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<h1>OWL Web Ontology Language <br/> Reference</h1>

<h2><a id="w3c-doctype" name="w3c-doctype"></a>
W3C Recommendation 10 February 2004</h2>

      <div id="owl_2_notice" style="border: solid black 1px; padding: 0.5em; background: #FFB;">

	<p style="margin-top: 0; font-weight: bold;">New Version
        Available: OWL 2 <span style="padding-left: 2em;"></span>
        (Document Status Update, 12 November 2009)</p>

	<p style="margin-bottom: 0;">The OWL Working Group has produced
	a W3C Recommendation for a new version of OWL which adds
	features to this 2004 version, while remaining compatible.
	Please see <a href="http://www.w3.org/TR/owl2-overview">OWL 2
	Document Overview</a> for an introduction to OWL 2 and a guide
	to the OWL 2 document set.</p>

      </div>



<dl>
<dt>This version: </dt>
<dd><a href="http://www.w3.org/TR/2004/REC-owl-ref-20040210/">
http://www.w3.org/TR/2004/REC-owl-ref-20040210/</a></dd>

<dt>Latest version:</dt>
<dd><a href="http://www.w3.org/TR/owl-ref/">
http://www.w3.org/TR/owl-ref/</a></dd>

<dt>Previous version:</dt>
<dd><a href="http://www.w3.org/TR/2003/PR-owl-ref-20031215/">
http://www.w3.org/TR/2003/PR-owl-ref-20031215/</a></dd>

<dt>Editors:</dt>

<dd>
<a href="http://www.daml.org/people/mdean/">Mike Dean</a>, 
BBN Technologies<br/>
<a href="http://www.cs.vu.nl/~guus/">Guus Schreiber</a>,
Free University Amsterdam<br/>
</dd>

<dt>Authors:</dt>

<dd>
<a href="http://www.cs.man.ac.uk/~seanb/">Sean Bechhofer</a>,
University of Manchester<br/>
<a href="http://www.cs.vu.nl/~frankh/"> Frank van Harmelen</a>,
Free University Amsterdam<br/>
<a href="http://www.cs.umd.edu/users/hendler/">Jim Hendler</a>,
University of Maryland<br/>
<a href="http://www.cs.man.ac.uk/~horrocks/">Ian Horrocks</a>,
University of Manchester<br/>
<a href="http://www.ksl.stanford.edu/people/dlm/">Deborah L. 
McGuinness</a>, Stanford University<br/>
<a href="http://www.bell-labs.com/user/pfps/">Peter F. 
Patel-Schneider</a>, Bell Labs Research, Lucent Technologies<br/>
<a href="http://faculty.olin.edu/~las/">Lynn Andrea Stein</a>,
Franklin W. Olin College of Engineering<br/>
</dd>
</dl>


<p>Please refer to the <a
href="http://www.w3.org/2001/sw/WebOnt/errata#owl-ref"><strong>errata</strong></a>
for this document, which may include some normative corrections.</p>

<p>See also <a href="http://www.w3.org/2001/sw/RDFCore/translation/owl-ref">translations</a>.</p>

<p class="copyright"><a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright"> Copyright</a> &#xa9; 2004 <a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>&#xae;</sup> (<a href="http://www.csail.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.org/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. W3C <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a>, <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> and <a href="http://www.w3.org/Consortium/Legal/copyright-software">software licensing</a> rules apply.</p>

<hr />
</div>

<h2><a id="abstract" name="abstract">Abstract</a></h2>

<p>The Web Ontology Language OWL is a semantic markup language for publishing
and sharing ontologies on the World Wide Web.  
OWL is developed as a vocabulary extension of  
RDF (the Resource Description Framework) and is derived from the DAML+OIL Web
Ontology Language. This document contains a structured informal description
of the full set of OWL language constructs and is meant to serve as
a reference for OWL users who want to construct OWL ontologies.  </p>

<h2><a id="status" name="status">Status of this document</a></h2>

<!-- Start Status-Of-This-Document Text -->

<p>This document has been reviewed by W3C Members and other interested
parties, and it has been endorsed by the Director as a <a
href="http://www.w3.org/2003/06/Process-20030618/tr.html#RecsW3C">W3C
Recommendation</a>.  W3C's role in making the Recommendation is to
draw attention to the specification and to promote its widespread
deployment. This enhances the functionality and interoperability of
the Web.</p>

<p>This is one of <a
href="http://www.w3.org/TR/2004/REC-owl-features-20040210/#s1.1">six
parts</a> of the W3C Recommendation for OWL, the Web Ontology
Language.  It has been developed by the <a
href="http://www.w3.org/2001/sw/WebOnt/">Web Ontology Working
Group</a> as part of the <a href="http://www.w3.org/2001/sw/">W3C
Semantic Web Activity</a> (<a
href="http://www.w3.org/2001/sw/Activity">Activity Statement</a>, <a
href="http://www.w3.org/2001/sw/WebOnt/charter">Group Charter</a>) for
publication on 10 February 2004.  </p>

<p>The design of OWL expressed in earlier versions of these documents
has been widely reviewed and satisfies the Working Group's <a
href="http://www.w3.org/TR/webont-req/"> technical requirements</a>.
The Working Group has addressed <a
href="http://lists.w3.org/Archives/Public/public-webont-comments/">
all comments received</a>, making changes as necessary.  Changes to
this document since <a
href="http://www.w3.org/TR/2003/PR-owl-ref-20031215/">the Proposed
Recommendation version</a> are detailed in the <a
href="./#changes-since-PR">change log</a>.</p>

<p>Comments are welcome at <a
href="mailto:public-webont-comments@w3.org">public-webont-comments@w3.org</a>
(<a
href="http://lists.w3.org/Archives/Public/public-webont-comments/">archive</a>)
and general discussion of related technology is welcome at <a
href="mailto:www-rdf-logic@w3.org">www-rdf-logic@w3.org</a> (<a
href="http://lists.w3.org/Archives/Public/www-rdf-logic/"
shape="rect">archive</a>).
</p>

<p>A list of <a href="http://www.w3.org/2001/sw/WebOnt/impls">
implementations</a> is available.</p>

<p>The W3C maintains a list of <a
href="http://www.w3.org/2001/sw/WebOnt/discl" rel="disclosure">any
patent disclosures related to this work</a>.
</p>

<p><em>This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the <a href="http://www.w3.org/TR/">W3C technical reports index</a> at http://www.w3.org/TR/.</em></p>

<!-- End Status-Of-This-Document Text -->


<h2><a id="acknowledge" name="acknowledge">Acknowledgments</a></h2>

<p>Parts of this document are derived from the DAML+OIL (March 2001) Reference
Description [<cite><a href="#ref-daml">DAML+OIL</a></cite>] which was
submitted as part of the 
<a href="http://www.w3.org/Submission/2001/12/">DAML+OIL W3C Note
</a>.  
The sponsors of this document and its 
predecessor documents are gratefully acknowledged.
</p>
<p>Jeremy Carroll, Jim Hendler, Brian McBride and
Peter Patel-Schneider provided 
substantive reviews and contributed text to this document. Jeff Heflin
contributed the section on deprecation. Jerome Euzenat
contributed the example for an enumerated datatype. 
</p>
<p>
This document is the result of extensive discussions within the
<a href="http://www.w3.org/2001/sw/WebOnt/">Web Ontology Working Group 
</a>as a whole.  The participants in this Working Group included: 
Yasser alSafadi, 
Jean-Fran&#231;ois Baget, 
James Barnette, 
Sean Bechhofer, 
Jonathan Borden, 
Frederik Brysse, 
Stephen Buswell, 
Jeremy Carroll, 
Dan Connolly, 
Peter Crowther, 
Jonathan Dale, 
Jos De Roo, 
David De Roure, 
Mike Dean, 
Larry Eshelman, 
J&#233;r&#244;me Euzenat, 
Tim Finin, 
Nicholas Gibbins, 
Sandro Hawke, 
Patrick Hayes, 
Jeff Heflin,
Ziv Hellman, 
James Hendler, 
Bernard Horan, 
Masahiro Hori, 
Ian Horrocks, 
Jane Hunter, 
Francesco Iannuzzelli, 
R&#252;diger Klein, 
Natasha Kravtsova, 
Ora Lassila, 
Massimo Marchiori, 
Deborah McGuinness, 
Enrico Motta, 
Leo Obrst, 
Mehrdad Omidvari, 
Martin Pike, 
Marwan Sabbouh, 
Guus Schreiber, 
Noboru Shimizu, 
Michael Sintek,
Michael K. Smith, 
John Stanton, 
Lynn Andrea Stein, 
Herman ter Horst, 
David Trastour, 
Frank van Harmelen, 
Bernard Vatant,
Raphael Volz, 
Evan Wallace, 
Christopher Welty, 
Charles White,
and John Yanosy.
</p>
 

<h2><a id="contents" name="contents">Contents</a></h2>

<ul class="toc">
  <li><a href="#abstract">Abstract</a></li>
  <li><a href="#status">Status of this document</a></li>
  <li><a href="#acknowledge">Acknowledgments</a></li>
  <li><a href="#Intro">1. Introduction</a>
    <ul class="toc">
      <li><a href="#Purpose">1.1 Purpose of this document</a></li>
      <li><a href="#Sublanguages">1.2 OWL Full/DL/Lite</a></li>
      <li><a href="#Syntax">1.3 OWL syntax</a></li>
      <li><a href="#Semantics">1.4 OWL and RDF semantics</a></li>
      <li><a href="#Examples">1.5 A note about the examples</a></li>
      <li><a href="#Privacy">1.6 Data aggregation and privacy</a></li>
      <li><a href="#AppendixList">1.7 Appendices of this document</a></li>
    </ul>
  </li>
  <li><a href="#OWLDocument">2. OWL document</a>
    <ul class="toc">
      <li><a href="#DocumentContent">2.1 Content</a></li>
      <li><a href="#owl-uri-namespace">2.2 OWL URI vocabulary and namespace</a></li>
      <li><a href="#MIMEType">2.3 MIME type</a></li>
    </ul>
  </li>
  <li><a href="#Class">3. Classes</a>
    <ul class="toc">
      <li><a href="#ClassDescription">3.1 Class descriptions</a>
        <ul class="toc">
          <li><a href="#EnumeratedClass">3.1.1 Enumeration</a></li>
          <li><a href="#Restriction">3.1.2 Property restriction</a>
            <ul class="toc">
              <li><a href="#ValueRestriction">3.1.2.1 Value constraints</a>
                <ul class="toc">
       	          <li><a href="#allValuesFrom-def">3.1.2.1.1
    	          owl:allValuesFrom</a></li> 
    	          <li><a href="#someValuesFrom-def">3.1.2.1.2
    	          owl:someValuesFrom</a></li>  
	          <li><a href="#hasValue-def">3.1.2.1.3
    	          owl:hasValue</a></li> 
                </ul>
              </li> 
              <li><a href="#CardinalityRestriction">3.1.2.2 Cardinality
	constraints</a>
                <ul class="toc">
  	          <li><a href="#maxCardinality-def">3.1.2.2.1
	          owl:maxCardinality</a></li> 
	          <li><a href="#minCardinality-def">3.1.2.2.2
	          owl:minCardinality</a></li> 
	          <li><a href="#cardinality-def">3.1.2.2.3
	          owl:cardinality</a></li> 
                </ul>
              </li>
            </ul>
          </li>
          <li><a href="#Boolean">3.1.3 Intersection, union and complement</a>
            <ul class="toc">
              <li><a href="#intersectionOf-def">3.1.3.1
              owl:intersectionOf</a></li> 
              <li><a href="#unionOf-def">3.1.3.2 owl:unionOf</a></li>
              <li><a href="#complementOf-def">3.1.3.3
              owl:complementOf</a></li> 
            </ul>
          </li>
        </ul>
      </li>
      <li><a href="#ClassAxioms">3.2 Class axioms</a>
        <ul class="toc">
          <li><a href="#subClassOf-def">3.2.1 rdfs:subClassOf</a></li>
          <li><a href="#equivalentClass-def">3.2.2
          owl:equivalentClass</a></li> 
          <li><a href="#DescriptionAxiom">3.2.3 Axioms for complete
          classes without using owl:equivalentClass</a></li>
          <li><a href="#disjointWith-def">3.2.4 owl:disjointWith</a></li>
        </ul>
      </li>
    </ul>
  </li>
  <li><a href="#Property">4. Properties</a>
    <ul class="toc">
      <li><a href ="#RDFSProperty">4.1 RDF Schema property constructs</a>
        <ul class="toc"> 
          <li><a href="#subPropertyOf-def">4.1.1 rdfs:subPropertyOf</a></li>
          <li><a href="#domain-def">4.1.2 rdfs:domain</a></li>
          <li><a href="#range-def">4.1.3 rdfs:range</a></li>
        </ul></li>
      <li><a href="#PropertyRelation">4.2 Relations to other properties</a>
        <ul class="toc">
          <li><a href="#equivalentProperty-def">4.2.1
          owl:equivalentProperty</a></li> 
          <li><a href="#inverseOf-def">4.2.2 owl:inverseOf</a></li>
        </ul></li>
      <li><a href="#PropertyCardinality">4.3 Global cardinality
          restrictions on properties</a> 
        <ul class="toc">
          <li><a href="#FunctionalProperty-def">4.3.1
          owl:FunctionalProperty</a></li>  
          <li><a href="#InverseFunctionalProperty-def">4.3.2
          owl:InverseFunctionalProperty</a></li> 
        </ul></li>
      <li><a href="#PropertyLogic">4.4 Logical characteristics of
          properties</a> 
        <ul class="toc">
          <li><a href="#TransitiveProperty-def">4.4.1
          owl:TransitiveProperty</a></li> 
          <li><a href="#SymmetricProperty-def">4.4.2
          owl:SymmetricProperty</a></li> 
        </ul></li>
    </ul></li>
  <li><a href="#Individual">5. Individuals</a>
    <ul class="toc">
      <li><a href="#IndividualAxiom">5.1 Class membership and property values</a></li>
      <li><a href="#IndividualIdentity">5.2 Individual identity</a>
        <ul class="toc">
          <li><a href="#sameAs-def">5.2.1 owl:sameAs</a></li> 
          <li><a href="#differentFrom-def">5.2.2 owl:differentFrom</a></li>
          <li><a href="#AllDifferent-def">5.2.3 owl:AllDifferent</a></li>
        </ul>
      </li>
    </ul>
  </li>
  <li><a href="#Datatype">6. Datatypes</a>
    <ul class="toc">
      <li><a href="#rdf-datatype">6.1 RDF Datatypes</a></li>
      <li><a href="#EnumeratedDatatype">6.2 Enumerated datatype using
      owl:oneOf</a></li>
      <li><a href="#DatatypeSupport">6.3 Support for datatype
      reasoning</a></li> 
    </ul>
  </li>
  <li><a href="#Header">7. Annotations, ontology header, imports and version information</a>
    <ul class="toc">
      <li><a href="#Annotations">7.1 Annotations</a></li>
      <li><a href="#Ontology-def">7.2 Ontology header</a></li>
      <li><a href="#imports-def">7.3 Importing ontologies</a></li>
      <li><a href="#VersionInformation">7.4 Version information</a>
        <ul class="toc">
          <li><a href="#versionInfo-def">7.4.1 owl:versionInfo</a></li>
          <li><a href="#priorVersion-def">7.4.2 owl:priorVersion</a></li>
          <li><a href="#backwardCompatibleWith-def">7.4.3
          owl:backwardCompatibleWith</a></li> 
          <li><a href="#incompatibleWith-def">7.4.4
          owl:incompatibleWith</a></li> 
         <li><a href="#Deprecation">7.4.5 owl:DeprecatedClass and
          owl:DeprecatedProperty</a></li> 
        </ul>
      </li>
    </ul>
  </li>
  <li><a href="#Sublanguage-def">8. OWL Full, OWL DL and OWL Lite</a>
  <ul class="toc">
    <li><a href="#OWLFull">8.1 OWL Full</a></li>
    <li><a href="#OWLDL">8.2 OWL DL</a></li>
    <li><a href="#OWLLite">8.3 OWL Lite</a></li>
  </ul></li>
  <li>Appendix A: <a href="#appA">Index of all language elements</a></li>
  <li>Appendix B: <a href="#appB">RDF Schema of OWL</a></li>
  <li>Appendix C: <a href="#appC">OWL Quick Reference</a></li>
  <li>Appendix D: <a href="#appD">Changes from DAML+OIL</a></li>
  <li>Appendix E: <a href="#app-DLinRDF">Rules of Thumb for OWL DL ontologies
  </a></li>
  <li>Appendix F: <a href="#changes-since-PR">Change Log since PR</a></li>
  <li><a href="#References">References</a></li>
</ul>


<hr/>

<h2><a name="Intro"></a>1. Introduction</h2>

<h3><a name="Purpose"></a>1.1 Purpose of this document</h3>

<p>This document gives a systematic, compact and informative description
of all the modelling primitives of OWL, using the RDF/XML
exchange syntax for OWL. We expect this document to
serve as a reference guide for users of the OWL language. </p>

<p>
This document is one component of the description of OWL, the Web Ontology
Language, being produced by the W3C Web Ontology Working Group.
The <a href="http://www.w3.org/TR/2004/REC-owl-features-20040210/#s1.1">Document Roadmap</a> section 
of the OWL Overview document describes each of the different parts
and how they fit together.
Readers
unfamiliar with OWL may wish to first consult the OWL Overview
document 
[<cite><a href="#ref-OWL-Overview">OWL Overview</a></cite>], 
and subsequently the OWL Guide 
[<cite><a href="#ref-owl-guide">OWL Guide</a></cite>] 
for a more narrative description and examples of the  use of
the language.</p>

<p>This document assumes the reader is familiar with the basic concepts of 
RDF [<cite><a href="#ref-rdf-concepts">RDF Concepts</a></cite>] and has a
working knowledge of the RDF/XML syntax 
[<cite><a href="#ref-rdf-syntax">RDF/XML Syntax</a></cite>] and of RDF
Schema [<cite><a href="#ref-rdf-vocabulary">RDF Vocabulary</a></cite>].</p>

<p>The normative reference on the precise syntax of the OWL language
constructs can be found in the OWL
Semantics and Abstract Syntax document 
[<cite><a href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>].  
That
document also contains a precise definition of the meaning of the
language constructs in the form of a model-theoretic
semantics. 
Notions such as consistency of OWL ontologies
are discussed in that document. </p>

<p>Use cases and requirements for the OWL language are described in the OWL
requirements document
[<cite><a href="#ref-owl-requirements">OWL Requirements</a></cite>].
Test cases for OWL tools (<em>e.g.</em>, entailment tests, consistency tests)
are specified in the Test document
[<cite><a href="#ref-owl-test">OWL Test Cases</a></cite>] . 
</p>

<h3><a name="Sublanguages" id="Sublanguages"></a>1.2 OWL Full/DL/Lite </h3>

<p>As also discussed in the 
OWL Overview document 
[<cite><a href="#ref-OWL-Overview">OWL Overview</a></cite>], 
and subsequently the OWL Guide 
[<cite><a href="#ref-owl-guide">OWL Guide</a></cite>], 
the OWL language provides two specific subsets that we believe will
be of use to implementors and language users.  OWL Lite was
designed for easy implementation and to provide users with a
functional subset that will get them started in the use of OWL.
OWL DL (where DL stands for "Description Logic") 
was designed to support the existing
Description Logic business segment and to provide a language subset
that has desirable computational properties for reasoning systems.
The complete OWL language (called OWL Full to distinguish it from the
subsets)  relaxes some of the constraints on OWL DL so as to make available
features which may be of use to many database and knowledge 
representation systems, but which violate the constraints of 
Description Logic reasoners.</p>

<p class="note">
NOTE: RDF documents will generally be in OWL Full, unless  they are
specifically constructed to be in OWL DL or Lite.
</p> 

<p>OWL Full and OWL DL support the same set of OWL language constructs. 
Their difference lies in restrictions on the use of some of those 
features and on the use of RDF features. 
OWL Full allows free mixing of OWL with RDF Schema and, 
like RDF Schema, does not enforce a strict separation of classes, 
properties, individuals and data values. OWL DL puts constraints on the mixing 
with RDF and requires disjointness of classes, properties, individuals 
and data values. The main reason for having the OWL DL sublanguage is 
that tool builders have developed powerful reasoning systems which 
support ontologies constrained by the restrictions required for OWL 
DL. For the formal definitions of  the differences between OWL Full 
and OWL DL the reader is referred to the Semantics and Abstract Syntax
document 
[<cite><a href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>]. 
<a href="#OWLDL">Sec. 8.2 "OWL DL"</a>
summarizes the differences between OWL Full and OWL DL.</p>

<p>OWL Lite is a sublanguage of OWL DL that supports only a subset of the 
OWL language constructs. OWL Lite is particularly targeted at tool 
builders, who want to support OWL, but want to start with a 
relatively simple basic set of language features.   
OWL Lite abides by the same semantic restrictions as OWL DL,
allowing reasoning engines to guarantee certain desirable properties. 
A summary of the language constructs allowed in OWL Lite is given in 
<a href="#OWLLite">Sec. 8.3</a>.
For a 
more formal description of the subset of OWL language constructs 
supported by OWL Lite the reader is referred to the Semantics and
Abstract Syntax  document
[<cite><a href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>]. </p>


<p class="note">
NOTE: RDF users upgrading to OWL should be aware that OWL Lite is
<em>not</em> simply an extension of RDF Schema. OWL Lite is a light
version of OWL DL and puts constraints on the use of the RDF
vocabulary (<em>e.g.</em>, disjointness of classes, properties,
etc.). OWL Full is designed for maximal RDF compatibility and is
therefore the natural place to start for RDF users. When opting for
either OWL DL or OWL Lite one should consider whether the advantages
of OWL DL/Lite (<em>e.g.</em>, reasoning support) outweigh the DL/Lite
restrictions on the use of OWL and RDF constructs.
</p>

<p class="note">
NOTE: OWL Lite is defined in this document as a number of additional 
restrictions on OWL DL. This
mean that, OWL DL constructs are also part of OWL Lite, unless
explicitly stated otherwise. 
<a href="#OWLLite">Sec. 8.3</a>.provides a summary of these additional
OWL Lite restrictions.</p>


