Quick Reference Guide

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Document title:: OWL 2 Web Ontology Language
Quick Reference Guide (Second Edition)

Authors: Jie Bao, Rensselaer Polytechnic Institute; Elisa F. Kendall, Sandpiper Software, Inc.; Deborah L. McGuinness, Rensselaer Polytechnic Institute
Contributors: Li Ding, Rensselaer Polytechnic Institute; Ankesh Khandelwal, Rensselaer Polytechnic Institute; Peter F. Patel-Schneider, Bell Labs Research, Alcatel-Lucent

Abstract: The OWL 2 Web Ontology Language, informally OWL 2, is an ontology language for the Semantic Web with formally defined meaning. OWL 2 ontologies provide classes, properties, individuals, and data values and are stored as Semantic Web documents. OWL 2 ontologies can be used along with information written in RDF, and OWL 2 ontologies themselves are primarily exchanged as RDF documents. The OWL 2 Document Overview describes the overall state of OWL 2, and should be read before other OWL 2 documents.

This document provides a quick reference guide to the OWL 2 language. It also provides links to other documents, including the OWL 2 Primer for language introduction and examples, the Syntax document for more details of the functional syntax, and the New Features and Rationale document for new feature descriptions.

This is an editors' draft. The intended final status of this document has not yet been determined; since it may become a Recommendation, it should be considered a Recommendation-Track document for now.
The OWL Working Group solicits feedback on how to improve and update this document.

1 Prefixes

The standard prefixes in OWL 2 are:

Prefix Name	Prefix IRI
rdf:	<http://www.w3.org/1999/02/22-rdf-syntax-ns#>
rdfs:	<http://www.w3.org/2000/01/rdf-schema#>
owl:	<http://www.w3.org/2002/07/owl#>
xsd:	<http://www.w3.org/2001/XMLSchema#>

2 OWL 2 constructs and axioms

We use the following notation conventions: 'C' is a class expression, 'D' is a data range, 'P' is an object property expression, 'R' is a data property, 'A' is an annotation property, 'a' is an individual, 'v' is a literal, 'n' is a non-negative integer (as a shorthand for "n"^^xsd:nonNegativeInteger), '_:x' is a blank node, 'O' is an ontology, and 'U' is an IRI. All of the previous can have subscripts. '(a₁ … a_n)' in the RDF syntax is an RDF list.

For an OWL 2 DL ontology, there are some global restrictions on axioms.

In the following tables, the first column gives links to Primer and New Features and Rationale (if applicable), the 2nd column gives links to (Functional) Syntax.

2.1 Classes

Predefined and Named Classes

Language Feature	Functional Syntax	RDF Syntax
named class	U	U
universal class	owl:Thing	owl:Thing
empty class	owl:Nothing	owl:Nothing

Boolean Connectives and Enumeration of Individuals

Language Feature	Functional Syntax	RDF Syntax
intersection	ObjectIntersectionOf(C₁ … C_n)	_:x rdf:type owl:Class. _:x owl:intersectionOf ( C₁ … C_n ).
union	ObjectUnionOf(C₁ … C_n)	_:x rdf:type owl:Class. _:x owl:unionOf ( C₁ … C_n ).
complement	ObjectComplementOf(C)	_:x rdf:type owl:Class. _:x owl:complementOf C.
enumeration	ObjectOneOf(a₁ … a_n)	_:x rdf:type owl:Class. _:x owl:oneOf ( a₁ … a_n ).

