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; Evan K. Wallace, NIST
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 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A draft printable version is available [1], but it is obsolete with respect to the current wiki version.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 complements the OWL 2 Primer, an updated version of which will be published in due course.
The OWL Working Group solicits feedback on how to improve and update this document.

Create inline hyperlinks to Syntax
Create hyperlinks to Direct Semantics and RDF-Based Semantics once the anchors in those documents are ready
Complete inline hyperlinks to Primer when the missing ones are ready
Create inline hyperlinks to New Features and Rationale
Make a new 2-page print version.
Design a similar guide for profiles with 1 page print version.

1 OWL/OWL 2 Vocabulary

Shaded constructs are only available in OWL 2.

OWL Classes

all OWL individuals	owl:Thing
empty class	owl:Nothing

Connectives and Enumeration

intersection	IntersectionOf(C₁ … C_n)	x owl:intersectionOf [ C₁ … C_n ].	C_j an OWL class
union	UnionOf(C₁ … C_n)	x owl:unionOf [ C₁ … C_n ].	C_j an OWL class
complement	ComplementOf(C)	x owl:complementOf C.	C an OWL class
enumeration	OneOf(i₁ … i_n)	x owl:oneOf [ i₁ … i_n ].	i_j an OWL individual

Restrictions Using Object Properties owl:Restriction

Every owl:Restriction is an owl:Class.

universal	AllValuesFrom(P C)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:allValuesFrom C	P an object property. C an OWL class
existential	SomeValuesFrom(P C)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:someValuesFrom C	P an object property. C an OWL class
individual value	HasValue(P i)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:hasValue i.	P an object property. i an individual
self	ExistsSelf(P)	x rdf:type owl:SelfRestriction. x owl:onProperty P.	P an object property
Cardinality Restrictions
exact cardinality	ExactCardinality(n P)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:cardinality n.	P an object property. n a nonNegativeInteger
maximum cardinality	MaxCardinality(n P)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:maxCardinality n.	P an object property. n a nonNegativeInteger
minimum cardinality	MinCardinality(n P)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:minCardinality n.	P an object property. n a nonNegativeInteger
Qualified Cardinality Restrictions
exact cardinality	ExactCardinality(n P C)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:qualifiedCardinality n. x owl:onClass C.	P an object property. n a nonNegativeInteger . C an OWL class
maximum cardinality	MaxCardinality(n P C)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:minQualifiedCardinality n. x owl:onClass C.	P an object property. n a nonNegativeInteger; C an OWL class
minimum cardinality	MinCardinality(n P C)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:maxQualifiedCardinality n. x owl:onClass C.	P an object property. n a nonNegativeInteger . C an OWL class

Restrictions Using Data Properties owl:Restriction

Every owl:Restriction is an owl:Class.

universal	AllValuesFrom(P D)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:allValuesFrom D.	P a data property. D a datatype
existential	SomeValuesFrom(P D)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:someValuesFrom D.	P a data property. D a datatype
n-ary universal	AllValuesFrom(P₁ … P_n D)	x rdf:type owl:Restriction. x owl:onProperties [ P₁ … P_n ]. x owl:allValuesFrom D.	P_i a data property. D an n-ary datatype
n-ary existential	SomeValuesFrom(P₁ … P_n D)	x rdf:type owl:Restriction. x owl:onProperties [ P₁ … P_n]. x owl:someValuesFrom D.	P_i a data property. D an n-ary datatype
individual value	HasValue(P v)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:hasValue v.	P an object property. v a literal
Cardinality Restrictions
exact cardinality	ExactCardinality(n P)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:cardinality n.	P a data property. n a nonNegativeInteger
maximum cardinality	MaxCardinality(n P)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:maxCardinality n.	P a data property. n a nonNegativeInteger
minimum cardinality	MinCardinality(n P)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:minCardinality n.	P a data property. n a nonNegativeInteger
Qualified Cardinality Restrictions
exact cardinality	ExactCardinality(n P D)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:qualifiedCardinality n. x owl:onDataRange D.	P a data property. n a nonNegativeInteger . D a datatype
maximum cardinality	MaxCardinality(n P D)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:maxQualifiedCardinality n. x owl:onDataRange D.	P a data property. n a nonNegativeInteger . D a datatype
minimum cardinality	MinCardinality(n P D)	x rdf:type owl:Restriction. x owl:onProperty P. x owl:minQualifiedCardinality n. x owl:onDataRange D.	P a data property. n a nonNegativeInteger . D a datatype

