Web Ontology Language (OWL) Abstract Syntax and Semantics
Section 4. Mapping to RDF Graphs

4. Mapping to RDF Graphs

The exchange syntax for OWL is RDF/XML [RDF Syntax], as specified in the OWL Reference Description [OWL Reference]. Further, the meaning of an OWL ontology in RDF/XML is determined only from the RDF graph [RDF Concepts] that results from the RDF parsing of the RDF/XML document. Thus one way of translating an OWL ontology in abstract syntax form into the exchange syntax is by giving a transformation of each directive into a collection of triples. As all OWL Lite constructs are special cases of constructs in the full abstract syntax, transformations are only provided for the OWL DL versions.

The syntax for triples used here is the one used in the RDF Model Theory [RDF MT]. In this variant, qualified names are allowed. As detailed in the RDF Model Theory, to turn this syntax into the standard one just expand the qualified names into URI references in the standard RDF manner by concatenating the namespace name with the local name, using the standard OWL namespaces.

4.1. Translation to RDF Graphs

The Transformation Table gives transformation rules that transform the abstract syntax to the OWL exchange syntax. In a few cases, notably for the DifferentIndividuals construct, there are different transformation rules. In such cases either rule can be chosen, resulting in a non-deterministic translation. In a few other cases, notably for class and property axioms, there are triples that may or may not be generated. These triples are indicated by flagging them with [opt]. In a couple of cases one of two triples must be generated. This is indicated by separating the triples with OR. These non-determinisms allow the generation of more RDF Graphs.

The left column of the table gives a piece of syntax (S), the center column gives its transformation (T(S)), and the right column gives an identifier for the main node of the transformation (M(T(S))), but only for syntactic constructs that can occur as pieces of directives. Repeating components are listed using ellipses, as in description₁; … description_n, this form allows easy specification of the transformation for all values of n allowed in the syntax. Optional portions of the abstract syntax (enclosed in square brackets) are optional portions of the transformation (signified by square brackets). As well, for any of the built-in OWL datatypes, rdfs:Literal, built-in OWL classes, built-in OWL annotation properties, and built-in OWL ontology properties the first rdf:type triple in the translation of it or any axiom for it is optional.

Some transformations in the table are for directives. Other transformations are for parts of directives. The last transformation is for sequences, which are not part of the abstract syntax per se. This last transformation is used to make some of the other transformations more compact and easier to read.

For many directives these transformation rules call for the transformation of components of the directive using other transformation rules. When the transformation of a component is used as the subject or object of a triple, even an optional triple, the transformation of the construct is part of the production (but only once per production) and the main node of that transformation should be used for that node of the triple.

Bnode identifiers here must be taken as local to each transformation, i.e., different identifiers should be used for each invocation of a transformation rule. Ontologies without a name are given a bnode as their main node; ontologies with a name use that name as their main node; this node is referred to as O below.

This transformation is not injective, as several OWL abstract ontologies that do not use the above reserved vocabulary can map into equal RDF graphs. However, the only cases where this can happen is with constructs that have the same meaning, such as several DisjointClasses axioms having the same effect as one larger one. It would be possible to define a canonical inverse transformation, if desired.

4.2. Definition of OWL DL and OWL Lite Ontologies in RDF Graph Form

When considering OWL Lite and DL ontologies in RDF graph form, care must be taken to prevent the use of certain vocabulary as OWL classes, properties, or individuals. If this is not done the built-in definitions or use of this vocabulary (in the RDF or OWL specification) would augment the information in the OWL ontology. Only some of the RDF vocabulary fits in this category, as some of the RDF vocabulary, such as rdf:subject, is given little or no meaning by the RDF specifications and its use does not present problems, as long as the use is consistent with any meaning given by the RDF specifications.

Definition: The disallowed vocabulary from RDF is rdf:type, rdf:Property, rdf:nil, rdf:List, rdf:XMLLiteral, rdf:first, rdf:rest, rdfs:domain, rdfs:range, rdfs:Resource, rdfs:Datatype, rdfs:Class, rdfs:subClassOf, rdfs:subPropertyOf, rdfs:member, rdfs:Container and rdfs:ContainerMembershipProperty. The disallowed vocabulary from OWL is owl:AllDifferent, owl:allValuesFrom, owl:AnnotationProperty, owl:cardinality, owl:Class, owl:complementOf, owl:DataRange, owl:DatatypeProperty, owl:DeprecatedClass, owl:DeprecatedProperty, owl:differentFrom, owl:disjointWith, owl:distinctMembers, owl:equivalentClass, owl:equivalentProperty, owl:FunctionalProperty, owl:hasValue, owl:intersectionOf, owl:InverseFunctionalProperty, owl:inverseOf, owl:maxCardinality, owl:minCardinality, owl:ObjectProperty, owl:oneOf, owl:onProperty, owl:Ontology, owl:Property, owl:Restriction, owl:sameAs, owl:sameIndividualAs, owl:someValuesFrom, owl:SymmetricProperty, owl:TransitiveProperty, and owl:unionOf. The disallowed vocabulary is the union of the disallowed vocabulary from RDF and the disallowed vocabulary from OWL.

Definition: The class-only vocabulary is rdf:Statement, rdf:Seq, rdf:Bag, and rdf:Alt. The datatype-only vocabulary is the built-in OWL datatypes and rdfs:Literal. The property-only vocabulary is rdf:subject, rdf:predicate, rdf:object, and all the container membership properties, i.e., rdf:_1, rdf:_2, ….

