4.3 RDF Graphs of OWL Lite Ontologies

An OWL Full document [Add definition and link] is an OWL Lite document if the imports closure [Link is into part 5 of ASS] of the associated RDF graph meets certain conditions.

These conditions are as follows:

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 appears as the subject or object of owl:imports, owl:backwardlyCompatibleWith, owl:priorVersion, owl:incompatibleWith.
   • It is one of the built-in URI references from RDF, RDFS, OWL or XML Schema datatypes. [link to list of built-ins]
   • It is the subject of at least one triple with predicate rdf:type. The objects of such triples are known as the explicit types of the subject.
   • It is a literal.
2. Every node with explicit type of rdf:Property, owl:FunctionalProperty, [are the following really necessary? Shouldn't they be subclasses of owl:ObjectProperty?] owl:InverseFunctionalProperty, owl:SymmetricProperty or owl:TranstiveProperty must also have explicit type of either owl:ObjectProperty or owl:DatatypeProperty.
3. No blank node occurs as the object of more than one triple.
4. No directed cycles of blank nodes occurs.
5. Every blank node can be assigned to one of the following categories:
   • blank individual node
   • restriction node
   • class list node
   • all different node
   • individual list node
   and every uriref node can be assigned to one of the following categories:
   • ontology node
   • uriref class node
   • uriref individual node
   • datatype node
   • simple datatype-property node
   • simple object-property node
   • transitive property node
   • constrained object-property node
   • constrained datatype-property node
   such that:
   • every triple in the graph matches one of the permitted triple templates below.
   • Every restriction node matches one of the restriction node templates below.
   • Every class list node matches one of the class list node templates below.
   • Every all different node matches one of the all different node templates below.
   • Every individual list node matches one of the individual list node templates below.

We note that such an RDF graph is finite, being constructed from a finite number of finite documents.

A brief, incomplete, gloss on each category is as follows:

ontology node

names an ontology, typically using the URL of a file where the ontology is found.

ontology metaproperty

One of the builtin properties: owl:imports, owl:backwardlyCompatibleWith, owl:priorVersion or owl:incompatibleWith.

uriref class node

the name of a class in an ontology

restriction node

an unnamed class defined by an owl:Restriction in an ontology

uriref individual node

a named individual in an ontology

blank individual node

an unnamed individual in an ontology

datatype node

identifies an RDF datatype [Link needed]

simple datatype-property node

identifies an unconstrained datatype property

simple object-property node

identifies an unconstrained individual property

transitive property node

identifies an individual property related to a transitive property

constrained object-property node

identifies an individual property related to one with cardinality constraints

constrained datatype-property node

identifies a datatype-property related to one with cardinality constraints

class list node

A node constructed from an rdf:parseType="Collection" list, whose members are class nodes.

individual list node

A node constructed from an rdf:parseType="Collection" list, whose members are uriref individual nodes.

all different node

A node of type owl:AllDifferent.

literal node

WG note: The multiplicty of property categories is motivated by the desire to describe the side condition on transitive property syntactically rather than semantically, since the semantic formulation was flawed. It also allows the use of simple properties (i.e. with no constraints of any kind) both in annotations and on individuals.

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.

4.3.1 Built-in URI references

The built-in URI references have the following categories.

4.3.2 OWL Lite Triple Templates

Every triple in an OWL Lite RDF Graph must be of one of the following forms: (an individual node is either a uriref individual node or a blank individual node).

4.3.3 OWL Lite Restriction Node Templates

If x is a restriction node then there must be three triples with x as subject and these must be one of the following sets:

The datatype URI reference xsd:nonNegativeInteger may be replaced by any built-in derived type of xsd:decimal (including itself) which contains the lexical form in its lexical space.

4.3.4 OWL Lite Class List Node Templates

No triples may have rdf:nil as subject.

If x is a class list node, other than rdf:nil then there must be three triples with x as subject and these must of the following form:

4.3.5 OWL Lite Individual List Node Templates

No triples may have rdf:nil as subject.

rdf:nil may be a class list node in one triple and an individual list node in another in the same graph.

