is true if and only if owl:ObjectPropertyType(x) and owl:DatatypeProperty and owl:AnnotationProperty are not in Type(x);
  • OnlyDP(x) is true if and only if owl:DatatypePropertyType(x) and owl:ObjectProperty and owl:AnnotationProperty are not in Type(x);
  • OnlyAP(x) is true if and only if owl:AnnotationPropertyType(x) and owl:ObjectProperty and owl:DatatypeProperty are not in Type(x).

The following partial functions are defined for each resource node x:

  • OP(x) assigns to x an object property expression;
  • DP(x) assigns to x a data property expression;
  • DRANGE(x) assigns to x a data range; and
  • DESC(x) assigns to x a description.

These functions are defined inductively by the following conditions. For the induction to correctly defined, it should be possible to order all resource nodes in G such that there are no cyclic dependencies in the second condition; if this is not possible, then G cannot be converted into an OWL 2 ontology.

  • If x is not a blank node, then set OP(x), DP(x), DRANGE(x), and DESC(x) to x.
  • For each triple pattern from the first column of Table 4 occurring in G, set OP(x) to the object property expression from the second column.
  • For each triple pattern from the first column of Table 5 occurring in G, set DRANGE(x) to the data range from the second column. In the mapping of DatatypeRestriction construct, faceti can be one of the facets listed in the Structural Specification, and xsd:faceti is an RDF resource whose namespace is equal to xsd: and whose fragment is equal to the facet name.
  • For each triple pattern from the first column of Table 6 occurring G, set DESC(x) to the description from the second column.
  • If there is more than one way of assigning a value to any one of these functions, then G cannot be mapped into an OWL 2 ontology. Also, if the value of one of these functions is not defined for some node occurring in the functional-style syntax encoding, then G cannot be mapped into an OWL 2 ontology.
Table 4. Mapping of Triples to Object Property Expressions
Pattern Object Property Expression
_:x owl2:inverseObjectPropertyExpression y InverseObjectProperty( OP(y) )
Table 5. Mapping of Triples to Data Ranges
Pattern Data Range
_:x rdf:type rdfs:Datatype
_:x owl:complementOf y
DataComplementOf( DRANGE(y) )
_:x rdf:type rdfs:Datatype
_:x owl:oneOf T(SEQ ct1 ... ctn)
DataOneOf( ct1 ... ctn )
_:x rdf:type rdfs:Datatype
_:x owl2:onDatatype y
_:x owl2:withRestrictions T(SEQ _:x1 ... _:xn)
_:xi xsd:faceti cti for 1 ≤ i ≤ n
DatatypeRestriction( DRANGE(y) facet1 ct1 ... facetn ctn )
Table 6. Mapping of Triples to Descriptions
Pattern Description
_:x rdf:type owl:Class
_:x owl:unionOf T(SEQ y1 ... yn)
ObjectUnionOf( DESC(y1) ... DESC(yn) )
_:x rdf:type owl:Class
_:x owl:intersectionOf T(SEQ y1 ... yn)
ObjectIntersectionOf( DESC(y1) ... DESC(yn) )
_:x rdf:type owl:Class
_:x owl:complementOf y
ObjectComplementOf( DESC(y) )
_:x rdf:type owl:Class
_:x owl:oneOf T(SEQ !y1 ... !yn)
ObjectOneOf( y1 ... yn )
_:x rdf:type owl2:SelfRestriction
_:x owl:onProperty y
ObjectExistsSelf( OP(y) )
_:x rdf:type owl2:ObjectRestriction
_:x owl:onProperty y
_:x owl:hasValue !z
ObjectHasValue( OP(y) z )
_:x rdf:type owl:Restriction
_:x owl:onProperty y
_:x owl:hasValue !z
{ OnlyOP(y) = true }
ObjectHasValue( OP(y) z )
_:x rdf:type owl2:ObjectRestriction
_:x owl:onProperty y
_:x owl:someValuesFrom z
ObjectSomeValuesFrom( OP(y) DESC(z) )
_:x rdf:type owl:Restriction
_:x owl:onProperty y
_:x owl:someValuesFrom z
{ OnlyOP(y) = true }
ObjectSomeValuesFrom( OP(y) DESC(z) )