<h3><a name="Syntax"></a>1.3 OWL syntax </h3>

<p>
An OWL ontology is an RDF graph 
[<cite><a href="#ref-rdf-concepts">RDF Concepts</a></cite>], 
which is in turn a set of RDF triples.
As with any RDF graph, an OWL ontology graph can be
written in many different syntactic forms (as described in the 
RDF/XML Syntax Specification (Revised)
[<cite><a href="#ref-rdf-syntax">RDF/XML Syntax</a></cite>]).
The current document 
uses some specific syntactic forms of RDF/XML for representing triples
(as does the Guide document) .
However, the meaning of an OWL ontology is solely determined by the
RDF graph. Thus, it is allowable to use  other syntactic RDF/XML
forms, as long as these  
result in the same underlying set of RDF triples. 
Such other syntactic forms would then carry exactly the same
meaning as the syntactic form used in this
document. </p>

<p>As a simple example of an alternative syntactic
form resulting in the same RDF triples, consider 
the following RDF/XML syntax:</p>

<pre>
&lt;owl:Class rdf:ID="Continent"/&gt; 
</pre>
      
<p>The following RDF/XML syntax:</p>

<pre>
&lt;rdf:Description rdf:about="#Continent"&gt;
  &lt;rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Class"/&gt;
&lt;/rdf:Description&gt; 
</pre>
      
<p>encodes the same set of RDF triples, and therefore
would convey the same meaning.</p>

<h3><a name="Semantics"></a>1.4 OWL and RDF semantics</h3>

<p>OWL is a vocabulary extension of RDF 
[<cite><a
href="#ref-RDF-Semantics">RDF Semantics</a></cite>].  
Thus any RDF graph
forms an OWL Full ontology.  Further, the meaning given to an RDF
graph by OWL includes the meaning given to the graph by RDF.  OWL Full
ontologies can thus include arbitrary RDF content, which is treated in
a manner consistent with its treatment by RDF.  OWL assigns an
additional meaning to certain RDF triples.  The OWL Semantics and
Abstract Syntax document [<cite><a href="#ref-owl-abstract-syntax">OWL
S&amp;AS</a></cite>] specifies exactly which triples are assigned a
specific meaning, and what this meaning is.</p>

<p class="note">
NOTE: As remarked before, OWL DL and OWL Lite extend the RDF
vocabulary, but also put restrictions on the use of this vocabulary.
Therefore, RDF documents will generally be in OWL Full, unless they
are specifically constructed to be in OWL DL or Lite.  </p>


<h3><a name="Examples">1.5 A note about the examples</a></h3>
 
<p>For readability purposes the examples in this document assume the 
XML entities <code>&amp;rdf;</code>, <code>&amp;rdfs;</code>,
<code>&amp;owl;</code> and <code>&amp;xsd;</code> (for XML Schema datatypes) 
are defined in the same way
as in <a href="#appB">Appendix B</a>. The same assumption holds for the
corresponding namespaces <code>rdf:</code>, <code>rdfs:</code>,
<code>owl:</code> and <code>xsd:</code>.</p>

<p>The examples in this document are meant to serve as illustrations of the
use of OWL language constructs. They do not form one consistent ontology. For
an extended  example the reader is referred to the Guide document
[<cite><a href="#ref-owl-guide">OWL Guide</a></cite>]. </p>

<h3><a id="Privacy" name="Privacy">1.6 Data Aggregation and Privacy</a></h3>

<p>
OWL's ability to express ontological information about individuals
appearing in multiple documents supports linking of data from diverse
sources in a principled way.  The underlying semantics provides
support for inferences over this data that may yield unexpected
results.  In particular, the ability to express equivalences using
<a href="#sameAs-def">owl:sameAs</a> 
can be used to state that seemingly
different individuals are actually the same.
Similarly,  
<a href="#InverseFunctionalProperty-def">owl:InverseFunctionalProperty</a> 
can be used to link
individuals together.
For example, if a property such as <code>SocialSecurityNumber</code>
is an
<code>owl:InverseFunctionalProperty</code>, then two separate individuals
could be inferred to be identical based on having the same value of
that property.  When individuals are determined to be the same by such
means, information about them from different sources can be
merged. This <em>aggregation</em> can be used to determine facts that
are not <em>directly</em> represented in any one source.
</p>

<p> 
The ability of the Semantic Web to link information from multiple
sources is a desirable and powerful feature that can be used in many
applications.
However, the capability to merge data from multiple sources, combined with the
inferential power of OWL, does have potential for abuse. It may even be illegal
to create or to process such linked information in countries with data
protection laws, especially in the EU, without having a valid legal reason for
such processing. Therefore, great care should be taken when using OWL with any
kind of personal data that might be linked with other data sources or
ontologies. Detailed security solutions were considered out of scope for the
Working Group.  Work currently underway elsewhere is expected to address these
issues with a variety of security and preference solutions -- 
see for example
<a href="http://www.oasis-open.org/committees/security/charter.php">
SAML</a> and
<a href="http://www.w3.org/P3P/">P3P</a>
</p>

<h3><a name="AppendixList">1.7 Appendices to this document</a></h3>

<p>
This document has a set of appendices containing additional information.
</p>

<p>Links in this document that are attached to definitions of 
language constructs provide access to the
OWL Semantics and Abstract Syntax 
[<cite><a href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>]. 
<a href="#appA">Appendix A</a> contains a
systematic set of links for each language construct to the
corresponding sections in the Guide and the S&amp;AS documents.</p>

<p><a href="#appB">Appendix B</a>
contains a RDF schema for the OWL language constructs. 
This schema provides information about the OWL vocabulary that could
be a useful reference point for ontology builders and tool
developers. The restrictions provided by the schema on the OWL classes
and properties are informative and not complete.  Also, this schema
does not make distinctions between OWL Full, OWL DL and OWL Lite.
Conventionally, classes
have a leading uppercase character; properties a leading
lowercase character. Thus, <code>owl:Ontology</code> is a class, and
<code>owl:imports</code> is a property.</p>

<p class="note">
NOTE: The RDF Schema file for OWL is not expected to be imported explicitly
(<em>i.e., </em> with <code>owl:imports</code>) into an ontology. The schema
has an informative status and is 
meant to provide the classes and properties to be used in the RDF/XML syntax.
People that do import this schema should expect the resulting ontology 
to be an  OWL Full ontology.</p>

<p>   
<a href="#appC">Appendix C</a> gives a tabular overview of the
OWL vocabulary in
terms of the built-in OWL classes and properties (the latter 
with their domain and range).</p>

<p>For readers familiar with DAML+OIL, <a href="#appD">Appendix D </a> lists
many of the changes between DAML+OIL and OWL.</p>

<p>Finally, <a href="#app-DLinRDF">Appendix E</a> provides a set of
practical guidelines for specifying OWL DL ontologies in RDF.</p>


<h2><a name="OWLDocument"></a>2. OWL document</h2>

Information in OWL is gathered into ontologies, which can then be
stored as documents in the World Wide Web.  One aspect of OWL, the
importing of ontologies, depends on this ability to store OWL
ontologies in the Web.

<h3><a name="DocumentContent">2.1 Content</a></h3>

<p>An OWL document consists of optional
<a href="#Header">ontology headers</a> (generally at most one) 
plus any number of 
<a href="#Class">class axioms</a>, <a
href="#Property">property axioms</a>,
and <a href="#Individual">facts about individuals</a>.
Please note that "axiom" is the formal term used in the S&amp;AS
document. These axioms are somewhat more informally called
"definitions" in the Guide and Overview documents.</p>

<p class="note">
NOTE: OWL does not impose any order on OWL components. 
Humans writing ontologies are likely to use some sort of ordering, for example
putting the ontology header in the beginning, but this has no impact on the
meaning. Tools should not assume any order.
</p>

<p>As with most RDF documents, the OWL code should be subelements of 
a <code>rdf:RDF</code> element. 
This enclosing element generally holds XML namespace and base declarations.  
Also, an OWL ontology document often starts with several entity declarations.
For a typical example of this sort of information, see the
example wine and food ontologies
discussed in the Guide document
[<cite><a href="#ref-owl-guide">OWL Guide</a></cite>].</p>


<h3><a name="owl-uri-namespace">2.2 OWL built-in vocabulary</a></h3>

<p>
The built-in vocabulary for OWL all comes from the OWL namespace </p>

<p class="note">
<code>http://www.w3.org/2002/07/owl#</code> 
</p>

<p>conventionally associated with the namespace name <code>owl</code>.  
It is
recommended that ontologies not use names from this namespace except
for the built-in vocabulary.  OWL tool builders should feel free to
signal a warning if other names from this namespace are used, but
should otherwise continue as normal.</p>


<h3><a name="MIMEType">2.3 MIME type</a></h3>

<p>
The Web Ontology Working Group has not requested a separate MIME type for OWL
documents. Instead, we recommend to use the MIME type requested by the RDF Core
Working Group, namely <code>application/rdf+xml</code>
[<cite><a href="#ref-rdf-concepts">RDF Concepts</a></cite>], 
or alternatively the
XML MIME type <code>application/xml</code>.</p>

<p>As file extension, we recommend to use either <code>.rdf</code> or
<code>.owl</code>. 
</p>


<!-- 
SECTION 3: Classes
-->

<h2><a name="Class" id="Class">3. Classes</a></h2>

<p>Classes provide an abstraction mechanism for grouping resources with
similar characteristics. Like RDF classes, every OWL 
class is associated with a set of individuals, called the <em>class
extension</em>. The individuals in the class extension are called the
<em>instances</em> of the class. A class has an intensional meaning
(the underlying concept) which is related but not equal to its class
extension. Thus, two classes may have the same class extension, but still be
different classes.</p> 

<p>When in this document we use wording such as "a class of individuals
..", this should be read as "a class with a class extension containing
individuals ...". 
</p>

<p class="note">
NOTE: In OWL Lite and OWL DL an individual can never be at the same time a
class: classes and individuals form disjoint domains (as do properties and data
values).  OWL Full allows the freedom of RDF Schema: a class may act as an
instance of another (meta)class.</p>


<p>OWL classes are described through "class descriptions", which can be
combined into "class axioms". We first describe class descriptions and
subsequently turn to class axioms. </p>

<h3><a name="ClassDescription" id="ClassDescription">3.1 Class descriptions</a></h3>

<p>A class description is the term used in this document (and in the OWL
Semantics and Abstract Syntax) for the basic building blocks of class axioms
(informally called class definitions in the Overview and Guide documents). 
A class description describes an OWL class, either by a class name or
by specifying the class extension of an unnamed anonymous class.</p>

<p>OWL distinguishes six types of class descriptions:
</p>
<ol>
  <li>a class identifier (a URI reference)</li>
  <li>an exhaustive <a href="#EnumeratedClass">enumeration</a> of individuals
  that together form the instances of a class</li>
  <li>a <a href="#Restriction">property restriction</a></li>
  <li>the <a href="#intersectionOf-def">intersection</a> of two or more class
  descriptions</li>
  <li>the <a href="#unionOf-def">union</a> of two or more class
  descriptions</li>
  <li>the <a href="#complementOf-def">complement</a> of a class
  description</li> 
</ol>
 
<p>The first type is special in the sense that it describes a class 
through a <em>class name</em> (syntactically represented as a URI
reference). 
The other five types of class descriptions describe an anonymous 
class by <em>placing
constraints on the class extension</em>. </p>

<p>Class descriptions of type 2-6
describe, respectively, 
a class that contains exactly the enumerated
individuals (2nd type), 
a class of all individuals which satisfy a
particular property restriction (3rd type), 
or a class that satisfies boolean combinations of
class descriptions (4th, 5th and 6th type).
Intersection, union and complement can be respectively seen as
the logical AND, OR and NOT operators.
The four latter types of class descriptions lead to nested class
descriptions and can thus in theory lead to arbitrarily complex class
descriptions. In practice, the level of nesting is usually limited. </p>

<p>A type 1 class description is syntactically represented as an named 
instance of
<code>owl:Class</code>, a subclass of <code>rdfs:Class</code>:</p>

<pre>
&lt;owl:Class rdf:ID="Human"/&gt;
</pre>

<p>This will assert the triple <code>"ex:Human rdf:type owl:Class
."</code>, where <code>ex:</code> is the namespace of the relevant 
ontology .</p>

<p class="note">NOTE: In OWL Lite and OWL DL, <code>owl:Class</code> 
(or <code>owl:Restriction</code>, see further) 
must be used for all class descriptions. </p>

<p class="note">NOTE: 
<code>owl:Class</code> is defined as a subclass of
<code>rdfs:Class</code>. The rationale for having a separate OWL 
class construct lies in the restrictions on OWL
DL (and thus also on OWL Lite), which imply that not all RDFS classes are legal
OWL DL classes. In OWL Full these restrictions do not exist and therefore
<code>owl:Class</code> and <code>rdfs:Class</code> are equivalent in
OWL Full. </p>

<p>The other five forms of class descriptions consist of a set of RDF triples 
in which a blank node represents the class being described.  That blank 
node has an <code>rdf:type</code> property whose value is
<code>owl:Class</code>.</p>

<p class="note">
NOTE: If one provides an RDF identifier for class descriptions of
the enumeration, intersection, union or complement type, 
this is not considered to be a class description, but a
special kind of class axiom for complete classes.
See <a href="#DescriptionAxiom">Sec. 3.2.3</a> for details.
</p>

<p class="note">
NOTE: In this document we sometimes use for readability purposes 
the shorthand "class description" to
refer to "the class being described by the class
description". Strictly speaking, these are different in the case of
class descriptions of type 2-6: the class is represented by the
corresponding blank node; the class description is represented by the
triples that have this blank node as their subject. 
</p>

<p>Two OWL class identifiers are predefined, namely the classes <a name="Thing-def"
id="Thing-def"></a> <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Thing">owl:Thing</a></span>
and <a name="Nothing-def" id="Nothing-def"></a> <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Nothing">owl:Nothing</a></span>.
The class extension of <code>owl:Thing</code> is the set of all
individuals. 
The class extension of <code>owl:Nothing</code> is the
empty set. Consequently, every OWL class is a
subclass of <code>owl:Thing</code> and <code>owl:Nothing</code> is a subclass
of every class (for the meaning of the subclass relation, see the section on <a
href="#subClassOf-def"><code>rdfs:subClassOf</code></a>).</p>


<h4><a name="EnumeratedClass" id="EnumeratedClass">3.1.1 Enumeration</a></h4>

<p>A <a name="oneOf-def" id="oneOf-def"></a> class description of the
"enumeration" kind is defined with the 
<span class="def"><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_oneOf">owl:oneOf</a></span>
property. The value of this built-in OWL property must be a 
list of individuals 
that are the <a href="#Individual">instances</a> of the class. 
This enables a class to be described by
exhaustively enumerating its instances.
The class extension of a class described with 
<code>owl:oneOf</code>
contains exactly the enumerated
individuals, no more, no less. The list of individuals is typically
represented with the help of the RDF construct
<code>rdf:parseType="Collection"</code>, which provides a convenient
shorthand for 
writing down a set of list elements. 
For example, the following RDF/XML syntax 
defines a class of all continents:</p>

<pre>
&lt;owl:Class&gt;
  &lt;owl:oneOf rdf:parseType="Collection"&gt;
    &lt;owl:Thing rdf:about="#Eurasia"/&gt;
    &lt;owl:Thing rdf:about="#Africa"/&gt;
    &lt;owl:Thing rdf:about="#NorthAmerica"/&gt;
    &lt;owl:Thing rdf:about="#SouthAmerica"/&gt;
    &lt;owl:Thing rdf:about="#Australia"/&gt;
    &lt;owl:Thing rdf:about="#Antarctica"/&gt;
  &lt;/owl:oneOf&gt;
&lt;/owl:Class&gt;
</pre>

<p> The RDF/XML syntax <code>&lt;owl:Thing rdf:about="..."/&gt;</code>
refers to some individual (remember: 
all individuals are by definition instances of
<code>owl:Thing</code>).</p>

<p>In the section on datatypes we will see another use of
the <code>owl:oneOf</code> construct, namely to define an <a
href="#EnumeratedDatatype">enumeration of data values</a>.</p>

<p class="note">NOTE: Enumeration is not part of OWL Lite</p>

<h4><a name="Restriction" id="Restriction">3.1.2 Property restrictions</a></h4>

<p>A property restriction is a special kind of class
description. It describes an anonymous class, namely a class of
all individuals that satisfy the restriction.
OWL distinguishes two kinds of property restrictions: value
constraints and cardinality constraints.</p>

<p>A <a href="#ValueRestriction">value constraint</a> puts constraints on the
range of the property <em>when applied to this particular class
description</em>.  
For example, we might want to
refer to those individuals whose value of the property <code>adjacentTo</code>
should be some <code>Region</code>, 
and then use this within a class axiom, perhaps
even a class axiom for <code>Region</code> itself.  
Note that this is different from  <code>rdfs:range</code>, which is
applied to all situations in which the property is used.</p>

<p>A <a href="#CardinalityRestriction">cardinality
constraint</a> puts constraints on the number of values a property can take,
<em>in the context of this particular class description</em>. 
For example, we might want to say that for a soccer team the
<code>hasPlayer</code> 
property has 11 values. For a basketball team the same property
would have only 5 values. </p>

<p>OWL also supports a limited set of constructs for defining global property
cardinality, namely <a href="#FunctionalProperty-def">owl:FunctionalProperty</a> and
<a href="#InverseFunctionalProperty-def"> owl:InverseFunctionalProperty</a>
(see the section on properties).</p> 

<p>Property restrictions have the following general form:</p>

<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="(some property)" /&gt;
  (precisely one value or cardinality constraint, see below)
&lt;/owl:Restriction&gt;
</pre>

<p>The class
<a name="Restriction-def" id="Restriction-def"></a><span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Restriction">owl:Restriction</a></span>
is defined as a subclass of <a href="#Class-def"><code>owl:Class</code></a>. 
A restriction class should
have exactly one triple linking 
the restriction to a particular property, using the <a
name="onProperty-def" id="onProperty-def"></a><span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_onProperty"> owl:onProperty</a></span>
property. The restriction class should also have exactly 
one triple that represents the value constraint <em>c.q.</em> cardinality
constraint on the property under consideration, <em>e.g.</em>, that the
cardinality of the property is exactly 1. </p>

<p>Property restrictions can be applied both to <a
href="#DatatypeProperty-def">datatype properties</a> (properties for
which the value is a data literal) and <a href="#ObjectProperty-def">object
properties</a>  (properties for which the value is an individual). For
more information about this distinction, see the section on 
<a href="#Property">properties</a>. </p> 

<h5><a name="ValueRestriction">3.1.2.1 Value constraints</a></h5>

<h6><a name="allValuesFrom-def" id="allValuesFrom-def">3.1.2.1.1
owl:allValuesFrom</a></h6> 

<p>The value constraint <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_allValuesFrom">owl:allValuesFrom</a></span>
is a built-in OWL 
property that links a restriction class to either a <a
href="#ClassDescription">class description</a> or a <a href="#DataRange">data
range</a>.  A restriction containing an <code>owl:allValuesFrom</code>
constraint is used to describe a class of all individuals for which all 
values of the property under consideration are either members of the class
extension of the class description or are data values within the specified data
range.  In other words, it defines a class of individuals x for which holds
that if the pair (x,y) is an instance of P (the property concerned), then y
should be an instance of the class description or a value in the data range,
respectively. </p>

<p>A simple example:</p>
<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="#hasParent" /&gt;
  &lt;owl:allValuesFrom rdf:resource="#Human"  /&gt;
&lt;/owl:Restriction&gt;
</pre>

<p>This example describes an anonymous OWL class of all individuals for which
the <code>hasParent</code> property only has values of class
<code>Human</code>. Note that this class description does not state
that the property 
always has values of this class; just that this is true for individuals
that belong to the class extension of the anonymous restriction class. </p>

<p class="note">
NOTE: In OWL Lite the only type of class description allowed as object of 
<code>owl:allValuesFrom</code> is a class name.
</p>

<p>An <code><a href="#allValuesFrom-def">owl:allValuesFrom</a></code>
constraint is analogous to the universal (for-all) quantifier of
Predicate logic - for each instance of the class that is
being described, every value for P must fulfill the constraint.  Also
notice that the correspondence of <code><a
href="#allValuesFrom-def">owl:allValuesFrom</a></code> with the
universal quantifier means that an <code><a
href="#allValuesFrom-def">owl:allValuesFrom</a></code> constraint for
a property P is trivially satisfied for an individual that has no
value for property P at all. To see why this is so, observe that the
<code><a href="#allValuesFrom-def">owl:allValuesFrom</a></code>
constraint demands that all values of P should be of type T, and if no
such values exist, the constraint is trivially true.</p>

<h6><a name="someValuesFrom-def" id="someValuesFrom-def">3.1.2.1.2
owl:someValuesFrom</a></h6> 

<p>The value constraint <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_someValuesFrom">owl:someValuesFrom</a></span>
is a built-in OWL property that links a restriction class to a <a 
href="#ClassDescription">class description</a> or a <a
href="#DataRange">data range</a>.  A restriction containing 
an <code>owl:someValuesFrom</code> constraint
describes a class of all individuals for which at least one value of the
property concerned is an instance of the class description or a data value in
the data range.  In other words, it defines a class of individuals x for
which there is at least one y (either an instance of the class description or
value of the data range) such that the pair (x,y) is an instance of P. This
does not exclude that there are other instances (x,y') of P for which y' does
not belong to the class description or data range.
</p>

<p>The following example defines a class of individuals which have at least one
parent who is a physician:</p>
<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="#hasParent" /&gt;
  &lt;owl:someValuesFrom rdf:resource="#Physician" /&gt;
&lt;/owl:Restriction&gt;
</pre>

<p>The <code><a href="#someValuesFrom-def">owl:someValuesFrom</a></code>
constraint is analogous to the existential quantifier of Predicate logic - for
each instance of the class that is being defined, there exists at
least one value for P that fulfills the constraint.</p>

<p class="note">
NOTE: In OWL Lite the only type of class description allowed as object of 
<code>owl:someValuesFrom</code> is a class name.
</p> 


<h6><a name="hasValue-def" id="hasValue-def">3.1.2.1.3 owl:hasValue</a></h6>

<p>The value constraint <span class="def"><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_hasValue">owl:hasValue</a></span>
is a built-in OWL property that links a restriction class 
to a value V, which can be either an <a href="#Individual">
individual</a> or a <a
href="#Datatype">data value</a>. 
A restriction containing a <code>owl:hasValue</code> constraint
describes a class of all individuals for
which the property concerned has at least one value <em>semantically</em> 
equal to V (it may have other values as well).</p>

