Quick Reference Guide

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Document title:

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

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 is intended to provide a quick reference to the OWL 2 language, similar to what was provided in the Language Synopsis section of the OWL Web Ontology Language Overview. Inspiration for this effort includes work by the ebiquity Research Group at the University of Maryland Baltimore County (UMBC) on earlier versions of a Reference Card for the Semantic Web.
A draft printable version is available [1], but it is obsolete with respect to the current wiki version.

Status of this Document

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 Quick Reference Guide provides links into other documents that it is intended to complement, particularly the OWL 2 Primer for examples, the New Features and Rationale document for selected feature descriptions, the Syntax document for more details of functional syntax, and the Mapping to RDF Graphs document for details of RDF syntax.
The OWL Working Group solicits feedback on how to improve and update this document.

Copyright © 2008-2009 W3C^® (MIT, ERCIM, Keio), All Rights Reserved. W3C liability, trademark and document use rules apply.

2 OWL 2 constructs and axioms

Constructs in bold are only available in OWL 2. Each table has columns:

• 1st: construct's name and link to Primer and New Features and Rationale (if applicable)(as "(N)")
• 2nd: functional syntax and link to Syntax
• 3rd: RDF syntax with link to Mapping to RDF Graphs

We use the following notation conventions: unless stated otherwise, "C" is an OWL class, "D" is a data range, "P" and "Q" are object properties, "R" and "S" are data properties, "a" is an OWL individual, "u" and "v" are literals, "n" is a non-negative integer, "_:x" is anonymous individual. All names may have subscripts. "(a₁ … a_n)" in the 3rd column stands for a rdf list.

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

2.1 Classes

Predefined Classes

all OWL individuals	owl:Thing	owl:Thing
empty class	owl:Nothing	owl:Nothing

Boolean Connectives and Enumeration of Individuals

intersection	ObjectIntersectionOf(C1 … Cn)	_:x rdf:type owl:Class. _:x owl:intersectionOf ( C1 … Cn ).
union	ObjectUnionOf(C1 … Cn)	_:x rdf:type owl:Class. _:x owl:unionOf ( C1 … Cn ).
complement	ObjectComplementOf(C)	_:x rdf:type owl:Class. _:x owl:complementOf C.
enumeration	ObjectOneOf(a1 … an)	_:x rdf:type owl:Class. _:x owl:oneOf ( a1 … an ).

Object Property Restrictions

Every owl:Restriction is an owl:Class.

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 i.
local reflexivity (N)	ObjectHasSelf(P)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:hasSelf "true"^^xsd:boolean.
Object Property Cardinality Restrictions C is optional in OWL 2 and not allowed in OWL 1. (N)
exact cardinality	ObjectExactCardinality(n P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:cardinality n. (without C) _:x owl:qualifiedCardinality n. _:x owl:onClass C. (with C)
maximum cardinality	ObjectMaxCardinality(n P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:minCardinality n. (without C) _:x owl:minQualifiedCardinality n. _:x owl:onClass C. (with C)
minimum cardinality	ObjectMinCardinality(n P C)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:maxCardinality n. (without C) _:x owl:maxQualifiedCardinality n. _:x owl:onClass C. (with C)

Data Property Restrictions

Every owl:Restriction is an owl:Class.

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 u)	_:x rdf:type owl:Restriction. _:x owl:onProperty R. _:x owl:hasValue u.
Data Property Cardinality Restrictions D is optional in OWL 2 and not allowed in OWL 1. (N)
exact cardinality	DataExactCardinality(n R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:cardinality "n"^^xsd:nonNegativeInteger. _:x owl:qualifiedCardinality "n"^^xsd:nonNegativeInteger. (without D) _:x owl:onDataRange D. (with D)
maximum cardinality	DataMaxCardinality(n R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty P. _:x owl:maxCardinality "n"^^xsd:nonNegativeInteger. (without D) _:x owl:maxQualifiedCardinality "n"^^xsd:nonNegativeInteger. _:x owl:onDataRange D. (with D)
minimum cardinality	DataMinCardinality(n R D)	_:x rdf:type owl:Restriction. _:x owl:onProperty P.(without D) _:x owl:minCardinality "n"^^xsd:nonNegativeInteger. _:x owl:minQualifiedCardinality "n"^^xsd:nonNegativeInteger. _:x owl:onDataRange D. (with D)

Restrictions Using n-ary Data Range

"Dⁿ" is a n-ary data range (cf #Data Ranges).

n-ary universal (N)	DataAllValuesFrom(R1 … Rn Dn)	_:x rdf:type owl:Restriction. _:x owl:onProperties ( R1 … Rn ). _:x owl:allValuesFrom Dn.
n-ary existential (N)	DataSomeValuesFrom(R1 … Rn Dn)	_:x rdf:type owl:Restriction. _:x owl:onProperties ( R1 … Rn). _:x owl:someValuesFrom Dn.