_:x rdf:type owl2:ObjectRestriction
_:x owl:onProperty y
_:x owl:allValuesFrom z
ObjectAllValuesFrom( OP(y) DESC(z) )
_:x rdf:type owl:Restriction
_:x owl:onProperty y
_:x owl:allValuesFrom z
{ OnlyOP(y) = true }
ObjectAllValuesFrom( OP(y) DESC(z) )
_:x rdf:type owl2:ObjectRestriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onClass z ]
ObjectMinCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl:Restriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onClass z ]
{ OnlyOP(y) = true }
ObjectMinCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl2:ObjectRestriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onClass z ]
ObjectMaxCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl:Restriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onClass z ]
{ OnlyOP(y) = true }
ObjectMaxCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl2:ObjectRestriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onClass z ]
ObjectExactCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl:Restriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onClass z ]
{ OnlyOP(y) = true }
ObjectExactCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl2:DataRestriction
_:x owl:onProperty y
_:x owl:hasValue ct
DataHasValue( DP(y) ct )
_:x rdf:type owl:Restriction
_:x owl:onProperty y
_:x owl:hasValue ct
{ OnlyDP(y) = true }
DataHasValue( DP(y) ct )
_:x rdf:type owl2:DataRestriction
_:x owl:onProperty y
_:x owl:someValuesFrom z
DataSomeValuesFrom( DP(y) DRANGE(z) )
_:x rdf:type owl:Restriction
_:x owl:onProperty y
_:x owl:someValuesFrom z
{ OnlyDP(y) = true }
DataSomeValuesFrom( DP(y) DRANGE(z) )
_:x rdf:type owl2:DataRestriction
_:x owl:onProperty T(SEQ y1 ... yn)
_:x owl:someValuesFrom z
DataSomeValuesFrom( DP(y1) ... DP(yn) DRANGE(z) )
_:x rdf:type owl:Restriction
_:x owl:onProperty T(SEQ y1 ... yn)
_:x owl:someValuesFrom z
{ OnlyDP(y) = true }
DataSomeValuesFrom( DP(y1) ... DP(yn) MDRANGE(z) )
_:x rdf:type owl2:DataRestriction
_:x owl:onProperty y
_:x owl:allValuesFrom z
DataAllValuesFrom( DP(y) DRANGE(z) )
_:x rdf:type owl:Restriction
_:x owl:onProperty y
_:x owl:allValuesFrom z
{ OnlyDP(y) = true }
DataAllValuesFrom( DP(y) DRANGE(z) )
_:x rdf:type owl2:DataRestriction
_:x owl:onProperty T(SEQ y1 ... yn)
_:x owl:allValuesFrom z
DataAllValuesFrom( DP(y1) ... DP(yn) DRANGE(z) )
_:x rdf:type owl:Restriction
_:x owl:onProperty T(SEQ y1 ... yn)
_:x owl:allValuesFrom z
{ OnlyDP(y) = true }
DataAllValuesFrom( DP(y1) ... DP(yn) DRANGE(z) )
_:x rdf:type owl2:DataRestriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onDataRange z ]
DataMinCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl:Restriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onDataRange z ]
{ OnlyDP(y) = true }
DataMinCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl2:DataRestriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onDataRange z ]
DataMaxCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl:Restriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onDataRange z ]
{ OnlyDP(y) = true }
DataMaxCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl2:DataRestriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onDataRange z ]
DataExactCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl:Restriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl2:onDataRange z ]
{ OnlyDP(y) = true }
DataExactCardinality( n DP(y) [ DRANGE(z) ] )

The ontology O, corresponding to the set of RDF triples G, is the samllest set containing the axioms occurring in the second column of Table 7 for each triple pattern from the first column.

