OWL 2 Web Ontology Language:
Mapping to RDF Graphs

1 Introduction and Preliminaries

2 Mapping from the Structural Specification to RDF Graphs

2.1 Translation of Axioms without Annotations

Table 1 presents the operator T that maps an OWL 2 ontology O into an RDF graph T(O), provided that no axiom in O is annotated. The mapping is defined recursively; that is, the mapping of a construct often depends on the mappings of its subconstructs, but in a slightly unusual way: if the mapping of a construct refers to the mapping of a subconstruct, then the triples generated by the recursive invocation of T are added to the graph under construction, and its main node is used in place of the invocation itself.

2.2 Translation of Annotations

The operator TANN, which translates annotations and attaches them to an IRI reference or a blank node, is defined in Table 2.

2.3 Translation of Axioms with Annotations

If an axiom ax contains embedded annotations annotation₁ ... annotation_m, its serialization into RDF depends on the type of the axiom. Let ax' be the axiom that is obtained from ax by removing all axiom annotations.

2.3.1 Axioms that Generate a Single Triple or that Have a Main Triple

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

This is the case for the following axioms: SubClassOf, DisjointClasses with two classes, SubPropertyOf without a property chain as the subproperty expression, PropertyDomain, PropertyRange, InverseProperties, FunctionalProperty, InverseFunctionalProperty, ReflexiveProperty, IrreflexiveProperty, SymmetricProperty, AsymmetricProperty, TransitiveProperty, DisjointProperties with two properties, ClassAssertion, PropertyAssertion, Declaration, DifferentIndividuals with two individuals, and AnnotationAssertion.

DisjointUnion, SubPropertyOf with a subproperty chain, and HasKey axioms are, without annotations, translated into several, and not a single triple. If such such axioms are annotated, then the main triple is subjected to the transformation described above. The other triples — called side triples — are output without any change.

2.3.2 Axioms that are Translated to Multiple Triples

If the axiom ax' is of type EquivalentClasses, EquivalentProperties, or SameIndividual, 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 triples obtained in the translation.

2.3.3 Axioms Represented by Blank Nodes

If the axiom ax' is of type NegativePropertyAssertion, DisjointClasses with more than two classes, DisjointObjectProperties or DisjointDataProperties with more than two properties, or DifferentIndividuals with 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 1, and then attaching the annotations of ax to _:x.

3 Mapping from RDF Graphs to the Structural Specification

3.1 Extracting Declarations and the IRIs of the Directly Imported Ontology Documents

This section specifies the result of step CP-2.2 of the canonical parsing process on an RDF graph G

3.1.1 Resolving Included RDF Graphs

For backwards compatibility with OWL DL, if G contains an owl:imports triple pointing to an RDF graph G' and G' does not have an ontology header, this owl:imports triple is interpreted as an include rather than an import — that is, the triples of G' are included into G and are not parsed into a separate ontology. To achieve this, the following transformation is applied to G as long as the following rule is applicable to G.

3.1.2 Parsing of the Ontology Header and Declarations

Next, the ontology header is extracted from G by matching patterns from Table 4 to G. It MUST be possible to match exactly one such pattern to G in exactly one way. The matched triples are removed from G. The set Imp(G) of the IRIs of ontology documents that are directly imported into G contains exactly all *:z₁, ..., *:z_k that are matched in the pattern.

Next, for backwards compatibility with OWL DL, certain redundant triples are removed from G. In particular, if the triple pattern from the left-hand side of Table 5 is matched in G, then the triples on the right-hand side of Table 5 are removed from G.

Next, for backwards compatibility with OWL DL, G is modified such that declarations can be properly extracted in the next step. When a triple pattern from the first column of Table 6 is matched in G, the matching triples are replaced in G with the triples from the second column. This matching phase stops when matching a pattern and replacing it as specified does not change G. Note that G is a set and thus cannot contain duplicate triples, so this last condition prevents infinite matches.

3.2 Populating an Ontology

This section specifies the result of step CP-3.3 of the canonical parsing process on an RDF graph G, the corresponding instance O_G of the Ontology class, and the set AllDecl(G) of all declarations for G computed as specified in step CP-3.1 of the canonical parsing process.

3.2.1 Analyzing Declarations

The following functions map an IRI reference or a blank node x occurring in G into an object of the structural specification. In particular,

• CE(x) maps x into a class expression,
• DR(x) maps x into a data range,
• OPE(x) maps x into an object property expression,
• DPE(x) maps x into a data property expression, and
• AP(x) maps x into an annotation property.

Initially, these functions are undefined for all IRIs and blank nodes occurring in G; this is written as CE(x) = ε, DR(x) = ε, OPE(x) = ε, DPE(x) = ε, and AP(x) = ε. The functions are updated as parsing progresses. All of the following conditions MUST be satisfied at any given point in time during parsing.

• For each x, at most one of OPE(x), DPE(x), and AP(x) is defined.
• For each x, at most one of CE(x) and DR(x) is defined.

Furthermore, the value of any of these functions for any x MUST NOT be redefined during parsing (i.e., if a function is not undefined for x, no attempt should be made to change the function's value for x).

The function OPEorDPE is defined as follows:

• OPEorDPE(x) = OPE(x) if OPE(x) ≠ ε;
• OPEorDPE(x) = DPE(x) if DPE(x) ≠ ε; and
• OPEorDPE(x) = ε otherwise.

Functions CE, DR, OPE, DPE, and AP are initialized as shown in Table 9.

3.2.2 Parsing of Annotations

The annotations in G are parsed next. The function ANN assigns a set of annotations ANN(x) to each IRI reference or a blank node x. This function is initialized by setting ANN(x) = ∅ for each each IRI reference or a blank node x. Next, the triple patterns from Table 10 are matched in G and, for each matched pattern, ANN(x) is extended with an annotation from the right column. Each time one of these triple patterns is matched, the matched triples are removed from G. This process is repeated until no further matches are possible.

3.2.3 Parsing of Ontology Annotations

Let x be the node that was matched in G to *:x or _:x according to the patterns from Table 4; then, ANN(x) determines the set of ontology annotations of O_G.

3.2.4 Parsing of Expressions

3.2.5 Parsing of Axioms

Next, O_G is populated with axioms. For clarity, the axiom patterns are split into two tables.

• Table 16 presents the patterns for axioms without annotations.
• Annotated axioms are parsed as follows:
  • In case of the patterns for owl:AllDisjointClasses, owl:AllDisjointProperties, owl:AllDifferent, and owl:NegativePropertyAssertion, axiom annotations are defined by ANN(_:x).
  • For all other axioms, axiom annotations are obtained by additionally matching patterns from Table 17 in G during axiom matching.

The axioms in G are parsed as follows:

• All annotated axioms are parsed first.
• Only when no pattern for annotated axioms can be matched in G, then the patterns for axioms without annotations are matched.

In either case, each time a triple pattern is matched, the matched triples are removed from G.

Next, for each blank node or IRI reference x such that x ∉ RIND, and for each annotation Annotation( annotation₁ ... annotation_n AP y ) ∈ ANN(x) with n possibly being equal to zero, the following annotation assertion is added to O_G:

4 Acknowledgments

5 References