<p class="note">
NOTE: for datatypes "semantically equal" means that 
the lexical representation of the literals maps to the same 
value. For individuals it means that they
either have the same URI reference or are defined as being the same
individual (see <a href="#sameAs-def">owl:sameAs</a>).</p>

<p class="note">
NOTE: the value constraint <code>owl:hasValue</code> 
is not included in OWL Lite.</p> 

<p>The following example describes the class of individuals who have the
individual referred to as <code>Clinton</code> as their parent:</p>

<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="#hasParent" /&gt;
  &lt;owl:hasValue rdf:resource="#Clinton" /&gt;
&lt;/owl:Restriction&gt;
</pre>

<h5><a name="CardinalityRestriction">3.1.2.2 Cardinality constraints</a></h5> 

<p>In OWL, like in RDF, it is assumed that any instance of a class may have an
arbitrary number (zero or more) of values for a particular property.  To make a
property required (at least one), to allow only a specific number of values for
that property, or to insist that a property must not occur, cardinality
constraints can be used.  OWL provides three constructs for restricting the
cardinality of properties locally within a class context.</p>
  
<p class="note">
NOTE: OWL Lite includes the use of all three types of cardinality
constraints, but only when used with the values "0" or "1".</p>

<h6><a name="maxCardinality-def" id="maxCardinality-def">3.1.2.2.1
owl:maxCardinality</a></h6> 

<p>The cardinality constraint <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_maxCardinality">
owl:maxCardinality</a></span>
is a built-in OWL property that 
links a restriction class to a data value belonging to the value space of
the XML Schema datatype <code>nonNegativeInteger</code>.  A restriction
containing an <code>owl:maxCardinality</code> constraint describes a class of
all individuals that have <em>at most</em> N semantically distinct values
(individuals or data
values) for the property concerned, where N is the value of the
cardinality constraint.  Syntactically, the cardinality constraint is
represented 
as an RDF property element with the corresponding <code>rdf:datatype</code>
attribute.</p>

<p>The following example describes a class of individuals that have at most
two parents:</p>

<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="#hasParent" /&gt;
  &lt;owl:maxCardinality rdf:datatype="&amp;xsd;nonNegativeInteger"&gt;2&lt;/owl:maxCardinality&gt;
&lt;/owl:Restriction&gt;
</pre>

<p>RDF datatyping  is discussed in more detail in
<a href="#Datatype">Sec. 6</a>.</p>


<h6><a name="minCardinality-def" id="minCardinality-def">3.1.2.2.2
owl:minCardinality</a></h6> 

<p>The cardinality constraint <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_minCardinality">
owl:minCardinality</a></span>
is a built-in OWL property that 
links a restriction class to a data value belonging to the value space of
the XML Schema datatype <code>nonNegativeInteger</code>.  A restriction
containing an <code>owl:minCardinality</code> constraint describes a class of
all individuals that have <em>at least</em> N semantically distinct values
(individuals or data
values) for the property concerned, where N is the value of the
cardinality constraint.  Syntactically, the cardinality constraint is represented
as an RDF property element with the corresponding <code>rdf:datatype</code>
attribute.</p>

<p>The following example describes a class of individuals that have at least
two parents:</p>

<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="#hasParent" /&gt;
  &lt;owl:minCardinality rdf:datatype="&amp;xsd;nonNegativeInteger"&gt;2&lt;/owl:minCardinality&gt;
&lt;/owl:Restriction&gt;
</pre>

<p>
Note that an <code>owl:minCardinality</code> of one or more means that
all instances of the class must have a value for the property.</p> 
 

<h6><a name="cardinality-def" id="cardinality-def">3.1.2.2.3
owl:cardinality</a></h6> 


<p>The cardinality constraint <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_cardinality">
owl:cardinality</a></span>
is a built-in OWL property that
links a restriction class to a data value belonging to the range of
the XML Schema datatype <code>nonNegativeInteger</code>.  A restriction
containing an <code>owl:cardinality</code> constraint describes a class of
all individuals that have <em> exactly</em> N semantically distinct values
(individuals or data
values) for the property concerned, where N is the value of the
cardinality constraint.  Syntactically, the cardinality constraint is represented
as an RDF property element with the corresponding <code>rdf:datatype</code>
attribute.</p>

<p>This construct is in fact redundant as it
can always be replaced by a pair of matching 
<a href="#minCardinality-def"><code>owl:minCardinality</code></a>
and
<a href="#maxCardinality-def"><code>owl:maxCardinality</code></a>
constraints with the same value. It is included as a convenient shorthand for
the user.</p>

<p>The following example describes a class of individuals that have exactly
two parents:</p>

<pre>
&lt;owl:Restriction&gt;
  &lt;owl:onProperty rdf:resource="#hasParent" /&gt;
  &lt;owl:cardinality rdf:datatype="&amp;xsd;nonNegativeInteger"&gt;2&lt;/owl:cardinality&gt;
&lt;/owl:Restriction&gt;
</pre>


<h4><a name="Boolean" id="Boolean">3.1.3 Intersection, union and complement</a></h4>

<p>The three types of class descriptions in this section represent the more
advanced class constructors that are used in Description Logic. They can be
viewed as representing the AND, OR and NOT operators on classes. 
The three operators get the standard set-operator
names: intersection, union and complement. These language constructs
also share the 
characteristic that they contain nested class descriptions, either 
one (complement) or more (union, intersection).</p>
  
<h5><a name="intersectionOf-def"
id="intersectionOf-def">3.1.3.1 owl:intersectionOf</a></h5>

<p>The <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_intersectionOf">owl:intersectionOf</a></span>
property links a class to a list of  
<a href="#ClassDescription">class descriptions.</a> 
An <code>owl:intersectionOf</code> statement
describes a  class for which the class extension contains
precisely those individuals 
that are members of the class extension of
all class descriptions in the list. </p>

<p>An example:</p>

<pre>
&lt;owl:Class&gt;
  &lt;owl:intersectionOf rdf:parseType="Collection"&gt;
    &lt;owl:Class&gt;
      &lt;owl:oneOf rdf:parseType="Collection"&gt;
        &lt;owl:Thing rdf:about="#Tosca" /&gt;
        &lt;owl:Thing rdf:about="#Salome" /&gt;
      &lt;/owl:oneOf&gt;
    &lt;/owl:Class&gt;
    &lt;owl:Class&gt;
      &lt;owl:oneOf rdf:parseType="Collection"&gt;
        &lt;owl:Thing rdf:about="#Turandot" /&gt;
        &lt;owl:Thing rdf:about="#Tosca" /&gt;
      &lt;/owl:oneOf&gt;
    &lt;/owl:Class&gt;
  &lt;/owl:intersectionOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>In this example the value of <code>owl:intersectionOf</code>
is a list of two
class descriptions, namely two enumerations, both describing a class
with two individuals. The resulting intersection is
a class with one individual, namely 
<code>Tosca</code>.  as this is the only individual that is 
common to both enumerations.</p>

<p class="note">
NOTE: This assumes that the three individuals are all
different. In fact, this is not by definition true in OWL. 
Different URI references may refer to the 
same individuals, because OWL does not have a "unique names" assumption. In
<a href="#Individual">Sec. 5</a>
one can find OWL language constructs for making
constraints about equality and difference of individuals.</p>

<p class="note"> NOTE: In this example we use enumerations to make
clear what the meaning is of this language construct. See the OWL
Guide [<cite><a href="#ref-owl-guide">OWL Guide</a></cite>] for more
typical examples. </p>

<p class="note">
NOTE: OWL Lite is restricted in its use of <code>owl:intersectionOf</code>.
This is discussed later in this document, see <a
href="#DescriptionAxiom">Sec. 3.2.3</a>
</p> 

<p><code>owl:intersectionOf</code>
can be viewed as being analogous to logical
conjunction.</p>

<h5><a name="unionOf-def" id="unionOf-def">3.1.3.2 owl:unionOf</a></h5>


<p>The <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_unionOf">owl:unionOf</a></span>
property links a class to a list of  
<a href="#ClassDescription">class descriptions.</a> 
An <code>owl:unionOf</code> statement
describes an anonymous class for which the class extension contains
those individuals 
that occur in at least one of the class extensions of the 
class descriptions in the list. </p>

<p>An example:</p>

<pre>
&lt;owl:Class&gt;
  &lt;owl:unionOf rdf:parseType="Collection"&gt;
    &lt;owl:Class&gt;
      &lt;owl:oneOf rdf:parseType="Collection"&gt;
        &lt;owl:Thing rdf:about="#Tosca" /&gt;
        &lt;owl:Thing rdf:about="#Salome" /&gt;
      &lt;/owl:oneOf&gt;
    &lt;/owl:Class&gt;
    &lt;owl:Class&gt;
      &lt;owl:oneOf rdf:parseType="Collection"&gt;
        &lt;owl:Thing rdf:about="#Turandot" /&gt;
        &lt;owl:Thing rdf:about="#Tosca" /&gt;
      &lt;/owl:oneOf&gt;
    &lt;/owl:Class&gt;
  &lt;/owl:unionOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>This class description describes a class for which the class extension
contains three individuals, namely <code>Tosca</code>, <code>Salome</code>, and <code>Turandot</code> 
(assuming they are all different).</p>

<p class="note">
NOTE: <code>owl:unionOf</code> is not part of OWL Lite.
</p>

<p><code>owl:unionOf</code> is analogous to logical disjunction. </p>

<h5><a name="complementOf-def" id="complementOf-def">3.1.3.3
owl:complementOf</a></h5> 

<p>An 
<span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_complementOf">owl:complementOf</a></span>
property links a class to precisely one <a href="#ClassDescription">class
description</a>. 
An <code>owl:complementOf</code> statement describes a class for which the class
extension contains exactly those individuals 
that do <em>not</em> belong to the class extension of the 
class description that is the object of the statement. 
<code>owl:complementOf</code> is
analogous to logical negation: the class extension consists of those
individuals that are NOT members of the class extension of the
complement class. </p>

<p>As an example of the use of complement, 
the expression "not meat" could be written
as:</p>

<pre>
&lt;owl:Class&gt;
  &lt;owl:complementOf&gt;
    &lt;owl:Class rdf:about="#Meat"/&gt;
  &lt;/owl:complementOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>The extension of this class description contains all individuals
that do not belong to the class <code>Meat</code>.</p>

<p class="note">
NOTE: <code>owl:complementOf</code> is not part of OWL Lite.
</p>

<h3><a name="ClassAxioms" id="ClassAxioms">3.2 Class axioms</a></h3>

<p>Class descriptions form the building blocks for defining classes
through class axioms. The simplest form of a class axiom is a class description
of type 1, It just states
the existence of a class, using
<a name="Class-def" id="Class-def"><code>owl:Class</code></a> with a class identifier.</p>

<p>For example, the following 
class axiom declares the URI reference <code>#Human</code> to be the
name of an OWL class:</p>
 
<pre>
&lt;owl:Class rdf:ID="Human"/&gt;
</pre>
 
<p>This is correct OWL, but does not tell us very much about the class
<code>Human</code>. Class axioms typically contain additional components that
state necessary and/or sufficient characteristics of a class. OWL contains
three language constructs for combining class descriptions into class
axioms:</p> 

 
<ul>
<li><a href="#subClassOf-def"><code>rdfs:subClassOf</code></a> allows one
to say that the class extension of a 
class description is a subset of the class extension of another class
description.</li>
<li><a href="#equivalentClass-def"><code>owl:equivalentClass</code></a> allows one
to say that a class description has exactly the 
same class extension as another class  description.</li>
<li><a href="#disjointWith-def"><code>owl:disjointWith</code></a> allows one
to say that the class extension of a class description has no members in
common with the class extension of another class description.</li>
</ul>

<p>Syntactically, these three language constructs
are properties that have a class description as
both domain and range. We discuss these properties in more
detail in the following subsections.</p>

<p>In addition, OWL allows class axioms in which a class description
of the enumeration or the set-operator type is given a name. These
class axioms are semantically equivalent to class axioms with a
<code>owl:equivalentClass</code> statement, so these will be discussed
right after that subsection (see <a
href="#DescriptionAxiom">Sec. 3.2.3 "Axioms for complete classes without
using owl:equivalentClass"</a>).</p>


<h4><a name="subClassOf-def">3.2.1 rdfs:subClassOf</a></h4>

<p class="note">
AXIOM SCHEMA:
<em>class description</em>  <code>rdfs:subClassOf</code> <em>class
description</em> </p>

<p>The <code>rdfs:subClassOf</code> construct is
 defined as part of RDF Schema
[<cite><a href="#ref-rdf-vocabulary">RDF Vocabulary</a></cite>]. Its meaning in OWL
is exactly the same: if the class description C1 is defined as a subclass of
class description C2, then the set of individuals in the class extension of C1
should be a subset of the set of individuals in the class extension of C2. 
A class is by definition a subclass of itself (as the subset may be
the complete set).</p>
 
<p>An example:</p>

<pre>
&lt;owl:Class rdf:ID="Opera"&gt;
  &lt;rdfs:subClassOf rdf:resource="#MusicalWork" /&gt;
&lt;/owl:Class&gt;
</pre>

<p>This class axiom declares a subclass relation between two OWL classes that
are described through their names (<code>Opera</code> and
<code>MusicalWork</code>).  
Subclass relations provide necessary conditions for belonging to a class. In
this case, to be an opera the individual also needs to be a musical work.</p>

<p class="note">
NOTE: In OWL Lite the subject of an 
<code>rdfs:subClassOf</code> statement must be a class identifier. The
object must be either a class identifier or a property restriction.</p>

<p>
For any class there may be any number of subClassOf axioms. 
For example, we could add the following axiom about the class
<code>Opera</code>:</p> 

<pre>
&lt;owl:Class rdf:about="#Opera"&gt;
  &lt;rdfs:subClassOf&gt;
    &lt;owl:Restriction&gt;
      &lt;owl:onProperty rdf:resource="#hasLibrettist" /&gt;
      &lt;owl:minCardinality rdf:datatype="&amp;xsd;nonNegativeInteger"&gt;1&lt;/owl:minCardinality&gt;
    &lt;/owl:Restriction&gt;
  &lt;/rdfs:subClassOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>This class axiom contains 
a property restriction. The example states that <code>Opera</code>
is a subclass of an anonymous OWL class (remember: <a href="#Restriction-def"><code>owl:Restriction</code></a>
is a subclass of <code>owl:Class</code>) that has as its class extension 
the set of all individuals
for which the property <code>hasLibrettist</code> has at least one
value. Thus, operas should have at least one librettist.</p>


<p>Class axioms can get more complex when class descriptions are nested.
For example, property restrictions with an 
<a href="#allValuesFrom-def"><code>owl:allValuesFrom</code></a>
or
<a href="#someValuesFrom-def"><code>owl:someValuesFrom</code></a>
statement may point to any class description.
Consider the following example: </p>

<pre>
&lt;owl:Class rdf:ID="TraditionalItalianOpera"&gt;
  &lt;rdfs:subClassOf rdf:resource="#Opera"/&gt;
  &lt;rdfs:subClassOf&gt;
    &lt;owl:Restriction&gt;
      &lt;owl:onProperty rdf:resource="#hasOperaType"/&gt;
      &lt;owl:someValuesFrom&gt;
        &lt;owl:Class&gt;
          &lt;owl:oneOf rdf:parseType="Collection"&gt;
            &lt;owl:Thing rdf:about="#OperaSeria"/&gt;
            &lt;owl:Thing rdf:about="#OperaBuffa"/&gt;
          &lt;/owl:oneOf&gt;
        &lt;/owl:Class&gt;
      &lt;/owl:someValuesFrom&gt;
    &lt;/owl:Restriction&gt;
  &lt;/rdfs:subClassOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>This example shows the use of the <code>owl:oneOf</code> construct. 
The class axiom defines traditional Italian opera as a subclass of 
a class of operas that have as opera type either <em>opera seria</em> or
<em>opera buffa</em> (without an additional cardinality constraint, it
could actually have both values).</p> 

<p>More examples can be found in the Guide document
[<cite><a href="#ref-owl-guide">OWL Guide</a></cite>].
Subclass axioms provide us with partial definitions: they represent necessary
but not sufficient conditions for establishing class membership of an
individual. In the next subsection we will see that for defining 
necessary <em>and</em> sufficient conditions OWL provides the
<a href="#equivalentClass-def"><code>owl:equivalentClass</code></a>
construct. As a stepping stone to such axioms,
consider the following example:</p>

<pre>
&lt;owl:Class rdf:ID="Operetta"&gt;
  &lt;rdfs:subClassOf rdf:resource="#MusicalWork"/&gt;
  &lt;rdfs:subClassOf&gt;
    &lt;owl:Restriction&gt;
      &lt;owl:onProperty rdf:resource="#hasLibrettist" /&gt;
      &lt;owl:minCardinality rdf:datatype="&amp;xsd;nonNegativeInteger"&gt;1&lt;/owl:minCardinality&gt;
    &lt;/owl:Restriction&gt;
  &lt;/rdfs:subClassOf&gt;
  &lt;rdfs:subClassOf&gt;
    &lt;owl:Class&gt;
      &lt;owl:complementOf rdf:resource="#Opera"/&gt;
    &lt;/owl:Class&gt;
  &lt;/rdfs:subClassOf&gt; 
&lt;/owl:Class&gt;
</pre>

<p>This class axiom states that an operetta is a musical work, that has a
at least one 
librettist and is not an opera. The use of the subclass relation leaves open
the possibility that there are other musical works that have a librettist and
are 
not operas. If we had wanted to say that operetta's are <em>exactly</em>
those musical works that have a librettist but are not operas, we
would need to use 
the 
<a href="#equivalentClass-def"><code>owl:equivalentClass</code></a>
construct.</p>


<h4><a name="equivalentClass-def">3.2.2 owl:equivalentClass</a></h4>

<p class="note">
AXIOM SCHEMA:
<em>class description</em>  <code>owl:equivalentClass</code> <em>class
description</em> </p>

<p>A class axiom may contain (multiple) 
<span class="def"><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_equivalentClass">owl:equivalentClass</a></span> 
statements. <code>owl:equivalentClass</code> is a built-in
property that links a class description
to another class description. 
The meaning of such a class axiom is that the two class descriptions involved 
have the same class extension
(i.e., both class extensions contain exactly the same set of individuals).</p>

<p>In its simplest form, an equivalentClass 
axiom states the equivalence (in terms of their class extension) 
of two named
classes. An example:</p>

<pre>
&lt;owl:Class rdf:about="#US_President"&gt;
  &lt;equivalentClass rdf:resource="#PrincipalResidentOfWhiteHouse"/&gt;
&lt;/owl:Class&gt;
</pre>

<p class="note">NOTE:
The use of <code>owl:equivalentClass</code> does not imply class
equality. Class equality means that the classes have the same intensional
meaning (denote the same concept). In the example above, the concept of
"President of the US" is related to, but not equal to the concept of the
principal resident of a certain estate.  
Real class equality can only be expressed with the <code><a
href="#sameAs-def">owl:sameAs</a></code> construct. 
As this requires treating classes as
individuals, class equality can only be expressed in OWL Full. </p>


<p>Axioms with <code>owl:equivalentClass</code> can also be used to
define an enumerated class by linking a type 1 class description (a
class identifier) to a type 2 class description (an enumeration).  An
example:</p>

<pre>
&lt;owl:Class rdf:ID="DaPonteOperaOfMozart"&gt;
  &lt;owl:equivalentClass&gt;
    &lt;owl:Class&gt;
      &lt;owl:oneOf rdf:parseType="Collection"&gt;
        &lt;Opera rdf:about="#Nozze_di_Figaro"/&gt;
        &lt;Opera rdf:about="#Don_Giovanni"/&gt;
        &lt;Opera rdf:about="#Cosi_fan_tutte"/&gt;
      &lt;/owl:oneOf&gt;
    &lt;/owl:Class&gt;
  &lt;/owl:equivalentClass&gt;
&lt;/owl:Class&gt;
</pre>

<p>This class axiom defines the class of operas 
that together represent the "Da Ponte operas of Mozart" (a
popular subject in musicology). By using the equivalentClass construct 
we can state
necessary and sufficient conditions for class membership, in this case
consisting of an enumeration of three individuals, no less, no more.</p> 

<p class="note"> NOTE: OWL DL does not put any constraints on the
types of class descriptions that can be used as subject and object
of an <code>owl:equivalentClass</code> statement. In OWL Lite
the subject must be a class name and the object must be either a class
name or a property restriction. </p>

<p class="note">
NOTE: Although in principle different types of class descriptions are allowed
as the subject of an equivalentClass statement, 
in practice it usually is some class
identifier. This is also true for the examples in this section.</p>

<p>It is possible to have multiple equivalentClass axioms about the same
class.
However, this requires care. Both axioms must lead to the same
outcome, i.e. exactly the same class extension. For example, an alternate
equivalentClass axiom for Mozart's "Da Ponte operas" could be the following
one:</p>  

<pre>
&lt;owl:Class rdf:about="#DaPonteOperaOfMozart"&gt;
  &lt;owl:equivalentClass&gt;
    &lt;owl:Class&gt;
      &lt;owl:intersectionOf rdf:parseType="Collection"&gt;
        &lt;owl:Restriction&gt;
          &lt;owl:onProperty rdf:resource="#hasComposer"/&gt;
          &lt;owl:hasValue rdf:resource="#Wolfgang_Amadeus_Mozart"/&gt;
        &lt;/owl:Restriction&gt;
        &lt;owl:Restriction&gt;
          &lt;owl:onProperty rdf:resource="#hasLibrettist"/&gt;
          &lt;owl:hasValue rdf:resource="#Lorenzo_Da_Ponte"/&gt;
        &lt;/owl:Restriction&gt;
      &lt;/owl:intersectionOf&gt;
    &lt;/owl:Class&gt;
  &lt;/owl:equivalentClass&gt;
&lt;/owl:Class&gt;
</pre>

<p>This states that the class extension of the Da Ponte operas of
Mozart corresponds exactly to those operas which are composed by
Mozart and for which the libretto is written by Da Ponte (note:
intersection = "and"). 
This axiom indeed defines a class with exactly the same instances as the
previous axiom. </p>

