Mapping to RDF Graphs

1 Introduction

This document provides mappings between the functional-style syntax of OWL 1.1 as given in the OWL 1.1 Specification [OWL 1.1 Specification] and RDF triples. Every OWL 1.1 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 1.1 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 1.1 DL 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 1.1 DL is backwards-compatible with OWL DL; that is, every OWL DL ontology in RDF is a valid OWL 1.1 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 1.1 Specification [OWL 1.1 Specification].

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 ... y_n) denotes the encoding of an RDF list as shown in Table 1.

2 Mapping from Functional-Style Syntax to RDF Graphs

As explained in the OWL 1.1 Specification [OWL 1.1 Specification], OWL 1.1 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:ObjectProperty ∈ Type(S,O);
• if the parse tree of O contains S under a dataPropertyURI node, then owl:DatatypeProperty ∈ Type(S,O);
• if the parse tree of O contains S under a annotationPropertyURI node, then owl:AnnotationProperty ∈ Type(S,O);
• if the parse tree of O contains S under a owlClassURI node, then owl:Class ∈ Type(S,O);
• if the parse tree of O contains S under a datatypeURI node, then rdfs:Datatype ∈ Type(S,O); and
• if the parse tree of O contains S under a individualURI node, then owl11:Individual ∈ Type(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:ObjectProperty ∈ Type(S,O) and owl:DatatypeProperty and owl:AnnotationProperty are not in Type(S,O);
• OnlyDP(S) is true if and only if owl:DatatypeProperty ∈ Type(S,O) and owl:ObjectProperty and owl:AnnotationProperty are not in Type(S,O);
• OnlyAP(S) is true if and only if owl:AnnotationProperty ∈ Type(S,O) and owl:ObjectProperty and owl:DatatypeProperty are not in Type(S,O).

The following shortcuts are used in the mapping of OWL 1.1 ontologies into RDF triples:

• 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,...,op_n] expands to rdfs:subPropertyOf if OnlyOP(op_i) = 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,...,op_n] expands to owl:equivalentProperty if OnlyOP(op_i) = true for each 1 ≤ i ≤ n, and to owl11:equivalentObjectProperty otherwise;
• EQUIVALENTPROPERTY[dp₁,...,dp_n] expands to owl:equivalentProperty if OnlyDP(dp_i) = 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 maps an OWL 1.1 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, facet_i can be one of the facets listed in the OWL 1.1 Specification section on Data Range Expressions, and xsd:facet_i 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.

2.1 Annotated Axioms

If an axiom ax contains embedded annotations Annotation(apID_i ct_i), 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 owl11:Axiom
_:x T(apID_i) T(ct_i) 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 owl11: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 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.

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:ObjectProperty ∈ Type(x) and owl:DatatypeProperty and owl:AnnotationProperty are not in Type(x);
• OnlyDP(x) is true if and only if owl:DatatypeProperty ∈ Type(x) and owl:ObjectProperty and owl:AnnotationProperty are not in Type(x);
• OnlyAP(x) is true if and only if owl:AnnotationProperty ∈ Type(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. In the mapping of DatatypeRestriction construct, facet_i can be one of the facets listed in the Structural Specification, and xsd:facet_i 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 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 mapped into an OWL 1.1 ontology.

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.

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 1.1 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 1.1 ontologies.

5 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/.