Class Axioms

subclasses	SubClassOf(C₁ C₂)	C₁ rdfs:subClassOf C₂.	C_i an OWL class
equivalent classes	EquivalentClasses(C₁ C₂)	C₁ owl:equivalentClass C₂.	C_i an OWL class
disjoint classes	DisjointClasses(C₁ C₂)	C₁ owl:disjointWith C₂.	C_i an OWL class
pairwise disjoint classes	DisjointClasses(C₁ … C_n)	x rdf:type owl:AllDisjointClasses. x owl:members [ C₁ … C_n ].	C_i an OWL class
disjoint union	DisjointUnionOf(C C₁ … C_n)	C owl:disjointUnionOf [ C₁ … C_n ].	C an OWL class. C_i an OWL class

Data Types rdfs:Datatype

datatype complement	ComplementOf(D)	x owl:datatypeComplementOf D.	D a datatype
enumeration	OneOf(v₁ … v_n)	x owl:oneOf [ v₁ … v_n ].	v_j a literal
datatype restriction	DatatypeRestriction(D f₁ v₁ … f_n v_n)	x owl:onDatatype D. x owl:withRestrictions [y1 ... yn]. y1 f₁ v₁. ... yn f_n v_n.	f_j a constraining facet, v_j a restriction value

Object Properties owl:ObjectProperty

universal object property	owl:topObjectProperty		= owl:Thing × owl:Thing
bottom object property	owl:bottomObjectProperty		empty binary relation
property chain	PropertyChain(P₁ … P_n)	x owl:propertyChain [P₁ … P_n].	P_i an object property

Object Property Axioms

subproperty	SubPropertyOf(P Q)	P rdfs:subPropertyOf Q.	P,Q object properties
complex subproperty	SubPropertyOf(PropertyChain(P₁ … P_n) Q)	x rdfs:subPropertyOf Q. x owl:propertyChain [P₁ … P_n].	P_i and Q object properties
property domain	PropertyDomain(P C)	P rdfs:domain C.	P an object property, C an OWL class
property range	PropertyRange(P C)	P rdfs:range C.	P an object property, C an OWL class
equivalent properties	EquivalentProperties(P Q)	P owl:equivalentProperty Q.	P,Q object properties
disjoint properties	DisjointProperties(P Q)	P owl:propertyDisjointWith Q.	P,Q object properties
pairwise disjoint properties	DisjointProperties(P₁ … P_n)	x rdf:type owl:AllDisjointProperties. x owl:members [ P₁ … P_n ].	P_i an object property
inverse properties	InverseProperties(P Q)	P owl:inverseOf Q.	P,Q object properties
functional property	FunctionalProperty(P)	P rdf:type owl:FunctionalProperty.	P an object property s P,o1. s P o2 => o1=o2
inverse functional property	InverseFunctionalProperty(P)	P rdf:type owl:InverseFunctionalProperty.	P an object property s1 P,o. s2 P o => s1=s2
reflexive property	ReflexiveProperty(P)	P rdf:type owl:ReflexiveProperty.	P an object property for all individual i, i P i
irreflexive property	IrreflexiveProperty(P)	P rdf:type owl:IrreflexiveProperty.	P an object property i1 p i2 => i1≠i2
symmetric property	SymmetricProperty(P)	P rdf:type owl:SymmetricProperty.	P an object property s p o => o p s
asymmetric property	AsymmetricProperty(P)	P rdf:type owl:AsymmetricProperty.	P an object property s P o => not o P s
transitive property	TransitiveProperty(P)	P rdf:type owl:TransitiveProperty.	P an object property i1 P i2. i2 P i3 => i1 P i3

Datatype Properties owl:DatatypeProperty

universal datatype property	owl:topDataProperty	= owl:Thing × rdfs:Literal
bottom datatype property	owl:bottomDataProperty	empty binary relation

Datatype Property Axioms

subproperty	SubPropertyOf(P Q)	P rdfs:subPropertyOf Q.	P,Q datatype properties
property domain	PropertyDomain(P C)	P rdfs:domain C.	P a datatype property, C an OWL class
property range	PropertyRange(P C)	P rdfs:range C.	P a datatype property, C a datatype
equivalent properties	EquivalentProperties(P Q)	P owl:equivalentProperty Q.	P,Q datatype properties
disjoint properties	DisjointProperties(P Q)	P owl:propertyDisjointWith Q.	P,Q datatype properties
pairwise disjoint properties	DisjointProperties(P₁ … P_n)	x rdf:type owl:AllDisjointProperties. x owl:members [ P₁ … P_n ].	P_i a datatype property
functional property	FunctionalProperty(P)	P rdf:type owl:FunctionalProperty.	P a datatype property s P,v1. s P v2 => v1=v2

Keys

Keys

HasKey(C P₁ … P_n)

C owl:hasKey [P₁ … P_n].