<p class="note">NOTE: If we wanted to "upgrade" an axiom of the form
"A subClassOf B" to "A equivalentClass B" (meaning that the class
extension of A is not just any subset, but in fact the same set as the
class extension of B), we could add a second subClassOf axiom of the
form (B subClassOf A), which by definition makes the two class
extensions equivalent (and thus has the same meaning as "A
equivalentClass B"). Such subClassOf "cycles" are explicitly allowed.
As OWL is usable in a distributed environment, this can be a useful
feature.</p>


<h4><a name="DescriptionAxiom">3.2.3 Axioms for complete classes without
using owl:equivalentClass</a></h4>

<p class="note">
AXIOM SCHEMA:
named <em>class description</em> of type 2 (with <code>owl:oneOf</code>) or
type 4-6 (with <code>owl:intersectionOf</code>, <code>owl:unionOf</code>
or <code>owl:complementOf</code>
</p>

<p>OWL allows users to define class axioms by giving a name to class
descriptions of the
enumeration or set-operator type. Such a class axiom defines necessary and
sufficient conditions for establishing class membership. 
An example: </p>

<pre>
&lt;owl:Class rdf:ID="DaPonteOperaOfMozart"&gt;
  &lt;owl:oneOf rdf:parseType="Collection"&gt;
    &lt;owl:Thing rdf:about="#Nozze_di_Figaro"/&gt;
    &lt;owl:Thing rdf:about="#Don_Giovanni"/&gt;
    &lt;owl:Thing rdf:about="#Cosi_fan_tutte"/&gt;
  &lt;/owl:oneOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>This class axiom should be interpreted as follows: the class extension of
the class <code>DaPonteOperaOfMozart</code> is 
exactly defined by the enumeration.</p>

<p>This class axiom is semantically equivalent to the
first opera example in the previous section, which included an additional 
<code>owl:equivalentClass</code> statement. Axioms of this type can also be
constructed with <code>owl:intersectionOf</code>,
<code>owl:unionOf</code> and <code>owl:complementOf</code>.
An example with a union could be:</p> 

<pre>
&lt;owl:Class rdf:ID="LivingBeing"&gt;
  &lt;owl:unionOf rdf:parseType="Collection"&gt;
    &lt;owl:Class rdf:about="#Plant"/&gt;
    &lt;owl:Class rdf:about="#Animal"/&gt;
  &lt;/owl:unionOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>This class axiom states that the class extension of 
<code>LivingBeing</code> exactly corresponds
to the union of the class extensions of <code>Plant</code> 
and <code>Animal</code>.</p>

<p class="note">
NOTE: OWL Lite only includes class axioms of this type which are constructed 
with the <code>owl:intersectionOf</code> property. The values of the
intersectionOf list must be class identifiers and/or property restrictions. 
Thus, "complete class" axioms
using enumeration, complement and
union are not allowed in OWL Lite. </p>


<h4><a name="disjointWith-def">3.2.4 owl:disjointWith</a></h4>

<p class="note">
AXIOM SCHEMA:
<em>class description</em>  <code>owl:disjointWith</code> <em>class
description</em> </p>

<p>A class axiom may also contain (multiple) 
<span class="def"><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_disjointWith">owl:disjointWith</a></span>
statements. 
<code>owl:disjointWith</code> is a
built-in OWL property with a class
description as domain and range. 
Each <code>owl:disjointWith</code> statement asserts that 
the class extensions of the two class descriptions
involved have no individuals in common. Like axioms with 
<code>rdfs:subClassOf</code>, declaring two classes to be disjoint is a partial
definition: it imposes a necessary but not sufficient condition on the
class.</p>

<p> This is a popular example of class disjointness:</p>

<pre>
&lt;owl:Class rdf:about="#Man"&gt;
  &lt;owl:disjointWith rdf:resource="#Woman"/&gt;
&lt;/owl:Class&gt;
</pre>

<p>Whether this is actually true is a matter for biologists to
decide. The following example shows a common use of class disjointness in
subclass hierarchies:</p>  

<pre>
&lt;owl:Class rdf:about="#MusicDrama"&gt;
  &lt;owl:equivalentClass&gt;
    &lt;owl:Class&gt;
      &lt;owl:unionOf rdf:parseType="Collection"&gt;
        &lt;owl:Class rdf:about="#Opera"/&gt;
        &lt;owl:Class rdf:about="#Operetta"/&gt;
        &lt;owl:Class rdf:about="#Musical"/&gt;
      &lt;/owl:unionOf&gt;
    &lt;/owl:Class&gt;
  &lt;/owl:equivalentClass&gt;
&lt;/owl:Class&gt;

&lt;owl:Class rdf:about="#Opera"&gt;
  &lt;rdfs:subClassOf rdf:resource="#MusicDrama"/&gt;
&lt;/owl:Class&gt;

&lt;owl:Class rdf:about="#Operetta"&gt;
  &lt;rdfs:subClassOf rdf:resource="#MusicDrama"/&gt;
  &lt;owl:disjointWith rdf:resource="#Opera"/&gt;
&lt;/owl:Class&gt;

&lt;owl:Class rdf:about="#Musical"&gt;
  &lt;rdfs:subClassOf rdf:resource="#MusicDrama"/&gt;
  &lt;owl:disjointWith rdf:resource="#Opera"/&gt;
  &lt;owl:disjointWith rdf:resource="#Operetta"/&gt;
&lt;/owl:Class&gt;
</pre>

<p>Here, <code>owl:disjointWith</code>
statements are used together with
<a href="#unionOf-def"><code>owl:unionOf</code></a>
in order to define a set of mutually disjoint and complete subclasses of a
superclass. In natural language: every <code>MusicDrama</code> is either an
opera, an <code>Operetta</code>, or a <code>Musical</code> (the subclass
partitioning is complete) and individuals belonging to one subclass,
<em>e.g.</em>, 
<code>Opera</code>,  cannot belong to another subclass, <em>e.g.</em>,
<code>Musical</code> (disjoint or non-overlapping subclasses). This is a common
modelling notion used in many data-modelling notations. </p>

<p class="note">
NOTE: OWL Lite does not allow the use of <code>owl:disjointWith</code>.
</p> 

<!-- 
SECTION 4: Properties
-->

<h2><a name="Property" id="Property">4. Properties</a></h2>

<p>OWL distinguishes between two main categories of properties that an
ontology builder may want to define:</p>
<ul>
  <li><em>Object properties</em> link individuals to individuals.</li>
  <li><em>Datatype properties</em> link individuals to data values.</li>
</ul>

<p class="note">
NOTE: OWL also has the notion of annotation properties
(<code>owl:AnnotationProperty</code>) and ontology properties
(<code>owl:OntologyProperty</code>). These are needed in OWL DL for semantic
reasons. See <a href="#Header">Sec. 7</a> 
and the OWL Semantics and Abstract Syntax document
[<cite><a href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>].  
</p>

<p>An object property is defined as an instance of the built-in OWL class  
<a name="ObjectProperty-def" id="ObjectProperty-def"></a> <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_ObjectProperty">owl:ObjectProperty</a></span>. 
A datatype property is defined as an instance of the built-in 
OWL class  <a
name="DatatypeProperty-def" id="DatatypeProperty-def"></a> <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DatatypeProperty">owl:DatatypeProperty</a></span>. 
Both <code>owl:ObjectProperty</code> and
<code>owl:DatatypeProperty</code> are subclasses of the RDF class
<code>rdf:Property</code> (see <a href="#appB">Appendix B</a>). 
</p>

<p class="note">
NOTE: In OWL Full, object properties and datatype properties are
not disjoint. Because data values can be treated as individuals, datatype
properties are effectively subclasses of object properties. 
In OWL Full <code>owl:ObjectProperty</code> is equivalent to
<code>rdf:Property</code> In practice, this
mainly has consequences for the use of 
<a href="#InverseFunctionalProperty-def"><code>owl:InverseFunctionalProperty</code></a>.
See also the OWL Full characterization in <a
href="#OWLFull">Sec. 8.1</a>.</p>

<p>
A property axiom defines characteristics of a property.
In its simplest form, a property axiom just defines the existence of
a property. For example:</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="hasParent"/&gt;
</pre>

<p>This defines a property with the restriction that its values should be
individuals.</p>

<p>Often, property axioms define additional characteristics of properties.  OWL
supports the following constructs for property axioms:</p>

<ul>
  <li>RDF Schema constructs: <code>rdfs:subPropertyOf</code>,
  <code>rdfs:domain</code> and <code>rdfs:range</code></li>
  <li>relations to other properties: <code>owl:equivalentProperty</code> and
  <code>owl:inverseOf</code></li> 
  <li>global cardinality constraints: <code>owl:FunctionalProperty</code> and
  <code>owl:InverseFunctionalProperty</code></li>
  <li>logical property characteristics: <code>owl:SymmetricProperty</code> and
  <code>owl:TransitiveProperty</code></li>
</ul>


<p>In the next subsections, the various types of property axioms are
discussed in more detail.</p>

<p class="note">NOTE: In this section we use the term "property extension" in
a similar fashion to "class extension". The property extension is the set of
instances that is associated with the property. Instances of properties are not
single elements, but subject-object pairs of property statements. In relational
database
terms, property instances would be  called "tuples" of a binary relation (the
property). </p>


<h3><a name ="RDFSProperty">4.1 RDF Schema constructs</a></h3> 

<p>The constructs in this section are discussed in detail in the RDF Schema
document [<cite><a href="#ref-rdf-vocabulary">RDF Vocabulary</a></cite>]. The
description in this section provides a synopsis of these constructs and
provides some OWL-specific aspects and examples. </p>


<h4><a name="subPropertyOf-def"
id="subPropertyOf-def">4.1.1 rdfs:subPropertyOf</a></h4>

<p>A <code>rdfs:subPropertyOf</code> axiom defines that the property 
is a subproperty of some other property.
Formally this means that if P1 is a subproperty of P2, then the property
extension of P1 (a set of pairs) should be a subset of the property extension
of P2 (also a set of pairs).</p>

<p>An example:</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="hasMother"&gt;
  &lt;rdfs:subPropertyOf rdf:resource="#hasParent"/&gt;
&lt;/owl:ObjectProperty&gt;
</pre>

<p>This states that all instances (pairs) contained in the property extension
of the property "hasMother" are also members of the property extension of the
property "hasParent".</p>

<p>Subproperty axioms can be applied to both datatype properties and object
properties.</p>

<p class="note"> 
NOTE: In OWL DL the subject and object of a subproperty statement 
must be either both datatype properties or both object properties.</p>

<h4><a name="domain-def" id="domain-def">4.1.2 rdfs:domain</a></h4>

<p>For a property one can define (multiple)
<code>rdfs:domain</code> axioms. 
Syntactically, <code>rdfs:domain</code> is a built-in 
property that links a property
(some instance of the class <code>rdf:Property</code>) 
to a <a href="#ClassDescription">class
description</a>. 
An <code>rdfs:domain</code> axiom asserts that the subjects of such 
property statements must belong to the class extension of
the indicated class description.
</p> 

<p>Multiple <code>rdfs:domain</code> 
axioms are allowed and should be interpreted as a conjunction: these 
restrict the domain of the property to those individuals that belong to the 
<em>intersection</em> of the class descriptions. If one would want to say
that multiple classes can act as domain, one should use a class description
of the <a href="#unionOf-def"><code>owl:unionOf</code></a> form. 
For example, if we want to say that the domain of the property
<code>hasBankAccount</code> can be either a <code>Person</code> or a <code>Corporation</code>, we would need to
say something like this:</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="hasBankAccount"&gt;
  &lt;rdfs:domain&gt;
    &lt;owl:Class&gt;    
      &lt;owl:unionOf rdf:parseType="Collection"&gt;
        &lt;owl:Class rdf:about="#Person"/&gt;
        &lt;owl:Class rdf:about="#Corporation"/&gt;
      &lt;/owl:unionOf&gt;
    &lt;/owl:Class&gt;    
  &lt;/rdfs:domain&gt;
&lt;/owl:ObjectProperty&gt;
</pre>


<p class="note">
NOTE: In OWL Lite the value of <code>rdfs:domain</code>
must be a class identifier.
</p>


<h4><a name="range-def" id="range-def">4.1.3 rdfs:range</a></h4>

<p>For a property one can define (multiple)
<code>rdfs:range</code> axioms. 
Syntactically, <code>rdfs:range</code> is a built-in 
property that links a property
(some instance of the class <code>rdf:Property</code>) to 
to either a <a href="#ClassDescription">class
description</a> or a <a href="#DataRange">data range</a>.  
An <code>rdfs:range</code> axiom asserts that the values of this 
property must belong to the class extension of
the class description or to data values in the specified data range.</p>

<p>Multiple range
restrictions are interpreted as stating that the range of the property is the
<em>intersection</em> of all ranges (i.e., 
the intersection of the class extension of the class descriptions
c.q. the intersection of the data ranges). Similar to 
<a href="#domain-def"><code>rdfs:domain</code></a>,
multiple alternative
ranges can be specified by using a class description of the
<a href="#unionOf-def"><code>owl:unionOf</code></a> form (see the previous
subsection). </p> 

<p>Note that, unlike any of the <a href="#ValueRestriction">value
constraints</a> described in the section on class descriptions, 
<code>rdfs:range</code> restrictions are
global.  Value constraints such as <a
href="#allValuesFrom-def"><code>owl:allValuesFrom</code></a> 
are used in a class description and are only
enforced on the property when applied to that class. In contrast,
<code>rdfs:range</code> restrictions apply to the property irrespective of the
class to which it is applied. 
Thus, <code>rdfs:range</code> should be
used with care.</p>

<p class="note">
NOTE: In OWL Lite the only type of class descriptions allowed as objects of 
<code>rdfs:range</code> are class names.
</p>

<h3><a name="PropertyRelation">4.2 Relations to other properties</a></h3>

<h4><a name="equivalentProperty-def" id="equivalentProperty-def">4.2.1
owl:equivalentProperty</a></h4>


<p>The <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_equivalentProperty">owl:equivalentProperty</a></span> 
construct can be used to state that two properties have the same property
extension. Syntactically, <code>owl:equivalentProperty</code> is a
built-in OWL property
with <code>rdf:Property</code> as both its domain and range.</p>

<p class="note">NOTE: Property equivalence is not the same as property
equality. Equivalent properties have the same "values" (i.e., 
the same property extension),
but may have different intensional meaning (i.e., denote different concepts).
Property equality should be expressed with the <a
href="#sameAs-def"><code>owl:sameAs</code></a> construct. As this
requires that properties are treated as individuals, such axioms are only
allowed in OWL Full.</p>

 
<h4><a name="inverseOf-def" id="inverseOf-def">4.2.2
owl:inverseOf</a></h4> 

<p>Properties have a direction, from domain to range. In practice, people often
find it useful to define relations in both directions: persons own
cars, cars are owned by persons.
The <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_inverseOf">owl:inverseOf</a></span>
construct can be used to define such an inverse relation between
properties.</p>

<p>Syntactically, <code>owl:inverseOf</code> is a built-in OWL
property with <code>owl:ObjectProperty</code> as its domain and
range.
An axiom of the
form <code>P1 owl:inverseOf P2</code> asserts
that for every pair
(x,y) in the property extension  of P1, there is a pair (y,x) in the property
extension of P2, and vice versa. Thus, <code>owl:inverseOf</code> is a
symmetric property.</p>

<p>An example:</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="hasChild"&gt;
  &lt;owl:inverseOf rdf:resource="#hasParent"/&gt;
&lt;/owl:ObjectProperty&gt;
</pre>


<h3><a name="PropertyCardinality">4.3 Global cardinality constraints on
properties</a></h3> 

<h4><a name="FunctionalProperty-def"
id="FunctionalProperty-def">4.3.1 owl:FunctionalProperty</a></h4> 

<p>A functional property is a property that can have only one 
(unique) value y for each instance x, i.e. there
cannot be two distinct values y1 and y2 such that the pairs (x,y1) and
(x,y2) are both instances of this property.  
Both object properties and datatype properties can be declared as
"functional". For this purpose, 
OWL defines the built-in class <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_FunctionalProperty">owl:FunctionalProperty</a></span>
as a special subclass of the RDF class 
<code>rdf:Property</code>. 
</p>

<p>The following axiom states that the <code>husband</code> property is
functional, <em>i.e.,</em> a woman can have at most one husband (a good
example of culture dependence of ontologies):</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="husband"&gt;
  &lt;rdf:type    rdf:resource="&amp;owl;FunctionalProperty" /&gt;
  &lt;rdfs:domain rdf:resource="#Woman" /&gt;
  &lt;rdfs:range  rdf:resource="#Man" /&gt;
&lt;/owl:ObjectProperty&gt;
</pre>

<p>As always, there are syntactic
variations. The example above 
is semantically equivalent to the one below:</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="husband"&gt;
  &lt;rdfs:domain rdf:resource="#Woman" /&gt;
  &lt;rdfs:range  rdf:resource="#Man" /&gt;
&lt;/owl:ObjectProperty&gt;

&lt;owl:FunctionalProperty rdf:about="#husband" /&gt;
</pre>


<h4><a name="InverseFunctionalProperty-def"
id="InverseFunctionalProperty-def">4.3.2
owl:InverseFunctionalProperty</a></h4> 

<p>If a
property is declared to be inverse-functional, then the object of a
property statement uniquely
determines the subject (some individual).  More formally, if we state that
P is an <code>owl:InverseFunctionalProperty</code>, then this asserts that a
value y can only be the value of P for a single instance x, i.e. there
cannot be two distinct instances x1 and x2 such that both pairs (x1,y) and
(x2,y) are instances of P.</p>

<p>Syntactically, an inverse-functional property axiom is specified by 
declaring the property to be an instance of the built-in OWL class
<span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_InverseFunctionalProperty">owl:InverseFunctionalProperty</a></span>,
which is a subclass of the OWL class <code>owl:ObjectProperty</code>.</p>

<p class="note">NOTE: Because in
OWL Full datatype properties are a subclass of object
properties, an inverse-functional property can be defined for 
datatype properties. In OWL DL object properties and datatype properties are
disjoint, so an inverse-functional property cannot be defined for datatype
properties. See also <a href="#OWLFull">Sec. 8.1</a> and <a
href="#OWLDL">Sec. 8.2</a>.</p>
  
<p>A typical example of an inverse-functional property:</p>

<pre>
&lt;owl:InverseFunctionalProperty rdf:ID="biologicalMotherOf"&gt;
  &lt;rdfs:domain rdf:resource="#Woman"/&gt;
  &lt;rdfs:range rdf:resource="#Human"/&gt;
&lt;/owl:InverseFunctionalProperty&gt;
</pre>

<p>This example states that for each object
of <code>biologicalMotherOf</code> statements (some human) one should be able
to uniquely identify a subject (some woman). Inverse-functional
properties resemble the notion of a key in databases. </p>

<p>One difference with functional properties is that for inverse-functional
properties no additional object-property or datatype-property axiom is
required: inverse-functional properties are by definition object properties. 
</p>

<p>Notice that <code><a
href="#FunctionalProperty-def">owl:FunctionalProperty</a></code> and <code><a
href="#InverseFunctionalProperty-def">owl:InverseFunctionalProperty</a></code>
specify global cardinality constraints. That is, no matter which class the
property is applied to, the cardinality constraints must hold. This is
different from the cardinality constraints contained in <a
href="#Restriction">property restrictions</a>. The latter are class
descriptions and are only enforced on the property when applied to that
class.</p>


<h3><a name="PropertyLogic">4.4 Logical characteristics of properties</a></h3>

<h4><a name="TransitiveProperty-def"
id="TransitiveProperty-def">4.4.1 owl:TransitiveProperty</a></h4>

<p>When one defines a property P to be a transitive property, this means 
that if a pair (x,y) is an instance
of P, and the pair (y,z) is also instance of P, then we can infer 
the the pair (x,z) is also
an instance of P. </p>

<p>Syntactically, a property is defined as being transitive by making it an
instance of the the built-in OWL class 
<span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_TransitiveProperty">owl:TransitiveProperty</a></span>,
which is defined as a subclass of <code><a
href="#ObjectProperty-def">owl:ObjectProperty</a></code>.</p>

<p>Typical examples of transitive properties are properties
representing certain part-whole relations.
For example, we might want to say that the
<code>subRegionOf</code> property between regions is transitive:</p>

<pre>
&lt;owl:TransitiveProperty rdf:ID="subRegionOf"&gt;
  &lt;rdfs:domain rdf:resource="#Region"/&gt;
  &lt;rdfs:range  rdf:resource="#Region"/&gt;
&lt;/owl:TransitiveProperty&gt;
</pre>

<p>From this an OWL reasoner should be able to derive that if 
<code>ChiantiClassico</code>, 
<code>Tuscany</code> and <code>Italy</code> are regions, and
<code>ChiantiClassico</code> is a subregion of <code>Tuscany</code>, and
<code>Tuscany</code> is a subregion of <code>Italy</code>, then 
<code>ChiantiClassico</code> is also a subregion of <code>Italy</code>.</p>

<p>Note that because <code>owl:TransitiveProperty</code> is a subclass of
<code>owl:ObjectProperty</code>, the following syntactic variant is equivalent
to the example above:</p>

<pre>
&lt;owl:ObjectProperty rdf:ID="subRegionOf"&gt;
  &lt;rdf:type rdf:resource="&amp;owl;TransitiveProperty"/&gt;
  &lt;rdfs:domain rdf:resource="#Region"/&gt;
  &lt;rdfs:range  rdf:resource="#Region"/&gt;
&lt;/owl:ObjectProperty&gt;
</pre>

<p class="note">
NOTE: OWL DL requires that for a transitive property no local or global
cardinality constraints should be declared on the property itself or its
superproperties, nor on the inverse of the property or its superproperties. 
</p>

<h4><a name="SymmetricProperty-def"
id="SymmetricProperty-def">4.4.2 owl:SymmetricProperty</a></h4>

<p>
A symmetric property is a property for which holds that 
if the pair (x,y) is an instance
of P, then the pair (y,x) is also
an instance of P. 
Syntactically, a property is defined as symmetric by making it an
instance of the built-in OWL class 
<span class="def"><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_SymmetricProperty">owl:SymmetricProperty</a></span>,
a subclass of <code><a
href="#ObjectProperty-def">owl:ObjectProperty</a></code>.
</p>

<p>A popular example of a symmetric property is the <code>friendOf</code> 
relation:
</p>