Object Property Restrictions

Language Feature	Functional Syntax	RDF Syntax
universal	ObjectAllValuesFrom(P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:allValuesFrom C
existential	ObjectSomeValuesFrom(P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:someValuesFrom C
individual value	ObjectHasValue(P a)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:hasValue a.
local reflexivity	ObjectHasSelf(P)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:hasSelf "true"^^xsd:boolean.
exact cardinality	ObjectExactCardinality(n P)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:cardinality n.
qualified exact cardinality	ObjectExactCardinality(n P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:qualifiedCardinality n. _:x owl:onClass C.
maximum cardinality	ObjectMaxCardinality(n P)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:minCardinality n.
qualified maximum cardinality	ObjectMaxCardinality(n P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:minQualifiedCardinality n. _:x owl:onClass C.
minimum cardinality	ObjectMinCardinality(n P)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:maxCardinality n.
qualified minimum cardinality	ObjectMinCardinality(n P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:maxQualifiedCardinality n. _:x owl:onClass C.

Data Property Restrictions

Language Feature	Functional Syntax	RDF Syntax
universal	DataAllValuesFrom(R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty R. _:x owl:allValuesFrom D.
existential	DataSomeValuesFrom(R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty R. _:x owl:someValuesFrom D.
individual value	DataHasValue(R v)	_:x rdf:type owl:Restriction. _:x owl:onProperty R. _:x owl:hasValue v.
exact cardinality	DataExactCardinality(n R)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:cardinality n.
qualified exact cardinality	DataExactCardinality(n R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:qualifiedCardinality n. _:x owl:onDataRange D.
maximum cardinality	DataMaxCardinality(n R)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:maxCardinality n.
qualified maximum cardinality	DataMaxCardinality(n R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:maxQualifiedCardinality n. _:x owl:onDataRange D.
minimum cardinality	DataMinCardinality(n R)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:minCardinality n.
qualified minimum cardinality	DataMinCardinality(n R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:minQualifiedCardinality n. _:x owl:onDataRange D.

Restrictions Using n-ary Data Range

"Dⁿ" is an n-ary data range.

Language Feature	Functional Syntax	RDF Syntax
n-ary universal	DataAllValuesFrom(R₁ … R_n Dⁿ)	_:x rdf:type owl:Restriction. _:x owl:onProperties ( R₁ … R_n ). _:x owl:allValuesFrom Dⁿ.
n-ary existential	DataSomeValuesFrom(R₁ … R_n Dⁿ)	_:x rdf:type owl:Restriction. _:x owl:onProperties ( R₁ … R_n). _:x owl:someValuesFrom Dⁿ.

Class Axioms

Language Feature	Functional Syntax	RDF Syntax
subclasses	SubClassOf(C₁ C₂)	C₁ rdfs:subClassOf C₂.
equivalent classes	EquivalentClasses(C₁ … C_n)	C_j owl:equivalentClass C_j+1. j=1…n-1
disjoint classes	DisjointClasses(C₁ C₂)	C₁ owl:disjointWith C₂.
pairwise disjoint classes	DisjointClasses(C₁ … C_n)	_:x rdf:type owl:AllDisjointClasses. _:x owl:members ( C₁ … C_n ).
disjoint union	DisjointUnionOf(C C₁ … C_n) _{C is a named class}	C owl:disjointUnionOf ( C₁ … C_n ).

2.2 Properties

Object Property Expressions

Language Feature	Functional Syntax	RDF Syntax
named object property	U	U
universal object property	owl:topObjectProperty	owl:topObjectProperty
empty object property	owl:bottomObjectProperty	owl:bottomObjectProperty
inverse property	ObjectInverseOf(P)	_:x owl:inverseOf P

Datatype Property Expressions

Language Feature	Functional Syntax	RDF Syntax
named datatype property	U	U
universal datatype property	owl:topDataProperty	owl:topDataProperty
empty datatype property	owl:bottomDataProperty	owl:bottomDataProperty