C an OWL class, P_i an object property or datatype property

x P_i z_i. y P_i z_i, for i => x=y

Assertions

individual equality	SameIndividual(a₁,a₂)	a₁ owl:sameAs a₂.	a₁,a₂ individuals
individual equality	SameIndividual(a₁ … a_n)	a_i owl:sameAs a_i+1. i=1…n-1	a_i an individual
individual inequality	DifferentIndividuals(a₁ a₂)	a₁ owl:differentFrom a₂.	a₁,a₂ individuals
pairwise individual inequality	DifferentIndividuals(a₁ … a_n)	x rdf:type owl:AllDifferent. x owl:members [a₁ … a_n].	a_i an individual
class assertion	ClassAssertion(C a)	a rdf:type C.	a an individual, C an OWL class
positive object property assertion	PropertyAssertion( P a₁ a₂ )	a₁ P a₂.	P an object property, a_i an individual
negative object property assertion	NegativePropertyAssertion(P a₁ a₂ )	x rdf:type owl:NegativePropertyAssertion. x owl:sourceIndividual a₁. x owl:assertionProperty P. x owl:targetIndividual a₂	P an object property, a_i an individual
negative datatype property assertion	NegativePropertyAssertion(P a₁ a₂ )	x rdf:type owl:NegativePropertyAssertion. x owl:sourceIndividual a₁. x owl:assertionProperty P. x owl:targetValue a₂	P a datatype property, a₁ an individual, a₂ a literal

Lists rdf:List (an RDF feature)

Note: in everywhere else of the document, we use only the concise N3 syntax.

concise N3 syntax	[a₁ … a_n]
triple-based N3 syntax	x₁ rdf:type rdf:List. x₁ rdf:first a₁. x₁ rdf:rest x₂. … x_n rdf:type rdf:List. x_n rdf:first a_n. x_n rdf:rest rdf:nil.

Declarations

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

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 reificated form

axioms

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.

Annotations

annotations	Annotation( P v)	x rdf:type owl:Annotation. x owl:subject y. x owl:predicate P. x owl:object v.	y the annotated resource P annotation property v a resource.
annotations	Annotation( P v)	y P v.	y the annotated resource P annotation property v a resource

Note: an annotated resource can be an ontology, an ontology entity, an axiom, an anonymous individual, or even another annotation.

Annotation Properties 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 Property Axioms

annotation subproperties	SubPropertyOf(P Q)	P rdfs:subPropertyOf Q.	P,Q annotation properties
annotation property domain	PropertyDomain(P U)	P rdfs:domain U.	P an annotation property, U a URI
annotation property range	PropertyRange(P U)	P rdfs:range U.	P an annotation property, U a URI

Deprecation

deprecated class	C Deprecated	C rdf:type owl:DeprecatedClass.	C an OWL class or a datatype
deprecated property	P Deprecated	P rdf:type owl:DeprecatedProperty.	P an object property, datatype property or annotation property.

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

OWL Ontologies owl:Ontology

OWL ontology	Ontology (O V)	O rdf:type owl:Ontology. O owl:versionInfo V.	O a URI; V a URI (optional)
Ontology Properties owl:OntologyProperty
importing	O Import(U)	O owl:imports U.	O an ontology, U an ontology URI
backwards compatibility		O owl:backwardCompatibleWith U.	O an ontology, U an ontology URI
incompatibility		O owl:incompatibleWith U.	O an ontology, U an ontology URI
prior version		O owl:priorVersion U.	O an ontology, U an ontology URI

Deprecated Vocabulary in OWL 2

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

2 Built-in Datatypes and Facets

2.1 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:realPlus and owl:real: (base datatype for other numeric datatypes, should not be directly instantiated)

owl:realPlus	the set of all real numbers plus +INF(positive infinity), -INF(negative infinity), -0(negative zero), NaN (not-a-number)
owl:real	the set of all real numbers

Other 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

URIs

xsd:anyURI

Time Instants

OWL 2 datatype

owl:dateTime

value space is set of numbers that represent difference

between the time instant and the first time instant of the 1st
of January 1 AD in the proleptic Gregorian calendar, in seconds

XSD datatypes

xsd:date	xsd:gDay	xsd:gYear
xsd:dateTime	xsd:gMonth	xsd:gYearMonth
xsd:duration	xsd:gMonthDay	xsd:time

XML Fragment

rdf:XMLLiteral

2.2 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 f	Datatype	Value v	Explanation
xsd:minInclusive, xsd:maxInclusive, xsd:minExclusive, xsd:maxExclusive	Numeric Datatype DT, owl:dateTime 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:langPattern	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

3 Name Spaces

Standard Namespaces and Prefixes used in OWL 2

Prefix	URI
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#
ox	http://www.w3.org/2006/12/owl2-xml#

Quick Reference Guide

From OWL

Contents

1 OWL/OWL 2 Vocabulary

2 Built-in Datatypes and Facets

2.1 Built-in Datatypes

2.2 Facets

3 Name Spaces

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