<pre>
&lt;owl:SymmetricProperty rdf:ID="friendOf"&gt;
  &lt;rdfs:domain rdf:resource="#Human"/&gt;
  &lt;rdfs:range  rdf:resource="#Human"/&gt;
&lt;/owl:SymmetricProperty&gt;
</pre>

<p>
The domain and range of a symmetric property are the same.
</p>
 

<h2><a name="Individual" id="Individual">5. Individuals</a></h2>

<p>Individuals are defined with individual axioms (also called "facts"). 
We discuss two types of facts:</p>
<ol>
  <li>Facts about class membership and property values of individuals</li>
  <li>Facts about individual identity</li>
</ol>

<h3><a name="IndividualAxiom">5.1 Class membership and property values</a></h3>

<p>Many facts typically are statements indicating class membership
of individuals and property values of individuals.
As an
example, consider the following set of statements about an instance of the
class <code>Opera</code>:</p>

<pre>
&lt;Opera rdf:ID="Tosca"&gt;
  &lt;hasComposer rdf:resource="#Giacomo_Puccini"/&gt;
  &lt;hasLibrettist rdf:resource="#Victorien_Sardou"/&gt;
  &lt;hasLibrettist rdf:resource="#Giuseppe_Giacosa"/&gt;
  &lt;hasLibrettist rdf:resource="#Luigi_Illica"/&gt;
  &lt;premiereDate rdf:datatype="&amp;xsd;date"&gt;1900-01-14&lt;/premiereDate&gt;
  &lt;premierePlace rdf:resource="#Roma"/&gt;
  &lt;numberOfActs rdf:datatype="&amp;xsd;positiveInteger"&gt;3&lt;/numberOfActs&gt; 
&lt;/Opera&gt;
</pre>

<p>This example includes a number of facts 
about the individual 
<code>Tosca</code>, an instance of the class <code>Opera</code>.
<code>Tosca</code> is 
composed by Giacomo Puccini. 
The opera has three libretto writers. The property
<code>premiereDate</code>  links an opera to a typed literal 
with the XML Schema datatype
<code>date</code>. The XML schema document on datatypes
[<cite><a href="#ref-xml-schema2">XML Schema Datatypes</a></cite>] 
contains the relevant information about syntax and semantics of
this datatype. </p>

<p>Individual axioms need not necessarily be about named individuals: they can
also refer to anonymous individuals. As an example, consider the piece of
RDF/XML below. The example defines some facts about an anonymous instance of
the class 
<code>Measurement</code>, a quantitative observation for which facts such as
the subject under observation, the observed phenomenon, the observed value, and
the observation time are listed:</p>

<pre>
&lt;Measurement&gt;
  &lt;observedSubject rdf:resource="#JaneDoe"/&gt;
  &lt;observedPhenomenon rdf:resource="#Weight"/&gt;
  &lt;observedValue&gt;
    &lt;Quantity&gt;
      &lt;quantityValue rdf:datatype="&amp;xsd;float"&gt;59.5&lt;/quantityValue&gt;
      &lt;quantityUnit rdf:resource="#Kilogram"/&gt;
    &lt;/Quantity&gt;
  &lt;/observedValue&gt;
  &lt;timeStamp rdf:datatype="&amp;xsd;dateTime"&gt;2003-01-24T09:00:08+01:00&lt;/timeStamp&gt;
&lt;/Measurement&gt;
</pre>

<p>This individual axiom contains two anonymous individuals, namely some
<code>Measurement</code> and some <code>Quantity</code>.  In natural language,
for
the subject Jane Doe the measured value of the phenomenon 
<code>Weight</code> is some
quantity, which has a value of 59.5 using the unit of kilogram.  The time of
measurement is January 24, 2003, eight seconds past nine in the morning, in the
time zone UTC+1 (winter time in Amsterdam, Berlin, Paris). As before,
<code>float</code> and <code>dateTime</code> are XML Schema datatypes, the
syntactic and semantic details of which can be found in the relevant XML Schema
documentation
[<cite><a href="#ref-xml-schema2">XML Schema Datatypes</a></cite>].</p>

<h3><a name="IndividualIdentity">5.2 Individual identity</a></h3>

<p>Many languages have a so-called "unique names" assumption: different names
refer to different things in the world. On the web, such an assumption is not
possible. For example, the same person could be referred to in many different
ways (i.e. with different URI references). For this reason OWL does not make
this assumption. Unless an explicit statement is being made that two URI
references refer to the same or to different individuals, OWL tools should in
principle assume either situation is possible.</p>

<p>OWL provides three constructs for stating facts about the identity of
individuals:</p>

<ul>
  <li><code>owl:sameAs</code> is used to state that two URI references refer to
  the same individual. </li>
  <li><code>owl:differentFrom</code> is used to state that two URI references
  refer to different individuals</li>
  <li><code>owl:AllDifferent</code> provides an idiom for stating that a list
  of individuals are all different.</li>
</ul>

<h4><a name="sameAs-def">5.2.1 owl:sameAs</a></h4>

<p>The built-in OWL property <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_sameAs">owl:sameAs</a></span>
links an individual to an individual. 
Such an <code>owl:sameAs</code> statement indicates that
two URI references actually refer to the same thing: the
individuals have the same "identity". </p> 

<p>For individuals such as "people" this
notion is relatively easy to understand. For example, we could state that
the following two URI references actually refer to the same person:</p>

<pre>
&lt;rdf:Description rdf:about="#William_Jefferson_Clinton"&gt;
  &lt;owl:sameAs rdf:resource="#BillClinton"/&gt;
&lt;/rdf:Description&gt;
</pre>

<p>The <code>owl:sameAs</code> statements are often used in defining mappings
between ontologies. It is unrealistic to assume  everybody will use the same
name to refer to individuals. That would require some grand design, which is
contrary to the spirit of the web. </p>

<p>In OWL Full, where a class can be treated as instances of
(meta)classes, we 
can use the <code>owl:sameAs</code> construct to define class equality,
thus indicating that two concepts have the same intensional meaning. 
An example: </p>
<pre>
&lt;owl:Class rdf:ID="FootballTeam"&gt;
  &lt;owl:sameAs rdf:resource="http://sports.org/US#SoccerTeam"/&gt;
&lt;/owl:Class&gt;
</pre>

<p>One could imagine this axiom to be part of a European sports
ontology. The two classes are treated here as individuals, in this
case as instances of the class <code>owl:Class</code>.  This allows us
to state that the class <code>FootballTeam</code> in some European
sports ontology denotes the same concept as the class
<code>SoccerTeam</code> in some American sports ontology. Note the
difference with the statement:</p>

<pre>
&lt;footballTeam owl:equivalentClass us:soccerTeam /&gt;
</pre>

<p>which states that the two classes have the same class extension,
but are not (necessarily) the same concepts. </p>

<p class="note">
NOTE: For details of comparison of URI references, see the section on 
RDF URI references in the RDF Concepts document 
[<cite><a href="#ref-rdf-concepts">RDF Concepts</a></cite>].
</p>

<h4><a name="differentFrom-def">5.2.2 owl:differentFrom</a></h4>

<p>
The built-in OWL <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_differentFrom">owl:differentFrom</a></span>
property links an individual to an individual. 
An <code>owl:differentFrom</code> statement indicates that two URI references
refer to different individuals. </p>

<p>An example:</p>

<pre>
&lt;Opera rdf:ID="Don_Giovanni"/&gt;

&lt;Opera rdf:ID="Nozze_di_Figaro"&gt;
  &lt;owl:differentFrom rdf:resource="#Don_Giovanni"/&gt;
&lt;/Opera&gt;

&lt;Opera rdf:ID="Cosi_fan_tutte"&gt;
  &lt;owl:differentFrom rdf:resource="#Don_Giovanni"/&gt;
  &lt;owl:differentFrom rdf:resource="#Nozze_di_Figaro"/&gt;
&lt;/Opera&gt;
</pre>

This states that there are three different operas. 


<h4><a name="AllDifferent-def">5.2.3 owl:AllDifferent</a></h4>

<p>For ontologies in which the unique-names assumption holds, the use
of <code>owl:differentFrom</code> is likely to lead to a large number
of statements, as all individuals have to be declared pairwise
disjoint. For such situations OWL provides a special idiom in the form
of the construct <a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_AllDifferent">owl:AllDifferent</a>.
<code>owl:AllDifferent</code> is a special built-in OWL class, for
which the property <a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_distinctMembers">owl:distinctMembers</a>
<a name="distinctMembers-def" id="distinctMembers-def"></a> is
defined, which links an instance of <code>owl:AllDifferent</code> to a
list of individuals. The intended meaning of such a statement is that
all individuals in the list are all different from each other.</p>

<p>An example:</p>

<pre>
&lt;owl:AllDifferent&gt;
  &lt;owl:distinctMembers rdf:parseType="Collection"&gt;
    &lt;Opera rdf:about="#Don_Giovanni"/&gt;
    &lt;Opera rdf:about="#Nozze_di_Figaro"/&gt;
    &lt;Opera rdf:about="#Cosi_fan_tutte"/&gt;
    &lt;Opera rdf:about="#Tosca"/&gt;
    &lt;Opera rdf:about="#Turandot"/&gt;
    &lt;Opera rdf:about="#Salome"/&gt;
  &lt;/owl:distinctMembers&gt;
&lt;/owl:AllDifferent&gt;
</pre>

<p>This states that these six URI references all
point to different operas. </p>

<p class="note">
NOTE: <code>owl:distinctMembers</code> is a special syntactical construct added
for convenience and should always be used with an <code>owl:AllDifferent</code>
individual as its subject.</p>


<h2><a name="Datatype" id="Datatype"></a>6. Datatypes</h2>

<p>
In a number of places in this document we have seen the notion of a 
<a name="DataRange">data range</a>
for specifying a range of data values. 
OWL allows three types of data range
specifications:</p>

<ul>
<li>A <a href="#rdf-datatype">RDF datatype</a> specification.</li>
<li>The RDFS class 
   <a href="http://www.w3.org/TR/rdf-schema/#ch_literal">rdfs:Literal</a>.</li>
<li>An <a href="#EnumeratedDatatype">enumerated datatype</a>, 
using the <code>owl:oneOf</code> construct.</li>
</ul>

<p>The minimal level of tool support for datatypes is discussed in
<a href="#DatatypeSupport">Sec. 6.3</a>.</p>

<h3><a name="rdf-datatype" id="rdf-datatype"></a>6.1 RDF Datatypes</h3>

<p>OWL makes use of the RDF datatyping scheme, which provides a mechanism for
referring to XML Schema datatypes
[<cite><a href="#ref-xml-schema2">XML Schema Datatypes</a></cite>]. For a
detailed description the reader is referred to the RDF documents,
<em>e.g.</em>,  
[<cite><a href="#ref-rdf-concepts">RDF Concepts</a></cite>].
For the convenience of
the reader, we provide here a 
synopsis of the use of RDF datatypes.</p>

<p>Data values are instances of the RDF Schema class
<code>rdfs:Literal</code>. Literals can be either 
plain (no datatype) or typed. Datatypes are instances of the class
<code>rdfs:Datatype</code>. 
In RDF/XML, the type of a literal is specified by an <code>rdf:datatype</code>
attribute of which
the value is recommended to be one of the following:</p>

<ul>
  <li>A canonical URI reference to an XML Schema datatype of the form:
    <pre>
       http://www.w3.org/2001/XMLSchema#NAME
    </pre>
  where "NAME" should be the name of a <em>simple</em> XML Schema
  <em>built-in</em> datatype, as defined in Section 3 of    
  [<cite><a href="#ref-xml-schema2">XML Schema Datatypes</a></cite>], with the
  provisos specified below.</li> 
  <li>The URI reference of the datatype <code>rdf:XMLLiteral</code>. 
  This datatype is used to
  include XML content into an RDF/OWL document. The URI reference of this
  datatype is:
  <pre>
    http://www.w3.org/1999/02/22-rdf-syntax-ns#XMLLiteral
  </pre>
  For details about this datatype, see the RDF Concepts document
 [<cite><a href="#ref-rdf-concepts">RDF Concepts</a></cite>]. 
  </li>
</ul>

<p>The RDF Semantics document 
[<cite><a href="#ref-RDF-Semantics">RDF Semantics</a></cite>, Section 5].  
recommends use of the following 
simple built-in XML Schema datatypes.</p>

<ul>
<li>The primitive datatype
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#string">
  <code>xsd:string</code></a>, 
plus the following datatypes derived from xsd:string:
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#normalizedString">
  <code>xsd:normalizedString</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#token">
  <code>xsd:token</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#language">
  <code>xsd:language</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#NMTOKEN">
  <code>xsd:NMTOKEN</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#Name">
  <code>xsd:Name</code></a>,and
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#NCName">
  <code>xsd:NCName</code></a>.</li>

<li>The primitive datatype 
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#boolean">
  <code>xsd:boolean</code></a>.</li>

<li>The primitive numerical datatypes
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#decimal">
  <code>xsd:decimal</code></a>, 
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#float">
  <code>xsd:float</code></a>, and
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#double">
  <code>xsd:double</code></a>, 
plus all derived types of xsd:decimal 
(<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#integer">
  <code>xsd:integer</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#positiveInteger">
  <code>xsd:positiveInteger</code></a>.
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#nonPositiveInteger">
  <code>xsd:nonPositiveInteger</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#negativeInteger">
  <code>xsd:negativeInteger</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#nonNegativeInteger">
  <code>xsd:nonNegativeInteger</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#long">
  <code>xsd:long</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#int">
  <code>xsd:int</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#short">
  <code>xsd:short</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#byte">
  <code>xsd:byte</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#unsignedLong">
  <code>xsd:unsignedLong</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#unsignedInt">
  <code>xsd:unsignedInt</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#unsignedShort">
  <code>xsd:unsignedShort</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#unsignedByte">
  <code>xsd:unsignedByte</code></a>)</li>

<li>The primitive time-related datatypes:
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#dateTime">
  <code>xsd:dateTime</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#time">
  <code>xsd:time</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#date">
  <code>xsd:date</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#gYearMonth">
  <code>xsd:gYearMonth</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#gYear">
  <code>xsd:gYear</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#gMonthDay">
  <code>xsd:gMonthDay</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#gDay">
  <code>xsd:gDay</code></a>, and
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#gMonth">
  <code>xsd:gMonth</code></a>.</li>

<li>The primitive datatypes
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#hexBinary">
  <code>xsd:hexBinary</code></a>,
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#base64Binary">
  <code>xsd:base64Binary</code></a>, and
<a href="http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/#anyURI">
  <code>xsd:anyURI</code></a>.</li>

</ul>


<p class="note">
NOTE: It is not illegal, although not recommended, for applications to define
their own datatypes by defining an instance of <code>rdfs:Datatype</code>. Such
datatypes are "unrecognized", but are treated in a similar fashion as
"unsupported datatypes" (see <a href="#DatatypeSupport">Sec. 6.3</a>
for details about how these should be treated by OWL tools). </p>


<p>
When using datatypes, please note that even if a property is defined
to have a range of a certain datatype, RDF/XML still requires that
the datatype be specified each time the property is used. 
An example could be the declaration of a property
that we used earlier in the <code>Measurement</code> example:</p>

<pre>
&lt;owl:DatatypeProperty rdf:about="#timeStamp"&gt;
  &lt;rdfs:domain rdf:resource="#Measurement"/&gt;
  &lt;rdf:range rdf:resource="&amp;xsd;dateTime"/&gt;
&lt;/owl:DatatypeProperty&gt;

&lt;Measurement&gt;
  &lt;timeStamp rdf:datatype="&amp;xsd;dateTime"&gt;2003-01-24T09:00:08+01:00&lt;/timeStamp&gt;  
&lt;/Measurement&gt;
</pre>


<h3><a name="EnumeratedDatatype"></a>6.2 Enumerated datatype</h3>

<p>In addition to the RDF datatypes, OWL provides one additional construct for
defining a range of data values, namely an enumerated datatype.  This datatype
format makes use of the <code>owl:oneOf</code> construct, that is also used for
describing an <a href="#EnumeratedClass">enumerated class</a>. In the case of
an enumerated datatype, the subject of <code>owl:oneOf</code> is a blank
node of class 
<a name="DataRange-def"><code>owl:DataRange</code></a> 
and the object is a list of
literals. Unfortunately, we cannot use the
<code>rdf:parseType="Collection"</code> idiom for specifying the literal list,
because RDF requires the collection to be a list of RDF node
elements. Therefore we have to specify the list of data values with the basic
list constructs <code>rdf:first</code>, <code>rdf:rest</code> and
<code>rdf:nil</code>.</p>

<p class="note">
NOTE: Enumerated datatypes are not part of OWL Lite.
</p>

<p>The example below specifies the range of the property
<code>tennisGameScore</code> to be the list of integer values {0, 15,
30, 40}:. </p>

<pre>
&lt;owl:DatatypeProperty rdf:ID="tennisGameScore"&gt;
  &lt;rdfs:range&gt;
    &lt;owl:DataRange&gt;
      &lt;owl:oneOf&gt;
        &lt;rdf:List&gt;
           &lt;rdf:first rdf:datatype="&amp;xsd;integer"&gt;0&lt;/rdf:first&gt;
           &lt;rdf:rest&gt;
             &lt;rdf:List&gt;
               &lt;rdf:first rdf:datatype="&amp;xsd;integer"&gt;15&lt;/rdf:first&gt;
               &lt;rdf:rest&gt;
                 &lt;rdf:List&gt;
                   &lt;rdf:first rdf:datatype="&amp;xsd;integer"&gt;30&lt;/rdf:first&gt;
                   &lt;rdf:rest&gt;
                     &lt;rdf:List&gt;
                       &lt;rdf:first rdf:datatype="&amp;xsd;integer"&gt;40&lt;/rdf:first&gt;
                       &lt;rdf:rest rdf:resource="&amp;rdf;nil" /&gt;
                     &lt;/rdf:List&gt;
                   &lt;/rdf:rest&gt;
                 &lt;/rdf:List&gt;
              &lt;/rdf:rest&gt;
            &lt;/rdf:List&gt;
          &lt;/rdf:rest&gt;
        &lt;/rdf:List&gt;
      &lt;/owl:oneOf&gt;
    &lt;/owl:DataRange&gt;
  &lt;/rdfs:range&gt;
&lt;/owl:DatatypeProperty&gt;
</pre>


<h3><a name="DatatypeSupport"></a>6.3 Support for datatype reasoning</h3>

<p>Tools may vary in terms of support for datatype reasoning. As a minimum,
tools must support datatype reasoning for the XML Schema datatypes
<code>xsd:string</code> and <code>xsd:integer</code>. 
OWL Full tools must also support <code>rdf:XMLLiteral</code>. 
For unsupported datatypes, lexically identical
literals should be considered equal, whereas lexically different literals 
would not be known to be either equal or unequal. 
Unrecognized datatypes should be treated in the same way as
unsupported datatypes. </p>





<h2><a name="Header" id="Header">7.  Annotations, ontology header, imports and
version information</a></h2>

<h3><a name="Annotations"></a>7.1 Annotations</h3>

<p>
OWL Full does not put any constraints on annotations in an ontology. 
OWL DL allows annotations on classes, properties, individuals
and ontology headers, but only under the  following conditions:
</p>
<ul>
  <li>The sets of object properties, datatype properties, annotation properties
  and ontology properties must be mutually disjoint. Thus, in OWL DL
  <code>dc:creator</code> cannot be at the same time a datatype property and
  an annotation property.</li> 
  <li>Annotation properties must have an explicit <a
  name="AnnotationProperty-def">typing triple</a> of the form:
  <pre>
    AnnotationPropertyID rdf:type owl:AnnotationProperty .
  </pre></li>
  <li>Annotation properties must not be used in property axioms. Thus, in OWL
  DL one cannot define subproperties or domain/range constraints for
  annotation properties.</li>
  <li>The object of an annotation property must be either a data literal, a URI
  reference, or an individual.</li>
</ul>
<p>Five annotation properties are predefined by OWL, namely:</p>
<ul>
  <li><code>owl:versionInfo</code></li>
  <li><code>rdfs:label</code></li>
  <li><code>rdfs:comment</code></li>
  <li><code>rdfs:seeAlso</code></li>
  <li><code>rdfs:isDefinedBy</code></li>
</ul>

<p>Here is an example of legal use of an annotation property in OWL DL:</p>

<pre>
&lt;owl:AnnotationProperty rdf:about="&amp;dc;creator"/&gt;

&lt;owl:Class rdf:about="#MusicalWork"&gt;
  &lt;rdfs:label&gt;Musical work&lt;/rdfs:label&gt;
  &lt;dc:creator&gt;N.N.&lt;/dc:creator&gt;
&lt;/owl:Class&gt;
</pre>

<p>The example assumes <code>&amp;dc;</code> and <code>dc:</code> point
respectively to the Dublin Core URI and namespace. Thus, using 
Dublin Core properties as annotation properties
in OWL DL requires an explicit typing triple. 
This ensures annotations are handled in a semantically correct fashion by OWL
DL reasoners  
(see the OWL Semantics and Abstract Syntax document [<cite><a
href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>] for details).</p>

<p>Once we define <code>dc:creator</code> 
as an annotation property, OWL DL does
NOT allow property axioms such as the range constraint below:</p>

<pre>
&lt;-- This is illegal in OWL DL --&gt;

&lt;owl:AnnotationProperty rdf:about="&amp;dc;creator"&gt;
  &lt;rdfs:range rdf:resource="&amp;xsd;string"/&gt;
&lt;/owl:AnnotationProperty&gt;
</pre>

<p>Note that one can still specify the value type of a literal  in an 
annotation-property statement:</p>

<pre>
&lt;Opera rdf:about="#Tosca"&gt;
  &lt;dc:creator rdf:datatype="&amp;xsd;string"&gt;Giacomo Puccini&lt;/dc:creator&gt;
&lt;/Opera&gt;
</pre>
 

<h3><a name="Ontology-def" id="Ontology-def">7.2 Ontology header</a></h3>

<p>A document describing an ontology typically contains information
about the ontology itself.  An ontology is a resource, so it may be
described using properties from the OWL and other namespaces, e.g.:</p> 

<pre>
&lt;owl:Ontology rdf:about=""&gt;
  &lt;owl:versionInfo&gt; ... &lt;/owl:versionInfo&gt;
  &lt;rdfs:comment&gt;...&lt;/rdfs:comment&gt;
  &lt;owl:imports rdf:resource="..."/&gt;
&lt;/owl:Ontology&gt;
</pre>