Object Property Axioms

Language Feature	Functional Syntax	RDF Syntax
subproperty	SubObjectPropertyOf(P₁ P₂)	P₁ rdfs:subPropertyOf P₂.
property chain inclusion	SubObjectPropertyOf(ObjectPropertyChain(P₁ … P_n) P)	P owl:propertyChainAxiom (P₁ … P_n).
property domain	ObjectPropertyDomain(P C)	P rdfs:domain C.
property range	ObjectPropertyRange(P C)	P rdfs:range C.
equivalent properties	EquivalentObjectProperties(P₁ … P_n)	P_j owl:equivalentProperty P_j+1. j=1…n-1
disjoint properties	DisjointObjectProperties(P₁ P₂)	P₁ owl:propertyDisjointWith P₂.
pairwise disjoint properties	DisjointObjectProperties(P₁ … P_n)	_:x rdf:type owl:AllDisjointProperties. _:x owl:members ( P₁ … P_n ).
inverse properties	InverseObjectProperties(P₁ P₂)	P₁ owl:inverseOf P₂.
functional property	FunctionalObjectProperty(P)	P rdf:type owl:FunctionalProperty.
inverse functional property	InverseFunctionalObjectProperty(P)	P rdf:type owl:InverseFunctionalProperty.
reflexive property	ReflexiveObjectProperty(P)	P rdf:type owl:ReflexiveProperty.
irreflexive property	IrreflexiveObjectProperty(P)	P rdf:type owl:IrreflexiveProperty.
symmetric property	SymmetricObjectProperty(P)	P rdf:type owl:SymmetricProperty.
asymmetric property	AsymmetricObjectProperty(P)	P rdf:type owl:AsymmetricProperty.
transitive property	TransitiveObjectProperty(P)	P rdf:type owl:TransitiveProperty.

Datatype Property Axioms

Language Feature	Functional Syntax	RDF Syntax
subproperty	SubDataPropertyOf(R₁ R₂)	R₁ rdfs:subPropertyOf R₂.
domain	DataPropertyDomain(R C)	R rdfs:domain C.
property range	DataPropertyRange(R D)	R rdfs:range D.
equivalent properties	EquivalentDataProperties(R₁ … R_n)	R_j owl:equivalentProperty R_j+1. j=1…n-1
disjoint properties	DisjointDataProperties(R₁ R₂)	R₁ owl:propertyDisjointWith R₂.
pairwise disjoint properties	DisjointDataProperties(R₁ … R_n)	_:x rdf:type owl:AllDisjointProperties. _:x owl:members ( R₁ … R_n ).
functional property	FunctionalDataProperty(R)	R rdf:type owl:FunctionalProperty.

2.3 Individuals & Literals

Language Feature	Functional Syntax	RDF Syntax
named individual	U	U
anonymous individual	:a _{'a' is a local label name}	_:a
literal (datatype value)	"abc"^^datatypeIRI	"abc"^^datatypeIRI

2.4 Data Ranges

Language Feature	Functional Syntax	RDF Syntax
named datatype	U	U
datatype definition	DatatypeDefinition(DT DR) _{DT a datatype, DR a data range}	DT owl:equivalentClass DR.
data range complement	DataComplementOf(D)	_:x rdf:type rdfs:Datatype. _:x owl:datatypeComplementOf D.
data range intersection	DataIntersectionOf(D₁…D_n)	_:x rdf:type rdfs:Datatype. _:x owl:intersectionOf (D₁…D_n).
data range union	DataUnionOf(D₁…D_n)	_:x rdf:type rdfs:Datatype. _:x owl:unionOf (D₁…D_n).
literal enumeration	DataOneOf(v₁ … v_n)	_:x rdf:type rdfs:Datatype. _:x owl:oneOf ( v₁ … v_n ).
datatype restriction	DatatypeRestriction(D f₁ v₁ … f_n v_n) _{D a datatype, f_j a facet, v_j a literal}	_:x rdf:type rdfs:Datatype. _:x owl:onDatatype D. _:x owl:withRestrictions (y1 ... yn). y_j f_j v_j. j=1…n

Note: datatypes are data ranges of arity one.

