Mapping to RDF Graphs

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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:
OWL 1.1 extends the W3C OWL Web Ontology Language with a small but useful set of features that have been requested by users, for which effective reasoning algorithms are now available, and that OWL tool developers are willing to support. The new features include extra syntactic sugar, additional property and qualified cardinality constructors, extended datatype support, simple metamodelling, and extended annotations. This document provides a mapping from the functional-style syntax of OWL 1.1 to the RDF exchange syntax for OWL 1.1, 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 a mapping from the functional-style syntax of OWL 1.1 as given in [OWL 1.1 Specification] to the RDF exchange syntax for OWL 1.1 and vice versa. Every OWL 1.1 ontology can be serialized in RDF, so every OWL 1.1 ontology in RDF is a valid OWL Full ontology. The RDF syntax of OWL 1.1 is backwards-compatible with OWL DL, this is, every OWL DL ontology in RDF is a valid OWL 1.1 ontology. The semantics OWL 1.1 is defined for ontologies in the functional-style syntax. OWL 1.1 ontologies serialized in RDF/XML are interpreted by translating them into the functional-style syntax and applying the OWL 1.1 semantics [OWL 1.1 Semantics]. The syntax for triples used here is the one used in the RDF Semantics document. Full URIs are abbreviated using namespaces as usual.

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 blank node;
  • x denotes a blank or a named node;
  • !x denotes a named node; 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 Translation 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 [OWL 1.1 Specification], OWL 1.1 syntax is fully typed -- that is, from the syntax, one can immediately see what is the intendend usage of some symbol. OWL 1.0 syntax is not typed; rather, OWL 1.0 relies on explicit statements that determine the type of each URI. For backwards compatibility, OWL 1.1 uses OWL 1.0 vocabulary whenever there is no ambiguity. This is made precise using the following definition.

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 annotationURI 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 owl11: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 in punned in an ontology O if Type(S,O) contains more than one element. Based on that, the following two conditions are defined:

  • 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 translation of OWL 1.1 ontologies into RDF:

  • RESTRICTION[op] expands to owl:Restriction if OnlyOP(op) = true, and to owl11:ObjectRestriction otherwise;
  • RESTRICTION[dp] expands to owl:Restriction if OnlyDP(dp) = true, and to owl11:DataRestriction otherwise;
  • SUBPROPERTYOF[op1,...,opn] expands to rdfs:subPropertyOf if OnlyOP(opi) = true for each 1 ≤ i ≤ n, and to owl11:subObjectPropertyOf otherwise;
  • SUBPROPERTYOF[dp1,dp2] expands to rdfs:subPropertyOf if OnlyDP(dp1) = true and OnlyDP(dp2) = true, and to owl11:subDataPropertyOf otherwise;
  • EQUIVALENTPROPERTY[op1,...,opn] expands to owl:equivalentProperty if OnlyOP(opi) = true for each 1 ≤ i ≤ n, and to owl11:equivalentObjectProperty otherwise;
  • EQUIVALENTPROPERTY[dp1,...,dpn] expands to owl:equivalentProperty if OnlyDP(dpi) = true for each 1 ≤ i ≤ n, and to owl11:equivalentDataProperty otherwise;
  • FUNCTIONALPROPERTY[op] expands to owl:FunctionalProperty if OnlyOP(op) = true, and to owl11:FunctionalObjectProperty otherwise;
  • FUNCTIONALPROPERTY[dp] expands to owl:FunctionalProperty if OnlyDP(dp) = true, and to owl11:FunctionalDataProperty otherwise;
  • DOMAIN[op] expands to rdfs:domain if OnlyOP(op) = true, and to owl11:objectPropertyDomain otherwise;
  • DOMAIN[dp] expands to rdfs:domain if OnlyDP(dp) = true, and to owl11:dataPropertyDomain otherwise;
  • RANGE[op] expands to rdfs:range if OnlyOP(op) = true, and to owl11:objectPropertyRange otherwise; and
  • RANGE[dp] expands to rdfs:range if OnlyDP(dp) = true, and to owl11:dataPropertyRange otherwise.