Table 7. Mapping of Triples to Axioms
Pattern Axiom
 !x !yi cti for 1 ≤ i ≤ n
{ rdfs:Datatype ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ n }
EntityAnnotation( Datatype(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
 !x !yi cti for 1 ≤ i ≤ n
{ owl:Class ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ n }
EntityAnnotation( OWLClass(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
 !x !yi cti for 1 ≤ i ≤ n
{ owl:ObjectProperty ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ n }
EntityAnnotation( ObjectProperty(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
 !x !yi cti for 1 ≤ i ≤ n
{ owl:DatatypeProperty ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ n }
EntityAnnotation( DataProperty(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
 !x !yi cti for 1 ≤ i ≤ n
{ owl:AnnotationProperty ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ n }
EntityAnnotation( AnnotationProperty(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
 !x !yi cti for 1 ≤ i ≤ n
{ owl2:Individual ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ n }
EntityAnnotation( Individual(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
x rdfs:subClassOf y SubClassOf( DESC(x) DESC(y) )
x owl:equivalentClass y EquivalentClasses( DESC(x) DESC(y) )
x owl:disjointWith y DisjointClasses( DESC(x) DESC(y) )
_:x rdf:type owl2:AllDisjointClasses
_:x owl2:members T(SEQ y1 ... yn)
DisjointClasses( DESC(y1) ... DESC(yn) )
x owl2:disjointUnionOf T(SEQ y1 ... yn) DisjointUnion( DESC(x) DESC(y1) ... DESC(yn) )
x owl2:subObjectPropertyOf y SubObjectPropertyOf( OP(x) OP(y) )
x rdfs:subPropertyOf y
{ OnlyOP(x) = true and OnlyOP(y) = true }
SubObjectPropertyOf( OP(x) OP(y) )
_:x owl2:subObjectPropertyOf y
_:x owl2:propertyChain T(SEQ x1 ... xn)
SubObjectPropertyOf(
subObjectPropertyChain( OP(x1) ... OP(xn) ) OP(y) )
_:x rdfs:subPropertyOf y
_:x owl2:propertyChain T(SEQ x1 ... xn)
SubObjectPropertyOf(
subObjectPropertyChain( OP(x1) ... OP(xn) ) OP(y) )
x owl2:equivalentObjectProperty y EquivalentObjectProperties( OP(x) OP(y) )
x owl:equivalentProperty y
{ OnlyOP(x) = true and OnlyOP(y) = true }
EquivalentObjectProperties( OP(x) OP(y) )
x owl2:disjointObjectProperties y DisjointObjectProperties( OP(x) OP(y) )
x owl2:objectPropertyDomain y ObjectPropertyDomain( OP(x) DESC(y) )
x rdfs:domain y
{ OnlyOP(x) = true }
ObjectPropertyDomain( OP(x) DESC(y) )
x owl2:objectPropertyRange y ObjectPropertyRange( OP(x) DESC(y) )
x rdfs:range y
{ OnlyOP(x) = true }
ObjectPropertyRange( OP(x) DESC(y) )
x owl:inverseOf y InverseObjectProperties( OP(x) OP(y) )
x rdf:type owl:TransitiveProperty TransitiveObjectProperty( OP(x) )
x rdf:type owl2:FunctionalObjectProperty FunctionalObjectProperty( OP(x) )
x rdf:type owl:FunctionalProperty
{ OnlyOP(x) = true }
FunctionalObjectProperty( OP(x) )
x rdf:type owl:InverseFunctionalProperty InverseFunctionalObjectProperty( OP(x) )
x rdf:type owl2:ReflexiveProperty ReflexiveObjectProperty( OP(x) )
x rdf:type owl2:IrreflexiveProperty IrreflexiveObjectProperty( OP(x) )
x rdf:type owl:SymmetricProperty SymmetricObjectProperty( OP(x) )
x rdf:type owl2:AsymmetricProperty AsymmetricObjectProperty( OP(x) )
x owl2:subDataPropertyOf y SubDataPropertyOf( DP(x) DP(y) )
x rdfs:subPropertyOf y
{ OnlyDP(x) = true and OnlyDP(y) = true }
SubDataPropertyOf( DP(x) DP(y) )
x owl2:equivalentDataProperty y EquivalentDataProperties(dp1 ... dpn)
x owl:equivalentProperty y
{ OnlyDP(x) = true and OnlyDP(y) = true }
EquivalentDataProperties(dp1 ... dpn)
