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dl as RDF Graphs

An OWL Full document [Add definition and link] is an OWL dl Ontology if and only if the imports closure of the RDF graph 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 URI references from RDF, RDFS, OWL or XML Schema datatypes.
   • 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. No blank node occurs as the object of more than one triple.
3. No directed cycle of blank nodes occurs.
4. Every blank node with explicit type rdf:List is the object of exactly one triple.
5. Every builtin uriref is assigned to one of its listed categories, or to itself.
6. Every other uriref is assigned to one of the following categories:
   • ontologyID
   • datatypeID
   • classID
   • individualID
   • dataRangeID
   • simpleDataPropID
   • complexDataPropID
   • simpleObjectPropID
   • complexObjectPropID
   • transitivePropID
7. Every blank node is assigned to one of the following categories:
   • allDifferent
   • description
   • listOfDataLiteral
   • listOfDescription
   • listOfIndividualID
   • restriction
   • unnamedDataRange
   • unnamedIndividual
8. With the given category assignments every triple in the graph appears in one of the following tables:
   • main table
   • blank nodes of category description
   • blank nodes of category listOfDataLiteral
   • blank nodes of category listOfDescription
   • blank nodes of category listOfIndividualID
   • blank nodes of category restriction
   • blank nodes of category unnamedDataRange
9. Every blank node is either of category unnamedIndividual or meets the structural requirements listed belo of ti+1, for i from 0 to n-1.

   Triple Table

   e-table" id="dl-triple-table" >Triple Table

   Subject	Predicate	Object
   classID or description or restriction	owl:disjointWith or owl:sameClassAs or rdfs:subClassOf	classID or description or restriction

   Subject	Predicate	Object
   classID or description or restriction	owl:disjointWith or owl:sameClassAs or rdfs:subClassOf	classID or description or restriction
   individualID or unnamedIndividual	complexObjectPropID or simpleObjectPropID or transitivePropID or owl:differentFrom or owl:sameIndividualAs	individualID or unnamedIndividual
   complexObjectPropID or transitivePropID	rdfs:domain or rdfs:range	classID or description or restriction
   classID or complexDataPropID or complexObjectPropID or dataRangeID or ontologyID or simpleDataPropID or simpleObjectPropID or transitivePropID	simpleObjectPropID	individualID or unnamedIndividual
   complexObjectPropID or simpleObjectPropID or transitivePropID	rdf:type	owl:DeprecatedProperty or owl:ObjectProperty or rdf:Property
   individualID or unnamedIndividual	rdf:type	classID or description or restriction or owl:Thing
   complexDataPropID or simpleDataPropID	rdf:type	owl:DatatypeProperty or owl:DeprecatedProperty or rdf:Property
   classID	owl:intersectionOf or owl:unionOf	listOfDescription or rdf:nil
   complexObjectPropID or transitivePropID	rdfs:subPropertyOf	simpleObjectPropID or transitivePropID
   individualID or unnamedIndividual	complexDataPropID or simpleDataPropID	literal
   allDifferent	owl:distinctMembers	listOfIndividualID
   allDifferent	owl:distinctMembers	rdf:nil
   allDifferent	rdf:type	owl:AllDifferent
   classID	simpleDataPropID	literal
   classID	owl:complementOf	classID
   classID	owl:complementOf	description
   classID	owl:complementOf	restriction
   classID	owl:oneOf	listOfIndividualID
   classID	owl:oneOf	rdf:nil
   classID	rdf:type	owl:Class
   classID	rdf:type	owl:DeprecatedClass
   classID	rdf:type	rdfs:Class
   complexDataPropID	simpleDataPropID	literal
   complexDataPropID	owl:samePropertyAs	complexDataPropID
   complexDataPropID	rdf:type	owl:FunctionalProperty
   complexDataPropID	rdfs:domain	classID
   complexDataPropID	rdfs:domain	description
   complexDataPropID	rdfs:domain	restriction
   complexDataPropID	rdfs:range	dataRangeID
   complexDataPropID	rdfs:range	datatypeID
   complexDataPropID	rdfs:range	unnamedDataRange
   complexDataPropID	rdfs:subPropertyOf	complexDataPropID
   complexDataPropID	rdfs:subPropertyOf	simpleDataPropID
   complexObjectPropID	simpleDataPropID	literal
   complexObjectPropID	owl:inverseOf	complexObjectPropID
   complexObjectPropID	owl:samePropertyAs	complexObjectPropID
   complexObjectPropID	rdf:type	owl:FunctionalProperty
   complexObjectPropID	rdf:type	owl:InverseFunctionalProperty
   complexObjectPropID	rdf:type	owl:SymmetricProperty
   complexObjectPropID	rdfs:subPropertyOf	complexObjectPropID
   dataRangeID	simpleDataPropID	literal
   dataRangeID	owl:oneOf	listOfDataLiteral
   dataRangeID	owl:oneOf	rdf:nil
   dataRangeID	rdf:type	owl:DataRange
   datatypeID	rdf:type	rdfs:Datatype
   ontologyID	metaPropertyID	ontologyID
   ontologyID	simpleDataPropID	literal
   ontologyID	rdf:type	owl:Ontology
   simpleDataPropID	simpleDataPropID	literal
   simpleDataPropID	owl:samePropertyAs	simpleDataPropID
   simpleDataPropID	rdfs:subPropertyOf	simpleDataPropID
   simpleObjectPropID	simpleDataPropID	literal
   simpleObjectPropID	owl:samePropertyAs	simpleObjectPropID
   simpleObjectPropID	rdfs:subPropertyOf	simpleObjectPropID
   transitivePropID	simpleDataPropID	literal
   transitivePropID	owl:inverseOf	transitivePropID
   transitivePropID	owl:samePropertyAs	transitivePropID
   transitivePropID	rdf:type	owl:TransitiveProperty