Table 2 presents the operator T that translates an OWL 1.1 ontology in functional-style syntax into a set of RDF triples. This table does not consider axioms with annotations: the translation of such axioms is described in Section 2.1.

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
ontologyURI
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
annotationURI annotationURI rdf:type owl:AnnotationProperty annotationURI
individualURI individualURI
constant constant
DataComplementOf(dr) _:x rdf:type owl:DataRange
_:x owl:complementOf T(dr)
_:x
DataOneOf(ct1 ... ctn) _:x rdf:type owl:DataRange
_:x owl:oneOf T(SEQ ct1 ... ctn)
_:x
DatatypeRestriction(dr facet1 ct1 ... facetn ctn) _:x rdf:type owl:DataRange
_:x owl11:onDataRange T(dr)
_:x owl11:withRestrictions T(SEQ _:x1 ... _:xn)
_:xi xsd:faceti cti 1 ≤ i ≤ n
_:x
InverseObjectProperty(op) _:x owl11: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 owl11: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 owl11: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 owl11: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 owl11: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 owl11: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 owl11: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 owl11: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(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 owl11:AllDisjointClasses
_:x owl11:members T(SEQ c1 ... cn)
DisjointUnion(cID c1 ... cn) T(cID) owl11: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 owl11: propertyChain T(SEQ op1 ... opn)
EquivalentObjectProperties(op1 ... opn) T(opi) EQUIVALENTPROPERTY[op1,...,opn] T(opi+1) 1 ≤ i ≤ n-1
DisjointObjectProperties(op1 ... opn) T(opi) owl11:disjointObjectProperties T(opj) 1 ≤ i, j ≤ n, i ≠ j
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 owl11:ReflexiveProperty
IrreflexiveObjectProperty(op) T(op) rdf:type owl11:IrreflexiveProperty
SymmetricObjectProperty(op) T(op) rdf:type owl:SymmetricProperty
AsymmetricObjectProperty(op) T(op) rdf:type owl11: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 ... dpn) T(dpi) owl11:disjointDataProperties T(dpj) 1 ≤ i, j ≤ n, i ≠ j
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 ... iIDn) T(iIDi) owl:differentFrom T(iIDj) 1 ≤ i, j ≤ n, i ≠ j
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 owl11: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 owl11:NegativeDataPropertyAssertion
_:x rdf:subject T(iID)
_:x rdf:predicate T(dp)
_:x rdf:object T(ct)
Declaration(Datatype(dID)) T(dID) owl11:declaredAs rdfs:Datatype
Declaration(OWLClass(cID)) T(cID) owl11:declaredAs owl:Class
Declaration(ObjectProperty(opID)) T(opID) owl11:declaredAs owl:ObjectProperty
Declaration(DataProperty(dpID)) T(dpID) owl11:declaredAs owl:DatatypeProperty
Declaration(Individual(iID)) T(iID) owl11:declaredAs owl11:Individual

2.1 Annotated Axioms

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

Axioms with annotations are reified. If s p o is the RDF serialization of the corresponding axiom without annotations given in Table 2 and the axiom contains annotations Annotation(apIDi cti), 1 ≤ i ≤ n, then, instead of being serialized as s p o, the axiom is serialized as follows:

_:x rdf:type owl11:Axiom
_:x T(apIDi) T(cti) 1 ≤ i ≤ n
_:x rdf:subject s
_:x rdf:predicate p
_:x rdf:object o

Negative object and data property assertions are already reified so only the following triples are added if an assertion contains an annotation:

_:x T(apIDi) T(cti) 1 ≤ i ≤ n

Note that the Label and Comment annotations are just abbreviations. They are serialized into RDF triples by expanding the abbreviation and then applying the transformation from Table 2.