2.1.1 Class Axioms

subclasses	SubClassOf(C1 C2)	C1 rdfs:subClassOf C2.
equivalent classes	EquivalentClasses(C1 … Cn)	C1 owl:equivalentClass C2. … Cn-1 owl:equivalentClass Cn.
disjoint classes	DisjointClasses(C1 C2)	C1 owl:disjointWith C2.
pairwise disjoint classes (N)	DisjointClasses(C1 … Cn)	_:x rdf:type owl:AllDisjointClasses. _:x owl:members ( C1 … Cn ).
disjoint union (N)	DisjointUnionOf(C C1 … Cn)	C owl:disjointUnionOf ( C1 … Cn ).

2.2 Properties

2.2.1 Property Expressions

• Object Properties

instances of owl:ObjectProperty

universal object property	owl:topObjectProperty	owl:topObjectProperty
bottom object property	owl:bottomObjectProperty	owl:bottomObjectProperty
inverse property	ObjectInverseOf(P)	_:x owl:inverseOf P

• Datatype Properties

instances of owl:DatatypeProperty

universal datatype property	owl:topDataProperty	owl:topDataProperty
bottom datatype property	owl:bottomDataProperty	owl:topDataProperty

2.2.2 Property Axioms

• Object Property Axioms

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

• Datatype Property Axioms

subproperty	SubDataPropertyOf(R S)	R rdfs:subPropertyOf S.
property domain	DataPropertyDomain(R C)	R rdfs:domain C.
property range	DataPropertyRange(R C)	R rdfs:range C.
equivalent properties	EquivalentDataProperties(R1 … Rn)	R1 owl:equivalentProperty R2. … Rn-1 owl:equivalentProperty Rn.
disjoint properties (N)	DisjointDataProperties(R S)	R owl:propertyDisjointWith S.
pairwise disjoint properties (N)	DisjointDataProperties(R1 … Rn)	_:x rdf:type owl:AllDisjointProperties. _:x owl:members ( R1 … Rn ).
functional property	FunctionalDataProperty(R)	R rdf:type owl:FunctionalProperty.

2.3 Data Ranges

Data ranges are sets of tuples of literals. All datatypes (rdfs:Datatype) are unary data ranges. Complex data ranges are constructed from data types and other data ranges.

n-ary data ranges are not directly provided by OWL 2. However, OWL 2 provides syntactical hooks for applications to add n-ary data range support.

data range complement	DataComplementOf(D)	_:x rdf:type rdfs:Datatype. _:x owl:datatypeComplementOf D.
data range intersection	DataUnionOf(D1…Dn)	_:x rdf:type rdfs:Datatype. _:x owl:unionOf (D1…Dn).
data range union	DataIntersectionOf(D1…Dn)	_:x rdf:type rdfs:Datatype. _:x owl:intersectionOf (D1…Dn).
literal enumeration	DataOneOf(v1 … vn)	_:x rdf:type rdfs:Datatype. _:x owl:oneOf ( v1 … vn ).
datatype restriction (N)	DatatypeRestriction(D f1 v1 … fn vn) fj a constraining facet, vj a restriction value	_:x rdf:type rdfs:Datatype. _:x owl:onDatatype D. _:x owl:withRestrictions (y1 ... yn). y1 f1 v1. ... yn fn vn.

2.4 Keys

Keys (N)

HasKey(C (P1 … Pm) (R1 … Rn) )

C owl:hasKey (P1 … Pm R1 … Rn).

2.5 Assertions

individual equality	SameIndividual(a1,a2)	a1 owl:sameAs a2.
individual equality	SameIndividual(a1 … an)	aj owl:sameAs aj+1. j=1…n-1
individual inequality	DifferentIndividuals(a1 a2)	a1 owl:differentFrom a2.
pairwise individual inequality	DifferentIndividuals(a1 … an)	_:x rdf:type owl:AllDifferent. _:x owl:members (a1 … an).
class assertion	ClassAssertion(C a)	i rdf:type C.
positive object property assertion	ObjectPropertyAssertion( P a1 a2 )	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 (N)	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 (N)	NegativeDataPropertyAssertion(R a u )	_:x rdf:type owl:NegativePropertyAssertion. _:x owl:sourceIndividual a. _:x owl:assertionProperty R. _:x owl:targetValue u

2.6 Declarations

class (N)	Declaration( Class( x ) )	x rdf:type owl:Class.
datatype (N)	Declaration( Datatype( x ) )	x rdf:type rdfs:Datatype.
object property (N)	Declaration( ObjectProperty( x ) )	x rdf:type owl:ObjectProperty.
datatype property (N)	Declaration( DataProperty( x ) )	x rdf:type owl:DatatypeProperty.
annotation property (N)	Declaration( AnnotationProperty( x ) )	x rdf:type owl:AnnotationProperty.
named individual (N)	Declaration( NamedIndividual( x ) )	x rdf:type owl:NamedIndividual.