   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 table.

   Subject	Predicate	Object
   Either:
   description	rdf:type	owl:Class
   description	owl:complementOf	classID or description or restriction
   Or:
   description	rdf:type	owl:Class
   description	owl:intersectionOf or owl:unionOf	listOfDescription or rdf:nil
   Or:
   description	rdf:type	owl:Class
   description	owl:oneOf	listOfIndividualID or rdf:nil

   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.

   Subject	Predicate	Object
   listOfDataLiteral	rdf:type	rdf:List
   listOfDataLiteral	rdf:first	literal
   listOfDataLiteral	rdf:rest	listOfDataLiteral or rdf:nil

   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.

   Subject	Predicate	Object
   listOfDescription	rdf:type	rdf:List
   listOfDescription	rdf:first	classID or description or restriction
   listOfDescription	rdf:rest	listOfDescription or rdf:nil

   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.

   Subject	Predicate	Object
   listOfIndividualID	rdf:type	rdf:List
   listOfIndividualID	rdf:first	individualID
   listOfIndividualID	rdf:rest	listOfIndividualID or rdf:nil

   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 table.

   Subject	Predicate	Object
   Either:
   restriction	rdf:type	owl:Restriction
   restriction	owl:allValuesFrom or owl:someValuesFrom	classID or description or restriction
   restriction	owl:onProperty	complexObjectPropID or transitivePropID
   Or:
   restriction	rdf:type	owl:Restriction
   restriction	owl:allValuesFrom or owl:someValuesFrom	dataRangeID or datatypeID or unnamedDataRange
   restriction	owl:onProperty	complexDataPropID
   Or:
   restriction	rdf:type	owl:Restriction
   restriction	owl:hasValue	individualID
   restriction	owl:onProperty	complexObjectPropID
   Or:
   restriction	rdf:type	owl:Restriction
   restriction	owl:hasValue	individualID
   restriction	owl:onProperty	transitivePropID
   Or:
   restriction	rdf:type	owl:Restriction
   restriction	owl:hasValue	literal
   restriction	owl:onProperty	complexDataPropID
   Or:
   restriction	rdf:type	owl:Restriction
   restriction	owl:maxCardinality or owl:minCardinality or owl:cardinality	nonNegativeInteger or 0^^ (xsd:nonNegativeInteger) or 1^^ (xsd:nonNegativeInteger)
   restriction	owl:onProperty	complexObjectPropID or complexDataPropID

   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 are no other triples in the graph in which such nodes are subjects.

   Subject	Predicate	Object
   unnamedDataRange	rdf:type	owl:DataRange
   unnamedDataRange	owl:oneOf	listOfDataLiteral or rdf:nil