2.5 Keys

Language Feature	Functional Syntax	RDF Syntax
Keys	HasKey(C (P₁ … P_m) (R₁ … R_n) )	C owl:hasKey (P₁ … P_m R₁ … R_n).

2.6 Assertions

Language Feature	Functional Syntax	RDF Syntax
individual equality	SameIndividual(a₁ … a_n)	a_j owl:sameAs a_j+1. j=1…n-1
individual inequality	DifferentIndividuals(a₁ a₂)	a₁ owl:differentFrom a₂.
pairwise individual inequality	DifferentIndividuals(a₁ … a_n)	_:x rdf:type owl:AllDifferent. _:x owl:members (a₁ … a_n).
class assertion	ClassAssertion(C a)	a rdf:type C.
positive object property assertion	ObjectPropertyAssertion( P a₁ a₂ ) _{P is a named object property}	a₁ P a₂.
positive inverse object property assertion	ObjectPropertyAssertion( ObjectInverseOf(P) a₁ a₂ )	a₂ P a₁.
positive data property assertion	DataPropertyAssertion( P a v )	a P v.
negative object property assertion	NegativeObjectPropertyAssertion(P a₁ a₂ )	_:x rdf:type owl:NegativePropertyAssertion. _:x owl:sourceIndividual a₁. _:x owl:assertionProperty P. _:x owl:targetIndividual a₂
negative datatype property assertion	NegativeDataPropertyAssertion(R a v )	_:x rdf:type owl:NegativePropertyAssertion. _:x owl:sourceIndividual a. _:x owl:assertionProperty R. _:x owl:targetValue v

2.7 Declarations

'C', 'D', 'P', 'R', 'A' and 'a' are all named ontology entities.

Language Feature	Functional Syntax	RDF Syntax
class	Declaration( Class( C ) )	C rdf:type owl:Class.
datatype	Declaration( Datatype( D ) )	D rdf:type rdfs:Datatype.
object property	Declaration( ObjectProperty( P ) )	P rdf:type owl:ObjectProperty.
datatype property	Declaration( DataProperty( R ) )	R rdf:type owl:DatatypeProperty.
annotation property	Declaration( AnnotationProperty( A ) )	A rdf:type owl:AnnotationProperty.
named individual	Declaration( NamedIndividual( a ) )	a rdf:type owl:NamedIndividual.

2.8 Annotations

In this section, 's' is any IRI (e.g., a named ontology, class, datatype, property or individual) or an anonymous individual, 't' can be any IRI, an anonymous individual or a literal.

Annotation of an object

Language Feature	Functional Syntax	RDF Syntax
annotation assertions	AnnotationAssertion( A s t) _{s the annotated object, t a resource.}	s A t. _{or (if the assertion itself has annotation)}s A t. _:x rdf:type owl:Annotation. _:x owl:subject s. _:x owl:predicate A. _:x owl:object t.

Annotation of an axiom, an ontology or other annotations

Language Feature	Functional Syntax	RDF Syntax
annotations	CONTAINER(Annotation( A t) )	s p o. _:x rdf:type owl:Axiom. _:x owl:subject s. _:x owl:predicate p. _:x owl:object o. _:x A t. _{If CONTAINER(...) becomes s p o.} _:x p o _:x A t. _{If CONTAINER(...) becomes _:x p o.}

Note 1: a CONTAINER can be an axiom, an ontology, or another annotation.

Note 2: for n-ary axioms of the types EquivalentClasses, EquivalentProperties or SameIndividual, they will first be broken up into several RDF triples of their binary forms, then each triple is reified using the above rule.