3 Translation from RDF Graphs to Functional-Style Syntax

This section specifies how to translate a set of RDF triples G into an OWL 1.1 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 owl11:ObjectRestriction owl:Class
x rdf:type owl11:DataRestriction owl:Class
x rdf:type owl:DataRange owl:DataRange
x rdf:type rdfs:Datatype owl:DataRange
x rdf:type owl:ObjectProperty owl:ObjectProperty
x rdf:type owl:TransitiveProperty owl:ObjectProperty
x rdf:type owl:SymmetricProperty owl:ObjectProperty
x rdf:type owl11:AsymmetricProperty owl:ObjectProperty
x rdf:type owl11:ReflexiveProperty owl:ObjectProperty
x rdf:type owl11:IrreflexiveProperty owl:ObjectProperty
x rdf:type owl11:FunctionalObjectProperty owl:ObjectProperty
x rdf:type owl:DatatypeProperty owl:DatatypeProperty
x rdf:type owl11:FunctionalDataProperty owl:DatatypeProperty
x rdf:type owl:AnnotationProperty owl:AnnotationProperty
x rdf:type owl11:Individual owl11:Individual

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 1.1 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.
  • For each tiple 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 translated into an OWL 1.1 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 translated into an OWL 1.1 ontology.
Table 4. Translation of Triples to Object Property Expressions
Pattern Object Property Expression
_:x owl11:inverseObjectPropertyExpression y InverseObjectProperty( OP(y) )
Table 5. Translation of Triples to Data Ranges
Pattern Data Range
_:x rdf:type owl:DataRange
_:x owl:complementOf y
DataComplementOf( DRANGE(y) )
_:x rdf:type owl:DataRange
_:x owl:oneOf T(SEQ ct1 ... ctn)
DataOneOf( ct1 ... ctn )
_:x rdf:type owl:DataRange
_:x owl11:onDataRange y
_:x owl11:withRestriction T(SEQ _:x1 ... _:xn)
_:xi xsd:faceti cti for 1 ≤ i ≤ n
DatatypeRestriction( DRANGE(y) facet1 ct1 ... facetn ctn )
Table 6. Translation 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 owl11:SelfRestriction
_:x owl:onProperty y
ObjectExistsSelf( OP(y) )
_:x rdf:type owl11: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 owl11: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 owl11: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 owl11:ObjectRestriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onClass z ]
ObjectMinCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl:Restriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onClass z ]
{ OnlyOP(y) = true }
ObjectMinCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl11:ObjectRestriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onClass z ]
ObjectMaxCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl:Restriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onClass z ]
{ OnlyOP(y) = true }
ObjectMaxCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl11:ObjectRestriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onClass z ]
ObjectExactCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl:Restriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onClass z ]
{ OnlyOP(y) = true }
ObjectExactCardinality( n OP(y) [ DESC(z) ] )
_:x rdf:type owl11: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 owl11: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 owl11: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 owl11: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 owl11: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 owl11:DataRestriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onDataRange z ]
DataMinCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl:Restriction
_:x owl:minCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onDataRange z ]
{ OnlyDP(y) = true }
DataMinCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl11:DataRestriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onDataRange z ]
DataMaxCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl:Restriction
_:x owl:maxCardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onDataRange z ]
{ OnlyDP(y) = true }
DataMaxCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl11:DataRestriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11:onDataRange z ]
DataExactCardinality( n DP(y) [ DRANGE(z) ] )
_:x rdf:type owl:Restriction
_:x owl:cardinality "n"^^xsd:nonNegativeInteger