2.7 Reification

If an axiom, when removed of all annotations, can be translated in a single RDF triple s p o, it can also be mapped to the following reified form

axioms

s p o

s p o. _:x rdf:type owl:Axiom. _:x owl:subject s. _:x owl:predicate p. _:x owl:object o.

s the subject, p the predicate, o the object of the triple.

Note:

• for axioms of type 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.
• for a axiom that is translated into a triple with s an anonymous node (e.g., in NegativePropertyAssertion), _:x is same to s.

2.8 Annotations

Annotation of a Resource.
y the annotated resource, P annotation property, v a resource

annotations

Annotation( P v)

y P v. or (when the annotation itself has annotations) y P v. _:x rdf:type owl:Annotation. _:x owl:subject y. _:x owl:predicate P. _:x owl:object v.

Note: in OWL 2, an annotated resource can be an ontology, an ontology entity (in a declaration axiom), an axiom, an anonymous individual, or another annotation.

Annotation Properties

all annotation properties are instances of owl:AnnotationProperty

human-readable name	Label	rdfs:label
human-readable description	Comment	rdfs:comment
additional information		rdfs:seeAlso
defining agent		rdfs:isDefinedBy
deprecation	Deprecated	owl:deprecated

Annotation Axioms

s the annotation subject, P annotation property, v a resource; P,Q annotation properties, U a URI.

annotation assertions	AnnotationAssertion( P s v)	s P v. or (if the assertion itself has annotation)s P v. _:x rdf:type owl:Annotation. _:x owl:subject s. _:x owl:predicate P. _:x owl:object v.
annotation subproperties	SubAnnotationPropertyOf(P Q)	P rdfs:subPropertyOf Q.
annotation property domain	AnnotationPropertyDomain(P U)	P rdfs:domain U.
annotation property range	AnnotationPropertyRange(P U)	P rdfs:range U.

Deprecation

C an OWL class or a datatype, P an object property, datatype property or annotation property.

deprecated class	C Deprecated	C rdf:type owl:DeprecatedClass.
deprecated property	P Deprecated	P rdf:type owl:DeprecatedProperty.

Note: "Deprecated" is the short for owl:deprecated "true"^^xsd:boolean

2.9 OWL Ontologies

O an ontology, U an ontology URI, V a URI.

OWL ontology	Ontology(O V) (V is optional)	O rdf:type owl:Ontology. O owl:versionIRI V.
Ontology Properties owl:OntologyProperty
importing	O Import(U)	O owl:imports U.
backwards compatibility		O owl:backwardCompatibleWith U.
incompatibility		O owl:incompatibleWith U.
prior version		O owl:priorVersion U.

2.10 Deprecated Vocabulary in OWL 2

owl:DataRange	replaced by rdfs:Datatype
owl:distinctMembers	replaced by owl:members

3 Built-in Datatypes and Facets

3.1 Built-in Datatypes

The value space is a set determining the set of values of the datatype. A literal value "abc" of the datatype DT can be given in the form "abc"^^DT.

• Numeric DataTypes

OWL Numeric Datetypes:

owl:rational	rational numbers
owl:real (N)	real numbers

XSD Numeric Datatypes

xsd:double	xsd:nonNegativeInteger	xsd:long	xsd:unsignedLong
xsd:float	xsd:nonPositiveInteger	xsd:int	xsd:unsignedInt
xsd:decimal	xsd:positiveInteger	xsd:short	xsd:unsignedShort
xsd:integer	xsd:negativeInteger	xsd:byte	xsd:unsignedByte

• Strings: value space is of the form <"abc", tag>

Strings with a Language Tag: tag is either an empty string or a lowercase language tag

rdf:text

internationalized strings

Strings without a Language Tag: tag is an empty string

xsd:string	xsd:NCName
xsd:normalizedString	xsd:NMTOKEN
xsd:token	xsd:language
xsd:Name

• Boolean Values

xsd:Boolean

value space has only two values: true and false

• Binary Data

xsd:base64Binary

xsd:hexBinary

• IRIs

xsd:anyURI

IRIs as defined in XML Schema Datatypes

• Time Instants

xsd:dateTime	time instants with time zone offset
xsd:dateTimeStamp	time instants 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 a URI 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(N) f	Datatype	Value v	Explanation
xsd:minInclusive, xsd:maxInclusive, xsd:minExclusive, xsd:maxExclusive	Numeric Datatype DT, Time instant DT	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	Nonnegative 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 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 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.