Annotation Properties

Language Feature	Functional Syntax	RDF Syntax
named annotation property	U	U
human-readable name	rdfs:label	rdfs:label
human-readable comment	rdfs:comment	rdfs:comment
additional information	rdfs:seeAlso	rdfs:seeAlso
defining agent	rdfs:isDefinedBy	rdfs:isDefinedBy
version information	owl:versionInfo	owl:versionInfo
deprecation	owl:deprecated	owl:deprecated

Annotation Axioms

Language Feature	Functional Syntax	RDF Syntax
annotation subproperties	SubAnnotationPropertyOf(A₁ A₂)	A₁ rdfs:subPropertyOf A₂.
annotation property domain	AnnotationPropertyDomain(A U)	A rdfs:domain U.
annotation property range	AnnotationPropertyRange(A U)	A rdfs:range U.

Deprecation

C a named class, P a named object property, named datatype property or named annotation property;

Language Feature	Functional Syntax	RDF Syntax
deprecated class	AnnotationAssertion(owl:deprecated C "true"^^xsd:boolean)	C rdf:type owl:DeprecatedClass.
deprecated property	AnnotationAssertion(owl:deprecated P "true"^^xsd:boolean)	P rdf:type owl:DeprecatedProperty.
deprecated IRI	AnnotationAssertion(owl:deprecated U "true"^^xsd:boolean)	U owl:deprecated "true"^^xsd:boolean.

2.9 Ontologies

Ontologies

Language Feature	Functional Syntax	RDF Syntax
OWL ontology (importing )	Ontology([O [U]] Import(O₁)... Annotation(A v)... )	O rdf:type owl:Ontology. [O owl:versionIRI U.] O owl:imports O₁. ... O A v. ...
prefix declaration	Prefix(p=U) _{p is a prefix name}	@prefix p U.

Note: O₁ an ontology IRI; if O is omitted, then in the RDF syntax O is replaced by _:x (an anonymous individual).

Annotation Properties for Ontologies

Language Feature	Functional Syntax	RDF Syntax
backwards compatibility	O Anntation(owl:backwardCompatibleWith U)	O owl:backwardCompatibleWith U.
incompatibility	O Anntation(owl:incompatibleWith U)	O owl:incompatibleWith U.
prior version	O Anntation(owl:priorVersion U)	O owl:priorVersion U.

3 Built-in Datatypes and Facets

3.1 Built-in Datatypes

universal datatype	rdfs:Literal
Numbers	owl:rational		owl:real
	xsd:double	xsd:float	xsd:decimal	xsd:integer
	xsd:long	xsd:int	xsd:short	xsd:byte
	xsd:nonNegativeInteger		xsd:nonPositiveInteger
	xsd:positiveInteger		xsd:negativeInteger
	xsd:unsignedLong		xsd:unsignedInt
	xsd:unsignedShort		xsd:unsignedByte
Strings	rdf:text (internationalized strings)
	xsd:string	xsd:NCName	xsd:Name	xsd:NMTOKEN
	xsd:token	xsd:language	xsd:normalizedString
Boolean Values	xsd:boolean (value space: true and false)
Binary Data	xsd:base64Binary		xsd:hexBinary
IRIs	xsd:anyURI
Time Instants	xsd:dateTime (with time zone offset)
	xsd:dateTimeStamp (without time zone offset)
XML Literals	rdf:XMLLiteral (Note: at Risk in OWL 2)

3.2 Facets

The facet space is a set of pairs of the form < f v >, where f is an IRI called a constraining facet, and v is a value. Each such pair is mapped to a subset of the value space of the datatype.

Notations: Numeric Datatype, String Datatype and Binary datatype refer to a set of datatypes based on the classification done in the prior section.