x owl2:disjointDataProperties y DisjointDataProperties( DP(x) DP(y) )
x owl2:dataPropertyDomain y DataPropertyDomain( DP(x) DESC(y) )
x rdfs:domain y
{ OnlyDP(x) = true }
DataPropertyDomain( DP(x) DESC(y) )
x owl2:dataPropertyRange y DataPropertyRange( DP(x) DRANGE(y) )
x rdfs:range y
{ OnlyDP(x) = true }
DataPropertyRange( DP(x) DRANGE(y) )
x rdf:type owl2:FunctionalDataProperty FunctionalDataProperty( DP(x) )
x rdf:type owl:FunctionalProperty
{ OnlyDP(x) = true }
FunctionalDataProperty( DP(x) )
!x owl:sameAs !y SameIndividual( x y )
!x owl:differentFrom !y DifferentIndividuals( x y )
_:x rdf:type owl:AllDifferent
_:x owl:distinctMembers T(SEQ x1 ... xn)
DifferentIndividuals( x1 ... xn )
 !x rdf:type y
{ y is not a part of RDF(S) or OWL 2 vocabulary }
ClassAssertion( x DESC(y) )
 !x !y !z
{ none of x, y, and z is a part of RDF(S) or OWL 2 vocabulary }
{ owl:AnnotationProperty is not in Type(y) }
ObjectPropertyAssertion( OP(y) x z )
_:x rdf:type owl2:NegativeObjectPropertyAssertion
_:x rdf:subject !w
_:x rdf:predicate !y
_:x rdf:object !z
NegativeObjectPropertyAssertion( OP(y) w z )
 !x !y ct
{ neither x not y is a part of RDF(S) or OWL 2 vocabulary }
{ owl:AnnotationProperty is not in Type(y) }
DataPropertyAssertion( DP(y) x ct )
_:x rdf:type owl2:NegativeDataPropertyAssertion
_:x rdf:subject !w
_:x rdf:predicate !y
_:x rdf:object ct
NegativeDataPropertyAssertion( DP(y) w ct )
 !x owl2:declaredAs rdfs:Datatype Declaration( Datatype(x) )
 !x owl2:declaredAs owl:Class Declaration( OWLClass(x) )
 !x owl2:declaredAs owl:ObjectProperty Declaration( ObjectProperty(x) )
 !x owl2:declaredAs owl:DatatypeProperty Declaration( DataProperty(x) )
 !x owl2:declaredAs owl:AnnotationProperty Declaration( AnnotationProperty(x) )
 !x owl2:declaredAs owl2:Individual Declaration( Individual(x) )
_:x rdf:type owl2:Axiom
_:x !yi cti 1 ≤ i ≤ n
_:x rdf:subject s
_:x rdf:predicate !p
_:x rdf:object o
The result is the axiom obtained by matching the triple pattern s p o.
The axiom contains the following annotations:
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
Table 8. Mapping of Triples to an Ontology
Pattern Ontology
 !x rdf:type owl:Ontology
 !x owl:imports y1 ... !x owl:imports yk
 !x !z1 !w1 ... !x !zn !wn
Ontology(!x
Import(y1) ... Import(yk)
Annotation(z1 w1) ... Annotation(zn wn)
The set of axioms obtained by matching the patters from Table 7.)
_:x rdf:type owl:Ontology
_:x owl:imports y1 ... _:x owl:imports yk
_:x !z1 !w1 ... _:x !zn !wn
Ontology(
Import(y1) ... Import(yk)
Annotation(z1 w1) ... Annotation(zn wn)
The set of axioms obtained by matching the patters from Table 7.)

If G contains some triple that is not matched by any triple pattern (including the patterns used to define Type(x)), then G cannot be mapped into an OWL 2 ontology.


4 Changes from Original Version of OWL

Multiple changes have been made to accommodate the improved functional-style syntax. As well

  • owl:DataRange is deprecated and its use is not suggested. However the mapping to the functional-style syntax still allows owl:DataRange in OWL 2 ontologies.

5 References

[OWL 2 Specification]
OWL 2 Web Ontology Language: Structural Specification and Functional-Style Syntax. Peter F. Patel-Schneider, Ian Horrocks, and Boris Motik, eds., 2006.
[OWL 2 Semantics]
OWL 2 Web Ontology Language: Model-Theoretic Semantics. Bernardo Cuenca Grau and Boris Motik, eds., 2006.
[RDF Semantics]
RDF Semantics. Patrick Hayes, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-mt-20040210/.