Definition: A collection of OWL DL ontologies in abstract syntax form, O, has a separated vocabulary if

1. the ontologies in O, taken together, do not use any URI reference as more than one of a class ID, a datatype ID, an individual ID, an individual-valued property ID, a data-valued property ID, an annotation property ID, ontology property ID, or an ontology ID;
2. the ontologies in O, taken together, provide a type for every individual ID;
3. the ontologies in O only use the class-only vocabulary as class IDs; only use the datatype-only vocabulary as datatype IDs; only use the property-only vocabulary as datavaluedProperty IDs, individualvaluedProperty IDs, or annotationProperty IDs; and do not mention any disallowed vocabulary.

Definition: An RDF graph is an OWL DL ontology in RDF graph form if it is equal (see below for a slight relaxation) to a result of the transformation to triples above of a collection of OWL DL ontologies in abstract syntax form that has a separated vocabulary. For the purposes of determining whether an RDF graph is an OWL DL ontology in RDF graph form, cardinality restrictions are explicitly allowed to use constructions like "1"^^xsd:decimal so long as the data value so encoded is a non-negative integer.

Definition: An RDF graph is an OWL Lite ontology in RDF graph form if it is as above except that the ontologies in O are OWL Lite ontologies in abstract syntax form.

Direct Formulation of OWL DL and OWL Lite Ontologies in RDF Graph Form

A finite RDF graph is an OWL DL or OWL Lite ontology in RDF graph form if and only if it meets the following conditions:

1. For every node of the graph and every URI reference used as a property or datatype at least one of the following holds:
   • It is one of the built-in OWL datatypes, rdfs:Literal, built-in OWL classes, built-in OWL annotation properties, or the built-in OWL ontology properties.
   • It is the subject of at least one triple with predicate rdf:type, and with object other than rdf:Property, rdfs:Class, owl:FunctionalProperty, owl:DeprecatedProperty, owl:DeprecatedClass. The objects of such triples are known as the explicit types of the subject.
   • It is a literal.
2. Every blank node with explicit type rdf:List or [DL only] owl:DataRange is the object of exactly one triple.
3. Any uriref which is a built-in OWL datatype or in the datatype-only vocabulary or rdfs:Literal is assigned to the category datatypeID. Any uriref which is a built-in OWL class or in the class-only vocabulary is assigned to the category classID. Any uriref which is a built-in OWL annotation property is assigned to the category annotationPropID. Any uriref which is a built-in OWL ontology property is assigned to the category ontologyPropertyID. Any uriref which is in the property-only vocabulary is assigned to one of the categories annotationPropID, dataPropID objectPropID or transitivePropID. Every uriref in the disallowed vocabulary is assigned to itself.
4. Every other uriref is assigned to one of the following categories:
   • ontologyID
   • datatypeID
   • annotationPropID
   • classID
   • individualID
   • dataPropID
   • objectPropID
   • transitivePropID
5. Every blank node is assigned to one of the following categories:
   • allDifferent
   • listOfDescription
   • listOfIndividualID
   • restriction
   • unnamedIndividual
   • [DL only] description
   • [DL only] listOfDataLiteral
   • [DL only] unnamedDataRange
6. With the given category assignments every triple in the graph appears in one of the following tables:
   • Main Lite table
   • [DL only] Main DL table
   • blank nodes of category allDifferent
   • blank nodes of category listOfDescription
   • blank nodes of category listOfIndividualID
   • blank nodes of category restriction
   • [DL only] blank nodes of category description
   • [DL only] blank nodes of category listOfDataLiteral
   • [DL only] blank nodes of category unnamedDataRange
7. Every blank node is either of category unnamedIndividual or meets the structural requirements listed below, in the appropriate table.
8. A blank node which occurs as the object of more than one triple must be of category restriction or [DL only] description.
9. Directed cycles of blank nodes may not occur in OWL Lite and in OWL DL must contain at least one triple with property owl:disjointWith or owl:equivalentClass.

Such an RDF graph which does not use any of the cases marked as DL only, is in OWL Lite.

A directed cycle of blank nodes is a sequence of triples t0, t1, ... tn, in which tn = t0, and in which the subjects and objects of all the triples are blank, and in which the object of ti is the subject of ti+1, for i from 0 to n-1.

Main Lite Table

Main DL Table

Rules for Blank Nodes of Category allDifferent

Every node of category allDifferent must fit the following pattern. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There are no other triples in the graph in which such nodes are subjects.

Rules for Blank Nodes of Category listOfDescription

Every node of category listOfDescription must fit the following pattern. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There are no other triples in the graph in which such nodes are subjects.

Rules for Blank Nodes of Category listOfIndividualID

Every node of category listOfIndividualID must fit the following pattern. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There are no other triples in the graph in which such nodes are subjects.

Rules for Blank Nodes of Category restriction

Every node of category restriction must fit one of these patterns. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There may be additional triples in which such nodes are subjects as listed in the main triple tables.

[DL only] Rules for Blank Nodes of Category description

Every node of category description must fit one of these patterns. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There may be additional triples in which such nodes are subjects as listed in the main triple tables.

[DL only] Rules for Blank Nodes of Category listOfDataLiteral

Every node of category listOfDataLiteral must fit the following pattern. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There are no other triples in the graph in which such nodes are subjects.

[DL only] Rules for Blank Nodes of Category unnamedDataRange

Every node of category unnamedDataRange must fit the following pattern. For each such node, exactly one instance of each triple in the pattern must be present in the graph. There may be additional triples in which such nodes are subjects as listed in the main triple tables.