_:x owl:onProperty y
[ _:x owl11: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. Translation of Triples to Axioms
Pattern Axiom
 !x !yi cti for 1 ≤ i ≤ n
{ rdfs:Datatype ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ }
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 ≤ }
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 ≤ }
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 ≤ }
EntityAnnotation( DataProperty(x)
Annotation( y1 ct1 ) ... Annotation( yn ctn ) )
 !x !yi cti for 1 ≤ i ≤ n
{ owl11:Individual ∈ Type(x) and OnlyAP(yi) = true for 1 ≤ i ≤ }
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 owl11:AllDisjointClasses
_:x owl11:members T(SEQ y1 ... yn)
DisjointClasses( DESC(y1) ... DESC(yn) )
x owl11:disjointUnionOf T(SEQ y1 ... yn) DisjointUnion( DESC(x) DESC(y1) ... DESC(yn) )
x owl11:subObjectPropertyOf y SubObjectPropertyOf( OP(x) OP(y) )
x rdfs:subPropertyOf y
{ OnlyOP(x) = true and OnlyOP(y) = true }
SubObjectPropertyOf( OP(x) OP(y) )
_:x owl11:subObjectPropertyOf y
_:x owl11:propertyChain T(SEQ x1 ... xn)
SubObjectPropertyOf(
subObjectPropertyChain( OP(x1) ... OP(xn) ) OP(y) )
_:x rdfs:subPropertyOf y
_:x owl11:propertyChain T(SEQ x1 ... xn)
SubObjectPropertyOf(
subObjectPropertyChain( OP(x1) ... OP(xn) ) OP(y) )
x owl11:equivalentObjectProperty y EquivalentObjectProperties( OP(x) OP(y) )
x owl:equivalentProperty y
{ OnlyOP(x) = true and OnlyOP(y) = true }
EquivalentObjectProperties( OP(x) OP(y) )
x owl11:disjointObjectProperties y DisjointObjectProperties( OP(x) OP(y) )
x owl11:objectPropertyDomain y ObjectPropertyDomain( OP(x) DESC(y) )
x rdfs:domain y
{ OnlyOP(x) = true }
ObjectPropertyDomain( OP(x) DESC(y) )
x owl11: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 owl11: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 owl11:ReflexiveProperty ReflexiveObjectProperty( OP(x) )
x rdf:type owl11:IrreflexiveProperty IrreflexiveObjectProperty( OP(x) )
x rdf:type owl:SymmetricProperty SymmetricObjectProperty( OP(x) )
x rdf:type owl11:AsymmetricProperty AsymmetricObjectProperty( OP(x) )
x owl11:subDataPropertyOf y SubDataPropertyOf( DP(x) DP(y) )
x rdfs:subPropertyOf y
{ OnlyDP(x) = true and OnlyDP(y) = true }
SubDataPropertyOf( DP(x) DP(y) )
x owl11:equivalentDataProperty y EquivalentDataProperties(dp1 ... dpn)
x owl:equivalentProperty y
{ OnlyDP(x) = true and OnlyDP(y) = true }
EquivalentDataProperties(dp1 ... dpn)
x owl11:disjointDataProperties y DisjointDataProperties( DP(x) DP(y) )
x owl11:dataPropertyDomain y DataPropertyDomain( DP(x) DESC(y) )
x rdfs:domain y
{ OnlyDP(x) = true }
DataPropertyDomain( DP(x) DESC(y) )
x owl11:dataPropertyRange y DataPropertyRange( DP(x) DRANGE(y) )
x rdfs:range y
{ OnlyDP(x) = true }
DataPropertyRange( DP(x) DRANGE(y) )
x rdf:type owl11: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 y
{ y is not a part of RDF(S) or OWL 1.1 vocabulary }
ClassAssertion( x DESC(y) )
 !x !y !z
{ none of x, y, and z is a part of RDF(S) or OWL 1.1 vocabulary }
{ owl:AnnotationProperty is not in Type(y) }
ObjectPropertyAssertion( OP(y) x z )
_:x rdf:type owl11: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 1.1 vocabulary }
{ owl:AnnotationProperty is not in Type(y) }
DataPropertyAssertion( DP(y) x ct )
_:x rdf:type owl11:NegativeDataPropertyAssertion
_:x rdf:subject !w
_:x rdf:predicate !y
_:x rdf:object ct
NegativeDataPropertyAssertion( DP(y) w ct )
 !x owl11:declaredAs rdfs:Datatype Declaration( Datatype(x) )
 !x owl11:declaredAs owl:Class Declaration( OWLClass(x) )
 !x owl11:declaredAs owl:ObjectProperty Declaration( ObjectProperty(x) )
 !x owl11:declaredAs owl:DatatypeProperty Declaration( DataProperty(x) )
 !x owl11:declaredAs owl11:Individual Declaration( Individual(x) )
_:x rdf:type owl11: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. Translation 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.)

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 translated into an OWL 1.1 ontology.


4 References

[OWL 1.1 Specification]
OWL 1.1 Web Ontology Language: Structural Specification and Functional-Style Syntax. Peter F. Patel-Schneider, Ian Horrocks, and Boris Motik, eds., 2006.
[OWL 1.1 Semantics]
OWL 1.1 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/.