Facet f	Datatype	Value v	Explanation
xsd:minInclusive, xsd:maxInclusive, xsd:minExclusive, xsd:maxExclusive	Numeric Datatype, Time instant Datatype	Literal in DT	Restricts the value-space to greater than (equal to) or lesser than (equal to) a value
xsd:minLength, xsd:maxLength, xsd:length	String Datatype, Binary Datatype, xsd:anyURI	Non-negative integer	Restricts the value-space based on the lengths of the literals
xsd:pattern	String Datatype, xsd:anyURI	xsd:string literal whose value is a regular expression	Restricts the value space to literals that match the regular expression
rdf:langRange	rdf:text	xsd:string literal whose value is a regular expression	Restricts the value space to literals with language tags that match the regular expression

4 Appendix

4.1 New Features in OWL 2

New features in OWL 2 are (with links to New Features and Rationale) are:

Class Expressions	local reflexivity (self restriction) object qualified exact/maximum/minimal cardinality restriction data qualified exact/maximum/minimal cardinality restriction universal restriction on n-ary data range existential restriction on n-ary data range
Class Axioms	pairwise disjoint classes class disjoint union
Property Expressions	universal object property empty object property universal datatype property empty datatype property inverse object property expression
Property Axioms	property chain inclusion binary and pairwise disjoint object properties binary and pairwise disjoint data properties reflexive object property irreflexive property asymmetric property
Data Ranges	datatype definition data range complement data range intersection data range union datatype restriction hook for n-ary datatype
Assertions	negative object property assertion negative datatype property assertion
Annotation	Annotation of an object Annotation of an axiom annotation subproperties annotation property domain annotation property range owl:deprecated annotation property
Built-in Extra Datatypes	owl:rational, owl:real, xsd:dateTimeStamp, rdf:text
Facets	xsd:minInclusive, xsd:maxInclusive, xsd:minExclusive, xsd:maxExclusive xsd:minLength, xsd:maxLength, xsd:length xsd:pattern rdf:langRange
Others	key declaration metamodeling capabilities anonymous individual

4.2 Deprecated Vocabularies in OWL 2

The following vocabularies are provided in OWL 1 but not encouraged in OWL 2.

OWL 1 Vocabulary	Status in OWL 2
owl:DataRange	replaced by rdfs:Datatype
owl:distinctMembers	replaced by owl:members

5 Acknowledgments

The starting point for the development of OWL 2 was the OWL1.1 member submission, itself a result of user and developer feedback, and in particular of information gathered during the OWL Experiences and Directions (OWLED) Workshop series. The working group also considered postponed issues from the WebOnt Working Group.

This document has been produced by the OWL Working Group (see below), and its contents reflect extensive discussions within the Working Group as a whole. The editors extend special thanks to Bernardo Cuenca Grau (Oxford University), Christine Golbreich (Université de Versailles St-Quentin and LIRMM), Ivan Herman (W3C/ERCIM), Bijan Parsia (University of Manchester) and Peter F. Patel-Schneider (Bell Labs Research, Alcatel-Lucent) for their thorough reviews.

The regular attendees at meetings of the OWL Working Group at the time of publication of this document were: Jie Bao (RPI), Diego Calvanese (Free University of Bozen-Bolzano), Bernardo Cuenca Grau (Oxford University Computing Laboratory), Martin Dzbor (Open University), Achille Fokoue (IBM Corporation), Christine Golbreich (Université de Versailles St-Quentin and LIRMM), Sandro Hawke (W3C/MIT), Ivan Herman (W3C/ERCIM), Rinke Hoekstra (University of Amsterdam), Ian Horrocks (Oxford University Computing Laboratory), Elisa Kendall (Sandpiper Software), Markus Krötzsch (FZI), Carsten Lutz (Universität Bremen), Deborah L. McGuinness (RPI), Boris Motik (Oxford University Computing Laboratory), Jeff Pan (University of Aberdeen), Bijan Parsia (University of Manchester), Peter F. Patel-Schneider (Bell Labs Research, Alcatel-Lucent), Sebastian Rudolph (FZI), Alan Ruttenberg (Science Commons), Uli Sattler (University of Manchester), Michael Schneider (FZI), Mike Smith (Clark & Parsia), Evan Wallace (NIST), Zhe Wu (Oracle Corporation), and Antoine Zimmermann (DERI Galway). We would also like to thank past members of the working group: Jeremy Carroll, Jim Hendler, and Vipul Kashyap.