<p>This is commonly called the ontology header and is typically found
near the beginning of the RDF/XML document.  The line</p>

<pre>
  &lt;owl:Ontology rdf:about=""&gt;
</pre>

<p>states that this block describes the current ontology.  More
precisely, it states the current base URI identifies an instance of
the class <code>owl:Ontology</code>.  
It is recommended that the
base URI be defined using an <code>xml:base</code> attribute in the 
<code>&lt;rdf:RDF&gt;</code> element at the beginning of the document.
</p>

<p>A sample ontology header could look like this:</p>

<pre>
&lt;owl:Ontology rdf:about=""&gt;
  &lt;owl:versionInfo&gt;v 1.17 2003/02/26 12:56:51 mdean&lt;/owl:versionInfo&gt;
  &lt;rdfs:comment&gt;An example ontology&lt;/rdfs:comment&gt;
  &lt;owl:imports rdf:resource="http://www.example.org/foo"/&gt;
&lt;/owl:Ontology&gt;
</pre>

<p>The following sections describe the various types of statements that are
typically used within the header.</p>

<p class="note">
NOTE: The ontology-import construct <a href="#imports-def">owl:imports</a>
and the ontology-versioning constructs  
<a href="#priorVersion-def">owl:priorVersion</a>,
<a href="#backwardCompatibleWith-def">owl:backwardCompatibleWith</a>
and
<a href="#incompatibleWith-def">owl:incompatibleWith</a>
are defined in the OWL vocabulary as instances of the OWL built-in
class <a name="OntologyProperty-def"><code>owl:OntologyProperty</code></a>. 
Instances of <code>owl:OntologyProperty</code> must have the class
<code>owl:Ontology</code> as their domain and range. 
It is permitted to define other instances of 
<code>owl:OntologyProperty</code>. In OWL DL for
ontology properties the same constraints hold as those specified for
annotation properties in <a href="#Annotations">Sec. 7.1</a>. 
</p>


<h3><a name="imports-def" id="imports-def">7.3 Importing an ontology</a></h3>

<p>An <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_imports"><code>owl:imports</code></a></span>
statement references another OWL ontology containing definitions, 
whose meaning  
is considered to be part of the meaning of 
the importing ontology.  Each reference consists of a URI
specifying from where the ontology is to be imported.
Syntactically, <code>owl:imports</code> is a property with the
class <code>owl:Ontology</code> as its domain and range. </p>

<p>The <code>owl:imports</code> statements are transitive, that is, if
ontology A imports B, and B imports C, then A imports both B and C.</p>
Importing an ontology into itself is considered a null action, so if
ontology A imports B and B imports A, then they are considered to be
equivalent.<p/> 

<p>Note that whether or not an OWL tool must load an imported ontology
depends on the purpose of the tool. If the tool is a complete reasoner
(including complete consistency checkers) then it must load all of the
imported ontologies. Other tools, such as simple editors and incomplete
reasoners, may choose to load only some or even none of the imported
ontologies.</p>

<p>
Although owl:imports and namespace declarations may appear
redundant, they actually serve different purposes. Namespace
declarations simply set up a shorthand for referring to identifiers.
They do not implicitly include the meaning of documents located at the
URI. On the other hand, owl:imports does not provide any shorthand
notation for referring to the identifiers from the imported document.
Therefore, it is common to have a corresponding namespace declaration
for any ontology that is imported.
</p>

<p class="note">NOTE: <code>owl:imports</code>
is an instance of <code>owl:OntologyProperty</code>.
</p>


<h3><a name="VersionInformation">7.4 Version information</a></h3>

<h4><a name="versionInfo-def" id="versionInfo-def">7.4.1
owl:versionInfo</a></h4> 

<p>An
<span class="def"><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_versionInfo"><code>owl:versionInfo</code></a></span>
statement generally has as its object a string giving information about this
version, for example RCS/CVS keywords.  This statement does not
contribute to the logical meaning of the ontology other than that
given by the RDF(S) model theory.</p>

<p>Although this property is typically used to make statements about
ontologies, it may be applied to any OWL construct. For example, one could
attach a <code>owl:versionInfo</code> statement to an OWL class. 
</p>

<p class="note">NOTE: <code>owl:versionInfo</code>
is an instance of <code>owl:AnnotationProperty</code>.
</p>

<h4> <a name="priorVersion-def" id="priorVersion-def">7.4.2
owl:priorVersion</a></h4> 

<p> An <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_priorVersion"><code>owl:priorVersion</code></a></span>
statement contains a reference to another ontology.  This identifies
the specified ontology as a prior version of the containing ontology.
This has no meaning in the model-theoretic semantics other than that
given by the RDF(S) model theory.  However, it may be used by software
to organize ontologies by versions.</p>

<p><code>owl:priorVersion</code> is a built-in OWL property with the class
<code>owl:Ontology</code> as its domain and range. 
</p>

<p class="note">NOTE: <code>owl:priorVersion</code>
is an instance of <code>owl:OntologyProperty</code>.
</p>


<h4><a name="backwardCompatibleWith-def"
id="backwardCompatibleWith-def">7.4.3
owl:backwardCompatibleWith</a></h4> 

<p>An <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_backwardCompatibleWith"><code>owl:backwardCompatibleWith</code></a></span>
statement contains a reference to another ontology.  This identifies
the specified ontology as a prior version of the containing ontology,
and further indicates that it is backward compatible with it.  In
particular, this indicates that all identifiers from the previous
version have the same intended interpretations in the new version.
Thus, it is a hint to document authors that they can safely change
their documents to commit to the new version (by simply updating
namespace declarations and <a href="#imports-def"><code>owl:imports</code></a> statements to refer to the URL of
the new version).  If <code>owl:backwardCompatibleWith</code> is not
declared for two versions, then compatibility should not be assumed.</p>

<p><code>owl:backwardCompatibleWith</code> 
has no meaning in the model theoretic semantics other than that given by the
RDF(S) model theory.</p> 

<p><code>owl:backwardCompatibleWith</code> is a built-in OWL 
property with the class <code>owl:Ontology</code> as its domain and range. 
</p>

<p class="note">NOTE: 
<code>owl:backwardCompatibleWith</code> 
is an instance of <code>owl:OntologyProperty</code>.
</p>


<h4><a name="incompatibleWith-def"
id="incompatibleWith-def">7.4.4 owl:incompatibleWith</a></h4>

<p>An <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_incompatibleWith"><code>owl:incompatibleWith</code></a></span>
statement contains a reference to another ontology.  This indicates that the
containing ontology is a later version of the referenced ontology, but is not
backward compatible with it.  Essentially, this is for use by ontology authors
who want to be explicit that documents cannot upgrade to use the new version
without checking whether changes are required.</p>

<p><code>owl:incompatibleWith</code>  has
no meaning in the model theoretic semantics other than that given by the
RDF(S) model theory.</p> 

<p><code>owl:incompatibleWith</code> is a built-in OWL property with
the class <code>owl:Ontology</code> as its domain and range. 
</p>


<p class="note">NOTE: 
<code>owl:backwardCompatibleWith</code> 
is an instance of <code>owl:OntologyProperty</code>.
</p>

<h4><a name="Deprecation" id="Deprecation">7.4.5 owl:DeprecatedClass
and owl:DeprecatedProperty</a></h4>  

<p> <a name="DeprecatedClass-def" id="DeprecatedClass-def"></a> <a
name="DeprecatedProperty-def" id="DeprecatedProperty-def"></a>
Deprecation is a feature commonly used in versioning software (for
example, see the Java programming language) to indicate that a
particular feature is preserved for backward-compatibility purposes,
but may be phased out in the future. Here, a specific identifier is
said to be of type <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DeprecatedClass">owl:DeprecatedClass</a></span>
or <span class="def"><a
href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DeprecatedProperty">owl:DeprecatedProperty</a></span>,
where <code>owl:DeprecatedClass</code> is a subclass of
<code>rdfs:Class</code> and <code>owl:DeprecatedProperty</code> is a
subclass of <code>rdf:Property</code>.  By deprecating a term, it
means that the term should not be used in new documents that commit to
the ontology.  This allows an ontology to maintain
backward-compatibility while phasing out an old vocabulary (thus, it
only makes sense to use deprecation in combination with backward
compatibility).  As a result, it it easier for old data and
applications to migrate to a new version, and thus can increase the
level of adoption of the new version.  This has no meaning in the
model theoretic semantics other than that given by the RDF(S) model
theory.  However, authoring tools may use it to warn users when
checking OWL markup.</p>

<p>An example of deprecation is:</p>

<pre>
&lt;owl:Ontology rdf:about=""&gt;
  &lt;rdfs:comment&gt;Vehicle Ontology, v. 1.1&lt;/rdfs:comment&gt;
  &lt;owl:backwardCompatibleWith
          rdf:resource="http://www.example.org/vehicle-1.0"/&gt;   
  &lt;owl:priorVersion rdf:resource="http://www.example.org/vehicle-1.0"/&gt;
&lt;/owl:Ontology&gt;

&lt;owl:DeprecatedClass rdf:ID="Car"&gt;
  &lt;rdfs:comment&gt;Automobile is now preferred&lt;/rdfs:comment&gt;
  &lt;owl:equivalentClass rdf:resource="#Automobile"/&gt;
  &lt;!-- note that equivalentClass only means that the classes have the same
       extension, so this DOES NOT lead to the entailment that
       Automobile is of type DeprecatedClass too --&gt;        
&lt;/owl:DeprecatedClass&gt;

&lt;owl:Class rdf:ID="Automobile" /&gt;

&lt;owl:DeprecatedProperty rdf:ID="hasDriver"&gt;
  &lt;rdfs:comment&gt;inverse property drives is now preferred&lt;/rdfs:comment&gt;
  &lt;owl:inverseOf rdf:resource="#drives" /&gt;
&lt;/owl:DeprecatedProperty&gt;

&lt;owl:ObjectProperty rdf:ID="drives" /&gt;
</pre>


<h2><a name="Sublanguage-def">8. OWL Full, OWL DL and OWL Lite</a></h2>

<p>In the introduction we briefly discussed the three sublanguages of OWL. In
this section an informative 
specification is given of the differences between the
three "species" of OWL. A formal account of the differences is given in the
Semantics and Abstract Syntax document [<cite><a
href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>].</p>


<h3><a name="OWLFull">8.1 OWL Full</a></h3>

<p>OWL Full is not actually a sublanguage. OWL Full contains all the OWL
language constructs and provides free, unconstrained use of RDF constructs. 
In OWL Full the resource <code>owl:Class</code> is equivalent to
<code>rdfs:Class</code>. This is different from OWL DL
and OWL Lite, where <code>owl:Class</code> is a proper subclass of
<code>rdfs:Class</code> (meaning that not all RDF classes are OWL
classes in OWL DL and OWL Lite). 
OWL Full also allows classes to be treated as individuals. For
example, it is perfectly legal in OWL Full to have a "Fokker-100" identifier
which acts both as a class name (denoting the set of Fokker-100 airplanes
flying around the world) and as an individual name (<em>e.g.</em>,
an instance of the
class <code>AirplaneType</code>). </p>

<p>In OWL Full all data values are considered also to be part of the individual
domain. In fact, in OWL Full the universe of individuals consists of 
all resources (<code>owl:Thing</code> 
is equivalent to <code>rdfs:Resource</code>).
This means that object properties and datatype properties are not
disjoint. In OWL Full <code>owl:ObjectProperty</code> is equivalent to
<code>rdf:Property</code>. The consequence is
that datatype properties are effectively 
a subclass of object properties. (Note: the fact that 
<code>owl:ObjectProperty</code> and <code>owl:DatatypeProperty</code> are both
subclasses of <code>rdf:Property</code> is not inconsistent with this). </p>

<p>OWL Full will typically be useful for people who want to combine the
expressivity of OWL with the flexibility and metamodelling features of RDF. 
However, use of the OWL Full features means that one loses some 
guarantees (see <a href="#OWLDL">below</a>) that OWL DL and OWL Lite
can provide for reasoning systems.</p>

<p class="note">
NOTE: RDF documents will generally be in OWL Full, unless  they are
specifically constructed to be in OWL DL or Lite.
</p> 

<p class="note">
NOTE: Thus, in OWL Full 
<code>owl:Thing</code> is equivalent to
<code>rdfs:Resource</code>, 
<code>owl:Class</code> is equivalent to
<code>rdfs:Class</code>, and
<code>owl:ObjectProperty</code> is equivalent to
<code>rdf:Property</code>, 
</p>

<h3><a name="OWLDL">8.2 OWL DL</a></h3>

<p>OWL DL is a sublanguage of OWL which places a number of constraints on
the use of the OWL language constructs.  Briefly, these constraints are the
following:</p>
<ul>
  <li>OWL DL requires a pairwise separation between classes, datatypes,
  datatype properties, object properties, annotation properties, ontology
  properties (<em>i.e.,</em> the import and versioning stuff),
  individuals, data values and the built-in vocabulary.  This means that, for 
  example, a class cannot be at the same time an individual.</li>
  <li>In OWL DL the set of object properties and datatype properties are 
  disjoint. This implies that the following four property characteristics: 
  <ul>
    <li><a href="#inverseOf-def">inverse of</a>,</li>
    <li><a href="#InverseFunctionalProperty-def">inverse functional</a>, </li>
    <li><a href="#SymmetricProperty-def">symmetric</a>, and </li>
    <li><a href="#TransitiveProperty-def">transitive</a></li>
  </ul>
  can never be specified for <a href="#DatatypeProperty-def">datatype
  properties</a></li>
  <li>OWL DL requires that no cardinality constraints (local nor global) 
  can be placed on   transitive properties or their inverses or any of their
  superproperties.</li>
  <li>Annotations are allowed only under certain conditions. See <a
  href="#Annotations">Sec. 7.1</a> for details. </li>
  <li>Most RDF(S) vocabulary cannot be used within OWL DL. See the OWL
  Semantics and Abstract Syntax document [<cite><a
  href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>] for details. </li>
  <li>All axioms must be well-formed, with no missing or extra components, and
  must form a tree-like structure.

  <p>The last constraint implies that all classes and properties that one
  refers to are explicitly typed as OWL classes or properties, respectively.
  For example, if the ontology contains the following component:</p>
  <pre>
  &lt;owl:Class rdf:ID="C1"&gt;
    &lt;rdfs:subClassOf rdf:resource="#C2" /&gt;
  &lt;/owl:Class&gt;
  </pre>
  <p>then the ontology (or an ontology imported into this ontology) 
  should contain a <code>owl:Class</code> triple for 
  <code>C2</code>.</p></li>
  <li>Axioms (facts) about individual equality and difference must be about
  named individuals. </li>
</ul>

<p>These constraints of OWL DL may seem like an arbitrary set, but in fact
they are not.  The constraints are based on work in the
area of reasoners for Description Logic, which require these restrictions to
provide the ontology builder or user with reasoning support.
In  particular, the OWL DL restrictions allow the maximal subset of OWL 
Full against which current research can assure that a decidable 
reasoning procedure can exist for an OWL reasoner.
</p>

<p class="note">
NOTE: <a href="#app-DLinRDF">Appendix E</a> provides a set of
practical guidelines for specifying OWL DL ontologies in RDF.</p>


<h3><a name="OWLLite">8.3 OWL Lite</a></h3>

<p>
OWL Lite abides by all the restrictions OWL DL puts on the use of the OWL
language constructs.  
In addition, OWL Lite forbids the use of:</p>
<ul>
  <li><a href="#oneOf-def">owl:oneOf</a></li>
  <li><a href="#unionOf-def">owl:unionOf</a></li>
  <li><a href="#complementOf-def">owl:complementOf</a></li>
  <li><a href="#hasValue-def">owl:hasValue</a></li>
  <li><a href="#disjointWith-def">owl:disjointWith</a></li>
  <li><a href="#DataRange-def">owl:DataRange</a></li>
</ul>

<p>OWL Lite also requires that:</p>
<ul>
  <li>the subject of <code>owl:equivalentClass</code> triples be class names 
  and the object of <code>owl:equivalentClass</code> triples be class names
  or restrictions.</li>
  <li>the subject of <code>rdfs:subClassOf</code> triples be class names 
  and the object of <code>rdfs:subClassOf</code> triples be class names or
  restrictions;</li>
  <li><code>owl:intersectionOf</code> be used only on lists of length greater 
  than one that contain only class names and restrictions;
    <p class="note">
    NOTE: This is a prototypical example of legal use of 
    <code>owl:intersectionOf</code> in OWL Lite:</p>
      <pre>
        &lt;owl:Class rdf:ID="Woman"&gt;
          &lt;owl:intersectionOf rdf:parseType="Collection"&gt;
            &lt;owl:Class rdf:about="#Female"/&gt;
            &lt;owl:Class rdf:about="#Human"/&gt;
          &lt;/owl:intersectionOf&gt;
        &lt;/owl:Class/&gt;
      </pre>
    </li>
  <li>the object of <code>owl:allValuesFrom</code> and 
  <code>owl:someValuesFrom</code> triples be class
  names or datatype names;</li>
  <li>the object of <code>rdf:type</code> triples be class names or
  restrictions;</li> 
  <li>the object of <code>rdfs:domain</code> triples be class names;
  and</li>
  <li>the object of <code>rdfs:range</code> triples be class names or
  datatype names. 
</li>
</ul>

<p>The idea behind the OWL Lite expressivity limitations is that they
provide a minimal useful subset of language features, that are
relatively straightforward for tool developers to support. The
language constructs of OWL Lite provide the basics for subclass
hierarchy construction: subclasses and property
restrictions.  In addition, OWL Lite allows properties to be made
optional or required.  The
limitations on OWL Lite place it in a lower complexity class than OWL
DL.  This can have a positive impact on the efficiency of complete
reasoners for OWL Lite. </p>

<p>Implementations that support only the OWL Lite vocabulary, 
but otherwise relax the restrictions of OWL DL, cannot make certain 
computational claims with respect to consistency and complexity. 
However, such implementations may be useful in providing 
interoperability of OWL systems with RDFS models, databases, markup
tools, or  other non-reasoning tools.  
The Web  Ontology Working Group has not provided a name for this
potentially useful subset. 
</p>
 

<h2><a name="appA" id="appA">Appendix A. Index of all language 
elements</a></h2>

<p class="note">
NOTE: This appendix only contains the OWL-specific constructs. For the RDF/RDFS
constructs see the relevant RDF documentation, in particular the RDF Schema document
[<cite><a href="#ref-rdf-vocabulary">RDF Vocabulary</a></cite>].</p>