If x is an individual list node, other than rdf:nil then there must be three triples with x as subject and these must of the following form:

4.3.6 All Different Node Template

If x is an all different node then there must be two triples with x as subject and these must of the following form:

4.4 RDF Graphs of OWL DL Ontologies

The set of OWL Full documents which are OWL DL documents is defined by modifications of the definition of OWL Lite.

In summary the modifications are:

• replacing the category of restriction node, with a more general category of description node
• adding a new category dataRange node
• adding additional triple templates for the new categories

An OWL Full document [Add definition and link] is an OWL DL document if the imports closure [Link is into part 5 of ASS] of the associated RDF graph meets certain conditions.

These conditions are as follows:

1. As for OWL Lite.
2. As for OWL Lite.
3. As for OWL Lite.
4. As for OWL Lite.
5. Every blank node can be assigned to one of the following categories:
   • blank individual node
   • description node
   • class list node
   • all different node
   • individual list node
   • dataRange node
   • dataRange list node
   and every uriref node can be assigned to one of the following categories:
   • ontology node
   • uriref class node
   • uriref individual node
   • datatype node
   • simple datatype-property node
   • simple object-property node
   • transitive property node
   • constrained object-property node
   • constrained datatype-property node
   such that:
   • every triple in the graph matches one of the OWL Lite permitted triple templates above or one of the OWL DL permitted triple templates below.
   • Every description node matches one of the restriction node templates below.
   • Every class list node matches one of the class list node templates below.
   • Every all different node matches one of the OWL Lite all different node templates above.
   • Every individual list node matches one of the OWL Lite individual list node templates above.
   • Every dataRange node matches one of the dataRange node templates below.
   • Every dataRange list node matches one of the dataRange list node templates below.

A brief, incomplete, gloss on each new category is as follows:

description node

a node representing a description of an OWL DL class.

dataRange node

a node representing a dataRange

dataRange list node

A node like an individual list node, whose members are literal values.

4.4.1 Built-in URI references

The built-in URI references have the same categories as in OWL Lite, except for rdf:nil which has the additional category of dataRange list node.

4.4.2 OWL DL Triple Templates

Every triple in an OWL DL RDF Graph must either match an OWL Lite triple template or be of one of the following forms: (an individual node is either a uriref individual node or a blank individual node).

4.4.3 Description Node Rules

If x is a description node then it must either match one of the OWL Lite Restriction node templates (with the generalization that any non-negative integer is allowed instead of "0" or "1" in the last template) or one of the OWL DL restriction templates below, or one of the OWL DL description templates below. Moreover it may be the subject of one additional triple of any of the following forms:

4.4.3.1 OWL DL Restriction Templates

A description node may match one of the following templates, consisting of exactly three triples with x as subject:

4.4.3.2 OWL DL Description Template

A description node may have exactly two triples with x as subject, one being:

x rdf:type owl:Class .

The other being of one of the following forms:

4.4.4 OWL DL Class List Node Templates

No triples may have rdf:nil as subject.

If x is a class list node, other than rdf:nil then there must be three triples with x as subject and these must of the following form:

4.4.5 dataRange Node Template

If x is a dataRange then there must be two triples with x as subject and these must of the following form:

4.4.6 dataRange Node Templates

No triples may have rdf:nil as subject.

If x is a dataRange list node, other than rdf:nil then there must be three triples with x as subject and these must of the following form:

Misc notes to be expanded

Bugs with AS:

• ontology and class annotation using OWL stuff and metaclasses not done.
• owl:Property in rdfs.html
• IOP in rdfs.html
• U in imports mapping rule
• transitive property flaw

Differences from AS:

• Can use object and datatype properties in annotations, as long as they are simple.
• Must assign types to blank nodes created in mapping rule.
• Do not have to assign type rdf:Datatype to datatypes.
• Can assign type rdf:Datatype to unused datatypes.
• Can have class expressions that are unused.
• rdfs:Class and rdf:Property legal.
• restrcitions with multiple parts not allowed. Use multiple type(r) or super(r) statements.
• do not permit multiple descriptions in DisjointClasses, or EquivalentClasses slightly different