<table border="1">
  <tr>
    <th>[OWL Reference]<br />(this document)</th>
    <th>[<cite><a href="#ref-owl-abstract-syntax">OWL Semantics</a></cite>]<br />(normative)</th>
    <th>[<cite><a href="#ref-owl-guide">OWL Guide</a></cite>]<br />(examples)</th>
  </tr>
  <tr>
    <td><a href="#AllDifferent-def">owl:AllDifferent</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_AllDifferent">owl:AllDifferent</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_AllDifferent">owl:AllDifferent</a></td>
  </tr>
  <tr>
    <td><a href="#allValuesFrom-def">owl:allValuesFrom</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_allValuesFrom">owl:allValuesFrom</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_allValuesFrom">owl:allValuesFrom</a></td>
  </tr>
  <tr>
    <td><a href="#AnnotationProperty-def">owl:AnnotationProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_AnnotationProperty">owl:AnnotationProperty</a></td>
    <td>  </td>
  </tr>
  <tr>
    <td><a href="#backwardCompatibleWith-def">owl:backwardCompatibleWith</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_backwardCompatibleWith">owl:backwardCompatibleWith</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_backwardCompatibleWith">owl:backwardCompatibleWith</a></td>
  </tr>
  <tr>
    <td><a href="#cardinality-def">owl:cardinality</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_cardinality">owl:cardinality</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_cardinality">owl:cardinality</a></td>
  </tr>
  <tr>
    <td><a href="#Class-def">owl:Class</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Class">owl:Class</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_Class">owl:Class</a></td>
  </tr>
  <tr>
    <td><a href="#complementOf-def">owl:complementOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_complementOf">owl:complementOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_complementOf">owl:complementOf</a></td>
  </tr>
  <tr>
    <td><a href="#EnumeratedDatatype">owl:DataRange</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DataRange">owl:DataRange</a></td>
    <td>  </td>
  </tr>
  <tr>
    <td><a href="#DatatypeProperty-def">owl:DatatypeProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DatatypeProperty">owl:DatatypeProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_DatatypeProperty">owl:DatatypeProperty</a></td>
  </tr>
  <tr>
    <td><a href="#DeprecatedClass-def">owl:DeprecatedClass</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DeprecatedClass">owl:DeprecatedClass</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_DeprecatedClass">owl:DeprecatedClass</a></td>
  </tr>
  <tr>
    <td><a href="#DeprecatedProperty-def">owl:DeprecatedProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_DeprecatedProperty">owl:DeprecatedProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_DeprecatedProperty">owl:DeprecatedProperty</a></td>
  </tr>
  <tr>
    <td><a href="#differentFrom-def">owl:differentFrom</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_differentFrom">owl:differentFrom</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_differentFrom">owl:differentFrom</a></td>
  </tr>
  <tr>
    <td><a href="#disjointWith-def">owl:disjointWith</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_disjointWith">owl:disjointWith</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_disjointWith">owl:disjointWith</a></td>
  </tr>
  <tr>
    <td><a href="#distinctMembers-def">owl:distinctMembers</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_distinctMembers">owl:distinctMembers</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_distinctMembers">owl:distinctMembers</a></td>
  </tr>
  <tr>
    <td><a href="#equivalentClass-def">owl:equivalentClass</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_equivalentClass">owl:equivalentClass</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_equivalentClass">owl:equivalentClass</a></td>
  </tr>
  <tr>
    <td><a href="#equivalentProperty-def">owl:equivalentProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_equivalentProperty">owl:equivalentProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_equivalentProperty">owl:equivalentProperty</a></td>
  </tr>
  <tr>
    <td><a href="#FunctionalProperty-def">owl:FunctionalProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_FunctionalProperty">owl:FunctionalProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_FunctionalProperty">owl:FunctionalProperty</a></td>
  </tr>
  <tr>
    <td><a href="#hasValue-def">owl:hasValue</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_hasValue">owl:hasValue</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_hasValue">owl:hasValue</a></td>
  </tr>
  <tr>
    <td><a href="#imports-def">owl:imports</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_imports">owl:imports</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_imports">owl:imports</a></td>
  </tr>
  <tr>
    <td><a href="#incompatibleWith-def">owl:incompatibleWith</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_incompatibleWith">owl:incompatibleWith</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_incompatibleWith">owl:incompatibleWith</a></td>
  </tr>
  <tr>
    <td><a href="#intersectionOf-def">owl:intersectionOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_intersectionOf">owl:intersectionOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_intersectionOf">owl:intersectionOf</a></td>
  </tr>
  <tr>
    <td><a href="#InverseFunctionalProperty-def">owl:InverseFunctionalProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_InverseFunctionalProperty">owl:InverseFunctionalProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_InverseFunctionalProperty">owl:InverseFunctionalProperty</a></td>
  </tr>
  <tr>
    <td><a href="#inverseOf-def">owl:inverseOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_inverseOf">owl:inverseOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_inverseOf">owl:inverseOf</a></td>
  </tr>
  <tr>
    <td><a href="#maxCardinality-def">owl:maxCardinality</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_maxCardinality">owl:maxCardinality</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_maxCardinality">owl:maxCardinality</a></td>
  </tr>
  <tr>
    <td><a href="#minCardinality-def">owl:minCardinality</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_minCardinality">owl:minCardinality</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_minCardinality">owl:minCardinality</a></td>
  </tr>
  <tr>
    <td><a href="#Nothing-def">owl:Nothing</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Nothing">owl:Nothing</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_Nothing">owl:Nothing</a></td>
  </tr>
  <tr>
    <td><a href="#ObjectProperty-def">owl:ObjectProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_ObjectProperty">owl:ObjectProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_ObjectProperty">owl:ObjectProperty</a></td>
  </tr>
  <tr>
    <td><a href="#oneOf-def">owl:oneOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_oneOf">owl:oneOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_oneOf">owl:oneOf</a></td>
  </tr>
  <tr>
    <td><a href="#onProperty-def">owl:onProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_onProperty">owl:onProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_onProperty">owl:onProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Ontology">owl:Ontology</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_Ontology">owl:Ontology</a></td>
  </tr>
  <tr>
    <td><a href="#OntologyProperty-def">owl:OntologyProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_OntologyProperty">
         owl:OntologyProperty</a></td>
    <td>  </td>
  </tr>
  <tr>
    <td><a href="#priorVersion-def">owl:priorVersion</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_priorVersion">owl:priorVersion</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_priorVersion">owl:priorVersion</a></td>
  </tr>
  <tr>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Restriction">owl:Restriction</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_Restriction">owl:Restriction</a></td>
  </tr>
  <tr>
    <td><a href="#sameAs-def">owl:sameAs</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_sameAs">owl:sameAs</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_sameAs">owl:sameAs</a></td>
  </tr>
  <tr>
    <td><a href="#someValuesFrom-def">owl:someValuesFrom</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_someValuesFrom">owl:someValuesFrom</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_someValuesFrom">owl:someValuesFrom</a></td>
  </tr>
  <tr>
    <td><a href="#SymmetricProperty-def">owl:SymmetricProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_SymmetricProperty">owl:SymmetricProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_SymmetricProperty">owl:SymmetricProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Thing-def">owl:Thing</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_Thing">owl:Thing</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_Thing">owl:Thing</a></td>
  </tr>
  <tr>
    <td><a href="#TransitiveProperty-def">owl:TransitiveProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_TransitiveProperty">owl:TransitiveProperty</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_TransitiveProperty">owl:TransitiveProperty</a></td>
  </tr>
  <tr>
    <td><a href="#unionOf-def">owl:unionOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_unionOf">owl:unionOf</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_unionOf">owl:unionOf</a></td>
  </tr>
  <tr>
    <td><a href="#versionInfo-def">owl:versionInfo</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/#owl_versionInfo">owl:versionInfo</a></td>
    <td><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/#owl_versionInfo">owl:versionInfo</a></td>
  </tr>
</table>

<h2><a name="appB" id="appB"></a>Appendix B. RDF Schema of OWL</h2>

<p>See <a href="#AppendixList">Sec. 1.7</a> for a description of the 
purpose of this appendix.  The RDF/XML version of this appendix can 
be found at  <a href="http://www.w3.org/2002/07/owl">
http://www.w3.org/2002/07/owl</a> 
</p>

<pre>
&lt;?xml version="1.0"?&gt;
&lt;!DOCTYPE rdf:RDF [
     &lt;!ENTITY rdf  "http://www.w3.org/1999/02/22-rdf-syntax-ns#" &gt;
     &lt;!ENTITY rdfs "http://www.w3.org/2000/01/rdf-schema#" &gt;
     &lt;!ENTITY xsd  "http://www.w3.org/2001/XMLSchema#" &gt;
     &lt;!ENTITY owl  "http://www.w3.org/2002/07/owl#" &gt;
   ]&gt;

&lt;rdf:RDF
  xmlns     ="&amp;owl;"
  xmlns:owl ="&amp;owl;"
  xml:base  ="http://www.w3.org/2002/07/owl"
  xmlns:rdf ="&amp;rdf;"
  xmlns:rdfs="&amp;rdfs;"
&gt;

&lt;Ontology rdf:about=""&gt;
  &lt;imports rdf:resource="http://www.w3.org/2000/01/rdf-schema"/&gt;
  &lt;rdfs:isDefinedBy rdf:resource="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/" /&gt;
  &lt;rdfs:isDefinedBy rdf:resource="http://www.w3.org/TR/2004/REC-owl-test-20040210/" /&gt;
  &lt;rdfs:isDefinedBy rdf:resource="http://www.w3.org/TR/2004/REC-owl-features-20040210/" /&gt;
  &lt;rdfs:comment&gt;This file specifies in RDF Schema format the
    built-in classes and properties that together form the basis of
    the RDF/XML syntax of OWL Full, OWL DL and OWL Lite.
    We do not expect people to import this file
    explicitly into their ontology. People that do import this file
    should expect their ontology to be an OWL Full ontology. 
  &lt;/rdfs:comment&gt;
  &lt;versionInfo&gt;10 February 2004&lt;/versionInfo&gt;
&lt;/Ontology&gt;

&lt;rdfs:Class rdf:ID="Class"&gt;
  &lt;rdfs:label&gt;Class&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdfs;Class"/&gt;
&lt;/rdfs:Class&gt;

&lt;Class rdf:ID="Thing"&gt;
  &lt;rdfs:label&gt;Thing&lt;/rdfs:label&gt;
  &lt;unionOf rdf:parseType="Collection"&gt;
    &lt;Class rdf:about="#Nothing"/&gt;
    &lt;Class&gt;
      &lt;complementOf rdf:resource="#Nothing"/&gt;
    &lt;/Class&gt;
  &lt;/unionOf&gt;
&lt;/Class&gt;

&lt;Class rdf:ID="Nothing"&gt;
  &lt;rdfs:label&gt;Nothing&lt;/rdfs:label&gt;
  &lt;complementOf rdf:resource="#Thing"/&gt;
&lt;/Class&gt;

&lt;rdf:Property rdf:ID="equivalentClass"&gt;
  &lt;rdfs:label&gt;equivalentClass&lt;/rdfs:label&gt;
  &lt;rdfs:subPropertyOf rdf:resource="&amp;rdfs;subClassOf"/&gt;
  &lt;rdfs:domain rdf:resource="#Class"/&gt;
  &lt;rdfs:range rdf:resource="#Class"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="disjointWith"&gt;
  &lt;rdfs:label&gt;disjointWith&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Class"/&gt;
  &lt;rdfs:range rdf:resource="#Class"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="equivalentProperty"&gt;
  &lt;rdfs:label&gt;equivalentProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subPropertyOf rdf:resource="&amp;rdfs;subPropertyOf"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="sameAs"&gt; 
  &lt;rdfs:label&gt;sameAs&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Thing"/&gt;
  &lt;rdfs:range rdf:resource="#Thing"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="differentFrom"&gt;
  &lt;rdfs:label&gt;differentFrom&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Thing"/&gt;
  &lt;rdfs:range rdf:resource="#Thing"/&gt;
&lt;/rdf:Property&gt;

&lt;rdfs:Class rdf:ID="AllDifferent"&gt;
  &lt;rdfs:label&gt;AllDifferent&lt;/rdfs:label&gt;
&lt;/rdfs:Class&gt;

&lt;rdf:Property rdf:ID="distinctMembers"&gt;
  &lt;rdfs:label&gt;distinctMembers&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#AllDifferent"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdf;List"/&gt;
&lt;/rdf:Property&gt;
  
&lt;rdf:Property rdf:ID="unionOf"&gt;
  &lt;rdfs:label&gt;unionOf&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Class"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdf;List"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="intersectionOf"&gt;
  &lt;rdfs:label&gt;intersectionOf&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Class"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdf;List"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="complementOf"&gt;
  &lt;rdfs:label&gt;complementOf&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Class"/&gt;
  &lt;rdfs:range rdf:resource="#Class"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="oneOf"&gt;
  &lt;rdfs:label&gt;oneOf&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="&amp;rdfs;Class"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdf;List"/&gt;
&lt;/rdf:Property&gt;

&lt;rdfs:Class rdf:ID="Restriction"&gt;
  &lt;rdfs:label&gt;Restriction&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="#Class"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdf:Property rdf:ID="onProperty"&gt;
  &lt;rdfs:label&gt;onProperty&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="allValuesFrom"&gt;
  &lt;rdfs:label&gt;allValuesFrom&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdfs;Class"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="hasValue"&gt;
  &lt;rdfs:label&gt;hasValue&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="someValuesFrom"&gt;
  &lt;rdfs:label&gt;someValuesFrom&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
  &lt;rdfs:range rdf:resource="&amp;rdfs;Class"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="minCardinality"&gt;
  &lt;rdfs:label&gt;minCardinality&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
  &lt;rdfs:range rdf:resource="&amp;xsd;nonNegativeInteger"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="maxCardinality"&gt;
  &lt;rdfs:label&gt;maxCardinality&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
  &lt;rdfs:range rdf:resource="&amp;xsd;nonNegativeInteger"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="cardinality"&gt;
  &lt;rdfs:label&gt;cardinality&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#Restriction"/&gt;
  &lt;rdfs:range rdf:resource="&amp;xsd;nonNegativeInteger"/&gt;
&lt;/rdf:Property&gt;

&lt;rdfs:Class rdf:ID="ObjectProperty"&gt;
  &lt;rdfs:label&gt;ObjectProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="DatatypeProperty"&gt;
  &lt;rdfs:label&gt;DatatypeProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdf:Property rdf:ID="inverseOf"&gt;
  &lt;rdfs:label&gt;inverseOf&lt;/rdfs:label&gt;
  &lt;rdfs:domain rdf:resource="#ObjectProperty"/&gt;
  &lt;rdfs:range rdf:resource="#ObjectProperty"/&gt;
&lt;/rdf:Property&gt;

&lt;rdfs:Class rdf:ID="TransitiveProperty"&gt;
  &lt;rdfs:label&gt;TransitiveProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="#ObjectProperty"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="SymmetricProperty"&gt;
  &lt;rdfs:label&gt;SymmetricProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="#ObjectProperty"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="FunctionalProperty"&gt;
  &lt;rdfs:label&gt;FunctionalProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="InverseFunctionalProperty"&gt;
  &lt;rdfs:label&gt;InverseFunctionalProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;owl;ObjectProperty"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="AnnotationProperty"&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdfs:Class&gt;

&lt;AnnotationProperty rdf:about="&amp;rdfs;label"/&gt;
&lt;AnnotationProperty rdf:about="&amp;rdfs;comment"/&gt;
&lt;AnnotationProperty rdf:about="&amp;rdfs;seeAlso"/&gt;
&lt;AnnotationProperty rdf:about="&amp;rdfs;isDefinedBy"/&gt;

&lt;rdfs:Class rdf:ID="Ontology"&gt;
  &lt;rdfs:label&gt;Ontology&lt;/rdfs:label&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="OntologyProperty"&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdf:Property rdf:ID="imports"&gt;
  &lt;rdfs:label&gt;imports&lt;/rdfs:label&gt;
  &lt;rdf:type rdf:resource="#OntologyProperty"/&gt;
  &lt;rdfs:domain rdf:resource="#Ontology"/&gt;
  &lt;rdfs:range rdf:resource="#Ontology"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="versionInfo"&gt;
  &lt;rdfs:label&gt;versionInfo&lt;/rdfs:label&gt;
  &lt;rdf:type rdf:resource="#AnnotationProperty"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="priorVersion"&gt;
  &lt;rdfs:label&gt;priorVersion&lt;/rdfs:label&gt;
  &lt;rdf:type rdf:resource="#OntologyProperty"/&gt;
  &lt;rdfs:domain rdf:resource="#Ontology"/&gt;
  &lt;rdfs:range rdf:resource="#Ontology"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="backwardCompatibleWith"&gt;
  &lt;rdfs:label&gt;backwardCompatibleWitesh&lt;/rdfs:label&gt;
  &lt;rdf:type rdf:resource="#OntologyProperty"/&gt;
  &lt;rdfs:domain rdf:resource="#Ontology"/&gt;
  &lt;rdfs:range rdf:resource="#Ontology"/&gt;
&lt;/rdf:Property&gt;

&lt;rdf:Property rdf:ID="incompatibleWith"&gt;
  &lt;rdfs:label&gt;incompatibleWith&lt;/rdfs:label&gt;
  &lt;rdf:type rdf:resource="#OntologyProperty"/&gt;
  &lt;rdfs:domain rdf:resource="#Ontology"/&gt;
  &lt;rdfs:range rdf:resource="#Ontology"/&gt;
&lt;/rdf:Property&gt;

&lt;rdfs:Class rdf:ID="DeprecatedClass"&gt;
  &lt;rdfs:label&gt;DeprecatedClass&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdfs;Class"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="DeprecatedProperty"&gt;
  &lt;rdfs:label&gt;DeprecatedProperty&lt;/rdfs:label&gt;
  &lt;rdfs:subClassOf rdf:resource="&amp;rdf;Property"/&gt;
&lt;/rdfs:Class&gt;

&lt;rdfs:Class rdf:ID="DataRange"&gt;
  &lt;rdfs:label&gt;DataRange&lt;/rdfs:label&gt;
&lt;/rdfs:Class&gt;

&lt;/rdf:RDF&gt;


</pre>



<h2><a name="appC" id="appC"></a>Appendix C.
OWL Quick Reference</h2>

<p>Classes in the OWL vocabulary:</p>

<table border="1">
  <tr>
    <th>rdfs:Class</th>
  </tr>
  <tr>
    <td><a href="#AllDifferent-def">owl:AllDifferent</a></td>
  </tr>
  <tr>
    <td><a href="#AnnotationProperty-def">owl:AnnotationProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Class-def">owl:Class</a></td>
  </tr>
  <tr>
    <td><a href="#DataRange-def">owl:DataRange</a></td>
  </tr>
  <tr>
    <td><a href="#DatatypeProperty-def">owl:DatatypeProperty</a></td>
  </tr>
  <tr>
    <td><a href="#DeprecatedClass-def">owl:DeprecatedClass</a></td>
  </tr>
  <tr>
    <td><a href="#DeprecatedProperty-def">owl:DeprecatedProperty</a></td>
  </tr>
  <tr>
    <td><a href="#FunctionalProperty-def">owl:FunctionalProperty</a></td>
  </tr>
  <tr>
    <td><a href="#InverseFunctionalProperty-def">owl:InverseFunctionalProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Nothing-def">owl:Nothing</a></td>
  </tr>
  <tr>
    <td><a href="#ObjectProperty-def">owl:ObjectProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
  </tr>
  <tr>
    <td><a href="#OntologyProperty-def">owl:OntologyProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
  </tr>
  <tr>
    <td><a href="#SymmetricProperty-def">owl:SymmetricProperty</a></td>
  </tr>
  <tr>
    <td><a href="#Thing-def">owl:Thing</a></td>
  </tr>
  <tr>
    <td><a href="#TransitiveProperty-def">owl:TransitiveProperty</a></td>
  </tr>
</table>

<p />

<p>Properties in the OWL vocabulary:</p>

<table border="1">
  <tr>
    <th>rdf:Property</th>
    <th>rdfs:domain</th>
    <th>rdfs:range</th>
  </tr>
  <tr>
    <td><a href="#allValuesFrom-def">owl:allValuesFrom</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td>rdfs:Class</td>
  </tr>
  <tr>
    <td><a href="#backwardCompatibleWith-def">owl:backwardCompatibleWith</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
  </tr>
  <tr>
    <td><a href="#cardinality-def">owl:cardinality</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td>xsd:nonNegativeInteger</td>
  </tr>
  <tr>
    <td><a href="#complementOf-def">owl:complementOf</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
  </tr>
  <tr>
    <td><a href="#differentFrom-def">owl:differentFrom</a></td>
    <td><a href="#Thing-def">owl:Thing</a></td>
    <td><a href="#Thing-def">owl:Thing</a></td>
  </tr>
  <tr>
    <td><a href="#disjointWith-def">owl:disjointWith</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
  </tr>
  <tr>
    <td><a href="#distinctMembers-def">owl:distinctMembers</a></td>
    <td><a href="#AllDifferent-def">owl:AllDifferent</a></td>
    <td>rdf:List</td>
  </tr>
  <tr>
    <td><a href="#equivalentClass-def">owl:equivalentClass</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
  </tr>
  <tr>
    <td><a href="#equivalentProperty-def">owl:equivalentProperty</a></td>
    <td>rdf:Property</td>
    <td>rdf:Property</td>
  </tr>
  <tr>
    <td><a href="#hasValue-def">owl:hasValue</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td></td>
  </tr>
  <tr>
    <td><a href="#imports-def">owl:imports</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
  </tr>
  <tr>
    <td><a href="#incompatibleWith-def">owl:incompatibleWith</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
  </tr>
  <tr>
    <td><a href="#intersectionOf-def">owl:intersectionOf</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
    <td>rdf:List</td>
  </tr>
  <tr>
    <td><a href="#inverseOf-def">owl:inverseOf</a></td>
    <td><a href="#ObjectProperty-def">owl:ObjectProperty</a></td>
    <td><a href="#ObjectProperty-def">owl:ObjectProperty</a></td>
  </tr>
  <tr>
    <td><a href="#maxCardinality-def">owl:maxCardinality</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td>xsd:nonNegativeInteger</td>
  </tr>
  <tr>
    <td><a href="#minCardinality-def">owl:minCardinality</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td>xsd:nonNegativeInteger</td>
  </tr>
  <tr>
    <td><a href="#oneOf-def">owl:oneOf</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
    <td>rdf:List</td>
  </tr>
  <tr>
    <td><a href="#onProperty-def">owl:onProperty</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td>rdf:Property</td>
  </tr>
  <tr>
    <td><a href="#priorVersion-def">owl:priorVersion</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
    <td><a href="#Ontology-def">owl:Ontology</a></td>
  </tr>
  <tr>
    <td><a href="#sameAs-def">owl:sameAs</a></td>
    <td><a href="#Thing-def">owl:Thing</a></td>
    <td><a href="#Thing-def">owl:Thing</a></td>
  </tr>
  <tr>
    <td><a href="#someValuesFrom-def">owl:someValuesFrom</a></td>
    <td><a href="#Restriction-def">owl:Restriction</a></td>
    <td>rdfs:Class</td>
  </tr>
  <tr>
    <td><a href="#unionOf-def">owl:unionOf</a></td>
    <td><a href="#Class-def">owl:Class</a></td>
    <td>rdf:List</td>
  </tr>
  <tr>
    <td><a href="#versionInfo-def">owl:versionInfo</a></td>
    <td></td>
    <td></td>
  </tr>
</table>

<h2><a name="appD" id="appD"></a>Appendix D. 
Changes from DAML+OIL</h2>

<p>This section summarizes the changes from
DAML+OIL
[<cite><a href="#ref-daml">DAML+OIL</a></cite>]
to OWL.
</p>

<ol>
<li>The semantics have changed significantly. With respect to the three
sublanguages, the DAML+OIL semantics are closest to the OWL DL semantics. </li> 
<li>The namespace was changed to
<a href="http://www.w3.org/2002/07/owl">http://www.w3.org/2002/07/owl</a>.
</li>
<li>Various updates to RDF and RDF Schema from the 
   <a href="http://www.w3.org/2001/sw/RDFCore/">RDF Core Working Group</a>
   were incorporated,
   including
  <ul>
<li>cyclic subclasses are now allowed</li>
<li>multiple 
<code>rdfs:domain</code>
and
<code>rdfs:range</code>
properties are handled as intersection</li>
<li>RDF Semantics [<cite><a href="#ref-RDF-Semantics">RDF Semantics</a></cite>]</li>
<li><a href="http://www.w3.org/TR/rdf-concepts/#section-Datatypes">datatypes</a>
  <ul>
    <li>RDF and OWL use the XML Schema namespace
        <a href="http://www.w3.org/2001/XMLSchema">http://www.w3.org/2001/XMLSchema</a>
        rather than
        <a href="http://www.w3.org/2000/10/XMLSchema">http://www.w3.org/2000/10/XMLSchema</a>.</li>
    <li>OWL does not support using datatypes as types, e.g.
<pre>
&lt;size&gt;
  &lt;xsd:integer rdf:value="10"/&gt;
&lt;/size&gt;
</pre>
Instead use
<pre>
&lt;size
rdf:datatype="http://www.w3.org/2001/XMLSchema#integer"&gt;10&lt;/size&gt;
</pre>
    </li>
  </ul>
</li>
<li>the <code>daml:List</code> construct used to represent closed collections
    was largely incorporated into RDF
  <ul>
    <li><a href="http://www.w3.org/TR/rdf-syntax-grammar/#section-Syntax-parsetype-Collection">rdf:parseType="Collection"</a>
        replaces
        <code>rdf:parseType="daml:collection"</code></li>
    <li><code>rdf:List</code>, <code>rdf:first</code>, <code>rdf:rest</code>
        and <code>rdf:nil</code>
        replace
        <code>daml:List</code>, <code>daml:first</code>, <code>daml:rest</code>,
        and <code>daml:nil</code></li>
    <li><code>daml:item</code>
        is not supported.
        As this feature was typically used to create 
        typed lists, we include here an example of creating such a list 
        without using <code>daml:item</code>:

        <pre>
        &lt;rdfs:Class rdf:ID="OperaList"&gt;
          &lt;rdfs:subClassOf rdf:resource="&amp;rdf;List"/&gt;
          &lt;rdfs:subClassOf&gt;
            &lt;owl:Restriction&gt;
              &lt;owl:onProperty rdf:resource="&amp;rdf;first"/&gt;
              &lt;owl:allValuesFrom rdf:resource="#Opera"/&gt;
            &lt;/owl:Restriction&gt;
          &lt;/rdfs:subClassOf&gt;
          &lt;rdfs:subClassOf&gt;
            &lt;owl:Restriction&gt;
              &lt;owl:onProperty rdf:resource="&amp;rdf;rest"/&gt;
              &lt;owl:allValuesFrom rdf:resource="#OperaList"/&gt;
            &lt;/owl:Restriction&gt;
          &lt;/rdfs:subClassOf&gt;
        &lt;/rdfs:Class&gt;
        </pre>
        This example defines a list of which the elements most be operas. This
	is achieved by two restrictions, one on the <code>rdf:first</code> 
        value (representing the type of the list element) and a second
	restriction on the <code>rdf:rest</code> value (which should the name
	of the list being defined). 
    </li>
  </ul>
</li>
  </ul>
</li>

<li>Qualified restrictions were removed from the language,
resulting in the removal of the following properties:
<ul>
  <li><code>daml:cardinalityQ</code></li>
  <li><code>daml:hasClassQ</code></li>
  <li><code>daml:maxCardinalityQ</code></li>
  <li><code>daml:minCardinalityQ</code></li>
</ul>
</li>

<li>Various properties and classes were renamed,
as shown in the following table:
<table border="1">
  <tr>
   <th>DAML+OIL</th>
   <th>OWL</th>
  </tr>
  <tr>
<td><code>daml:differentIndividualFrom</code></td>
<td><code><a href="#differentFrom-def">owl:differentFrom</a></code></td>
  </tr>
  <tr>
<td><code>daml:equivalentTo</code></td>
<td><code><a href="#sameAs-def">owl:sameAs</a></code></td>
  </tr>
  <tr>
<td><code>daml:sameClassAs</code></td>
<td><code><a href="#equivalentClass-def">owl:equivalentClass</a></code></td>
  </tr>
  <tr>
<td><code>daml:samePropertyAs</code></td>
<td><code><a href="#equivalentProperty-def">owl:equivalentProperty</a></code></td>
  </tr>
  <tr>
<td><code>daml:hasClass</code></td>
<td><code><a href="#someValuesFrom-def">owl:someValuesFrom</a></code></td>
  </tr>
  <tr>
<td><code>daml:toClass</code></td>
<td><code><a href="#allValuesFrom-def">owl:allValuesFrom</a></code></td>
  </tr>
  <tr>
<td><code>daml:UnambiguousProperty</code></td>
<td><code><a href="#InverseFunctionalProperty-def">owl:InverseFunctionalProperty</a></code></td>
  </tr>
  <tr>
<td><code>daml:UniqueProperty</code></td>
<td><code><a href="#FunctionalProperty-def">owl:FunctionalProperty</a></code></td>
  </tr>
</table>
</li>

<li>
<code><a href="#SymmetricProperty-def">owl:SymmetricProperty</a></code>
was added.
</li>

<li>Also added were 
<code><a href="#AnnotationProperty-def">owl:AnnotationProperty</a></code>,
<code><a href="#OntologyProperty-def">owl:OntologyProperty</a></code> and
<code><a href="#DataRange-def">owl:DataRange</a></code>.
</li>

<li>An
<code><a href="#DatatypeProperty-def">owl:DatatypeProperty</a></code>
may be an
<code><a href="#InverseFunctionalProperty-def">owl:InverseFunctionalProperty</a></code>
in OWL Full.
</li>

<li>
Synonyms for RDF and RDF Schema classes and properties were removed from the language,
resulting in the removal of:
<ul>
  <li><code>daml:comment</code></li>
  <li><code>daml:domain</code></li>
  <li><code>daml:label</code></li>
  <li><code>daml:isDefinedBy</code></li>
  <li><code>daml:Literal</code></li>
  <li><code>daml:Property</code></li>
  <li><code>daml:range</code></li>
  <li><code>daml:seeAlso</code></li>
  <li><code>daml:subClassOf</code></li>
  <li><code>daml:subPropertyOf</code></li>
  <li><code>daml:type</code></li>
  <li><code>daml:value</code></li>
</ul>
</li>

<li>
  <code>daml:disjointUnionOf</code>
  was removed from the language,
  since it can be effected using
  <code><a href="#unionOf-def">owl:unionOf</a></code>
  or
  <code><a href="#subClassOf-def">rdfs:subClassOf</a></code>
  and
  <code><a href="#disjointWith-def">owl:disjointWith</a></code>.
</li>

<li>
  <code>daml:equivalentTo</code>
  was renamed to
  <code><a href="#sameAs-def">owl:sameAs</a></code>,
  and is no longer a superproperty of
  <code><a href="#equivalentClass-def">owl:equivalentClass</a></code> and
  <code><a href="#equivalentProperty-def">owl:equivalentProperty</a></code>,
</li>
<li>
  The following properties and classes were added to support versioning:
  <ul>
<li><a href="#backwardCompatibleWith-def">owl:backwardCompatibleWith</a></li>
<li><a href="#DeprecatedClass-def">owl:DeprecatedClass</a></li>
<li><a href="#DeprecatedProperty-def">owl:DeprecatedProperty</a></li>
<li><a href="#incompatibleWith-def">owl:incompatibleWith</a></li>
<li><a href="#priorVersion-def">owl:priorVersion</a></li>
  </ul>
</li>
<li><a href="#AllDifferent-def">owl:AllDifferent</a>
    and
    <a href="#distinctMembers-def">owl:distinctMembers</a>
    were added to address the
    Unique Names Assumption.
</li>
</ol>

<h2><a name="app-DLinRDF" id="app-DLinRDF"></a>Appendix E. 
Rules of Thumb for OWL DL ontologies</h2> 

<p>The OWL Abstract Syntax and Semantics document
[<cite><a href="#ref-owl-abstract-syntax">OWL S&amp;AS</a></cite>]
provides a characterization of OWL ontologies in terms of an abstract
syntax, along with a mapping to RDF triples.</p>

<p>The following rules give an informal characterization of the
conditions for an RDF graph to be a DL ontology. This is not intended
to replace the characterization given in S&amp;AS, but instead gives
some general pointers &mdash; the idea is that if you stick to these
guidelines, you're more likely to produce OWL DL ontologies. Nor is
this intended to tell you how to turn the triple representation into
something closer to the abstract syntax.</p>

<h3><a name="nomess" id="nomess"></a>Don't mess with the vocabulary</h3>

<p>The built-in properties and classes should <strong>not</strong> be
redefined. In general this means that things in the OWL, RDF or RDFS
namespaces should not appear as subjects of triples.
</p>

<h3><a name="typeEverything"></a>Provide Explicit Typing</h3>

<p>Everything should have a type<a href="#1"><sup>1</sup></a>. If any
URI reference <code>x</code> is used where a class is expected, the
graph should contain a triple stating that </p>

<pre class="code">
x rdf:type owl:Class
</pre>
<p>
Similarly, if a property <code>p</code> is used where an object
property is expected then there should be a triple<a
href="#2"><sup>2</sup></a>
</p>
<pre class="code">
p rdf:type owl:ObjectProperty
</pre> 
<p>If a property <code>q</code> is used where a data property is
expected then there should be a triple</p>
<pre class="code">
q rdf:type owl:DatatypeProperty
</pre> 

<p>If a property <code>o</code> is used where an ontology property is
expected then it should either be one of the built in ontology properties
(<code>owl:imports</code>, <code>owl:priorVersion</code>,
<code>owl:backwardCompatibleWith</code>, and
<code>owl:incompatibleWith</code>) or there should be a triple:</p>
<pre class="code">
o rdf:type owl:OntologyProperty
</pre> 

<p>If a property <code>a</code> is used where an annotation property
is expected then it should either be one of the built in annotation
properties (<code>owl:versionInfo</code>, <code>rdfs:label</code>,
<code>rdfs:comment</code>, <code>rdfs:seeAlso</code>, and
<code>rdfs:isDefinedBy</code>) or there should be a triple:</p>
<pre class="code">
a rdf:type owl:AnnotationProperty
</pre> 

<p>
Any individuals that occur in the ontology should have at least one
type specified, i.e. for an individual <code>i</code>, there must be
a triple:</p>
<pre class="code">
i rdf:type c
</pre>
<p>where <code>c</code> is an <code>owl:Class</code> or
<code>owl:Restriction</code>.
</p>

<h3><a name="separatenames" id="separatenames"></a>Keep names separate</h3>

<p>URI references for classes, properties (object, datatype, ontology
and annotation) and individuals should be disjoint. Thus we cannot
have things like:
</p>
<pre class="code">
x rdf:type owl:Class
x rdf:type owl:ObjectProperty
</pre>

<p>
In particular, this means that we cannot use <em>classes as
instances</em>, i.e.
</p>

<pre class="code">
x rdf:type owl:Class
y rdf:type owl:Class
x rdf:type y
</pre>

<p>
is not valid OWL DL. A general rule here is that if there is a node
<code>x</code> in the graph with a triple:
</p>

<pre class="code">
x rdf:type owl:Class
</pre>

<p>
then <code>x</code> should not appear as the subject of any other
triple with predicate <code>rdf:type</code>.<a href="#3"><sup>3</sup></a>
</p>

<h3><a name="Restrictions" id="Restrictions"></a>Restrictions</h3>

<p>If a node <code>x</code> has <code>rdf:type</code>
<code>owl:Restriction</code> then the following should be the case:
</p>
<ul>
<li>It is a blank node (i.e. unnamed).</li>
<li>It is not the subject of any other triple with predicate <code>rdf:type</code><a href="#3"><sup>3</sup></a>.</li>
<li>It is the subject of exactly <strong>one</strong> triple with predicate
<code>owl:onProperty</code>, with the object of that triple being an
<code>owl:ObjectProperty</code> or
<code>owl:DatatypeProperty</code>.</li>
<li>It is the subject of exactly <strong>one</strong> of:
 <ul>
  <li>A triple with predicate <code>owl:someValuesFrom</code>. In this
  case, the type of the property which is the object of the
  <code>owl:onProperty</code> triple should be appropriate. By this we
  mean that if the object of this triple is a datatype, the property
  should be an
  <code>owl:DatatypeProperty</code>. If the object is a class
  description, the property should be an
  <code>owl:ObjectProperty</code>. This typing information should be
  present (due to the restrictions outlined <a
  href="#typeEverything">above</a>).</li>
  <li>A triple with predicate <code>owl:allValuesFrom</code>. Similar
  restrictions hold as for <code>owl:someValuesFrom</code></li>
  <li>A triple with predicate <code>owl:hasValue</code>. If the type of the
  property involved in the <code>owl:onProperty</code> triple is
  <code>owl:ObjectProperty</code> then the object of this triple should
  be an individual. If the type of the
  property involved in the <code>owl:onProperty</code> triple is
  <code>owl:DatatypeProperty</code> the the object of this triple
  should be a data literal. </li>
  <li>A triple with predicate <code>owl:minCardinality</code>. The object
  of this triple should be a data literal representing a non negative
  integer.</li>
  <li>A triple with predicate <code>owl:maxCardinality</code>. Restriction
  as for <code>owl:minCardinality</code>. </li>
  <li>A triple with predicate <code>owl:cardinality</code>. Restriction as
  for <code>owl:minCardinality</code>. </li>
 </ul>
</li>
<li>Any other triples in which <code>x</code> is the subject should
have predicate <code>owl:equivalentClass</code> or
<code>owl:disjointWith</code>.</li>
</ul>

<h3><a name="ClassAxioms2" id="ClassAxioms2"></a>Class axioms</h3>

<p>For any triples with predicate <code>rdfs:subClassOf</code> or
<code>owl:equivalentClass</code> or <code>owl:disjointWith</code>,
both the subject and object of the triples should be an
<code>owl:Class</code> or <code>owl:Restriction</code>, i.e. if we
have:</p>

<pre class="code">
x rdfs:subClassOf y
</pre>

<p>then the graph must contain one of:</p>

<pre class="code">
x rdf:type owl:Class
</pre>

<p>or</p>

<pre class="code">
x rdf:type owl:Restriction.
</pre>

<p>and one of</p>

<pre class="code">
y rdf:type owl:Class
</pre>

<p>or</p>

<pre class="code">
y rdf:type owl:Restriction.
</pre>

<h3><a name="PropertyAxioms" id="PropertyAxioms"></a>Property axioms</h3>

<p>For any triples with predicate <code>rdfs:subPropertyOf</code> or
<code>owl:equivalentProperty</code>, both the subject and object of the
triples should have the same type which should be one of
<code>owl:ObjectProperty</code> or <code>owl:DatatypeProperty</code>,
i.e. if we have:</p>

<pre class="code">
p owl:equivalentProperty q
</pre>

<p>
then the graph must contain either:
</p>

<pre class="code">
p rdf:type owl:ObjectProperty
q rdf:type owl:ObjectProperty.
</pre>

<p>
or
</p>

<pre class="code">
p rdf:type owl:DatatypeProperty
q rdf:type owl:DatatypeProperty.
</pre>

<p>
Triples with predicate <code>rdfs:domain</code> should have as their
subject an <code>owl:ObjectProperty</code> or
<code>owl:DatatypeProperty</code> and as their object an
<code>owl:Class</code> or <code>owl:Restriction</code>.
</p>

<p>
Triples with predicate <code>rdfs:range</code> should have as their subject
either an <code>owl:ObjectProperty</code> or an
<code>owl:DatatypeProperty</code>. In the case of the former, the
object of the triple should then be an <code>owl:Class</code> or
<code>owl:Restriction</code>, in the case of the latter, the object
should be either an XML Schema datatype, <code>rdfs:Literal</code>, 
or an <code>owl:oneOf</code>
specifying a data range with type <code>owl:DataRange</code>.
</p>

<p>Both the subject and object of an <code>owl:inverseOf</code> triple
must have type <code>owl:ObjectProperty</code>.</p>

<h3><a name="individualaxioms" id="individualaxioms"></a>Individual axioms</h3>

<p>For any triples with predicate
<code>owl:sameAs</code> or
<code>owl:differentFrom</code>, the subject and object must be individuals.</p>

<p>
Note that relating two classes via
<code>owl:sameAs</code> is a very different thing to
relating them via <code>owl:equivalentClass</code>. The former says
that the two objects are in fact the same, is actually an example of
<em>class as instance</em>, and thus pushes the ontology out of OWL
DL. The latter is an assertion that the extension (e.g. the collection
of members) of the classes is equivalent.
</p>

<p>
Similarly, relating classes via <code>owl:differentFrom</code> is not
the same as relating them via <code>owl:disjointWith</code> (and is
again an example of an OWL Full construct). Two classes may be
different objects but still share the same extension.
</p>

<p>If
a node <code>x</code> has <code>rdf:type</code>
<code>owl:AllDifferent</code>, then the following should be the
case:</p>
<ul>
<li>It is a blank node (i.e. unnamed).</li>
<li>It is the subject of a triple with predicate
<code>owl:distinctMembers</code>, the object of which should be a
(well-formed) <code>rdf:List</code>, all of whose elements are
individuals.</li>
<li>It is not the subject (or object) of any other triples.</li>
</ul>

<h3><a name="booleanclassexpressions" id="booleanclassexpressions"></a>Boolean class expressions</h3>

<p>Boolean Operators (and, or, not) are represented in OWL using
<code>owl:intersectionOf</code>, <code>owl:unionOf</code> and
<code>owl:complementOf</code>. 
</p>

<p>The subject of an <code>owl:complementOf</code> triple must be an
<code>owl:Class</code>, the object must be either an
<code>owl:Class</code> or <code>owl:Restriction</code>.</p>

<p>The subject of an <code>owl:unionOf</code>or
<code>owl:intersectionOf</code> triple must be an
<code>owl:Class</code>, the object must be a (well-formed)
<code>rdf:List</code>, all of whose elements are either
<code>owl:Class</code> or
<code>owl:Restriction</code>. These could either be represented
explicitly using expanded <code>rdf:Lists</code>, or if RDF-XML is
being used, an <code>rdf:parseType="Collection"</code> attribute.</p>

<pre class="code">
&lt;owl:Class&gt;
 &lt;owl:intersectionOf rdf:parseType="Collection"&gt;
  &lt;owl:Class rdf:about="x"/&gt;
  &lt;owl:Class rdf:about="y"/&gt;
 &lt;/owl:intersectionOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>If the <code>owl:Class</code> is a blank node (i.e. the class is
unnamed), then it can only be the subject of at most one triple with
predicate
<code>owl:intersectionOf</code>,
<code>owl:unionOf</code> or <code>owl:complementOf</code>. If the
class is named, any number of such triples are allowed.</p>

<h3><a name="Enumerations" id="Enumerations"></a>Enumerations</h3>

<p>The subject of any triple with predicate <code>owl:oneOf</code> must be
either an <code>owl:Class</code> or an <code>owl:DataRange</code>. In
the case of the former, the object must be a (well-formed)
<code>rdf:List</code>, all of whose elements are individuals. In the case of the latter, the object must be a
(well-formed) <code>rdf:List</code>, all of whose elements are data
literals. Again, as with the boolean operators,
<code>rdf:parseType="Collection"</code> can be used.
</p>

<h3><a name="oaproperties" id="oaproperties"></a>Ontology and Annotation Properties</h3>

<p>The subject and object of any triple with an ontology predicate
should be an ontology, e.g. a node <code>x</code> such that there is a
triple:</p>
<pre class="code">
x rdf:type owl:Ontology
</pre>

<p>The subject of any triple with an annotation predicate should be a
named (i.e. non-bnode) class, a property, an individual or an
ontology. The object of a triple with an annotation predicate should
be an individual, a data literal or an arbitrary URI reference.</p>

<p>With the exception of predicates within the OWL, RDF and RDFS
vocabularies, annotation properties are the <strong>only</strong>
predicates that should appear in triples with a class or property as the
subject.</p> 

<p>Annotation and ontology properties themselves should be
<a href="#typeEverything">typed</a>, and should not appear as the
subject or object of triples other than as the subject of a triple
with predicate <code>rdf:type</code> or an annotation property.</p>

<h3><a name="nosharing" id="nosharing"></a>Avoid structure sharing</h3>

<p>In general, the S&amp;AS description of OWL does not permit
<em>structure sharing</em> in the RDF representation. This effectively
means that an anonymous node in the RDF graph representing a
particular description should only occur once (as the object of a
triple). Thus things like:</p>
<pre class="code">
x1 rdf:type owl:Class
x1 rdfs:subClassOf _:y
x2 rdf:type owl:Class
x2 rdfs:subClassOf _:y
_:y rdf:type owl:Class
_:y owl:complementOf z
</pre>

<p>
should be avoided. There are some tricky corner cases where this
<em>is</em> permitted. In general, however, graphs should use distinct
blank nodes whenever a class description is used in more than one place.
</p>

<h3><a name="noorphan" id="noorphan"></a>Avoid orphan blank nodes</h3>

<p>In general, blank nodes occurring in the graph either represent unnamed
individuals, or should be exactly
<strong>one</strong> of the following:</p>
<ul>
<li>The object of an <code>rdfs:subClassOf</code>,
<code>owl:equivalentClass</code>, <code>owl:disjointWith</code>,
<code>owl:someValuesFrom</code>, <code>owl:allValuesFrom</code> or
<code>rdf:type</code> triple.</li>
<li>The subject of an <code>rdf:type</code> triple with object
<code>owl:AllDifferent</code>.</li>
<li>An element in an <code>rdf:List</code>.</li>
</ul>

<p>Orphan blank nodes, i.e. those which are not the object of a triple are,
in general, not allowed (other than the <code>owl:AllDifferent</code>
case described above).</p>

<h3><a name="GroundFacts" id="GroundFacts"></a>Ground facts</h3>

<p>Ontologies may contain assertions of ground facts (e.g. triples
that assert the properties of individuals). The properties used in
these assertions must be an
<code>owl:ObjectProperty</code> or
<code>owl:DatatypeProperty</code>. The subject of any such triple must
be an individual (which should be <a
href="#typeEverything">typed</a>). The object can either be a reference
to an individual (if the property is an
<code>owl:ObjectProperty</code>) or a data literal (if the property is
an <code>owl:DatatypeProperty</code>).
</p>


<h3><a name="OWLLite2" id="OWLLite2"></a>OWL Lite</h3>

<p>OWL Lite documents should follow the same rules as OWL DL
documents, with a number of extra restrictions, primarily concerning
the vocabulary allowed. An OWL Lite document should
not use any of the following vocabulary:</p>

<ul>
<li><code>owl:unionOf</code></li>
<li><code>owl:complementOf</code></li>
<li><code>owl:oneOf</code></li>
<li><code>owl:hasValue</code></li>
<li><code>owl:disjointWith</code></li>
</ul>

<p>Any objects which are the object or subject of a triple with
predicate <code>owl:equivalentClass</code> should not be b-nodes.</p>

<p>The object of any triples with predicate
<code>owl:minCardinality</code>, <code>owl:maxCardinality</code> or
<code>owl:cardinality</code> should be a data literal representing the
integer 0 or 1.</p>

<p>The situation regarding the use of <code>owl:intersectionOf</code>
in OWL Lite is a little more complex. The predicate should
<strong>not</strong> be used to form arbitrary expressions, but <strong>is</strong>
needed in order to represent complete class definitions. The
restrictions above tell us that the subject of any triple with predicate
<code>owl:intersectionOf</code> should be a <code>owl:Class</code>. In
OWL Lite, we have the further restriction that this class should be
named, i.e. the subject should not be a bnode.</p>

<h3><a name="Miscellaneous" id="Miscellaneous"></a>Miscellaneous</h3>

<p>Be careful of the use of <code>owl:Thing</code>. For example, the
following OWL-RDF fragment:</p>

<pre class="code">
&lt;owl:Class rdf:about="#A"&gt;
  &lt;rdfs:subClassOf&gt;
    &lt;owl:Thing/&gt;
  &lt;/rdfs:subClassOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>does <strong>not</strong> describe a class <code>A</code> that is a
subclass of <code>owl:Thing</code>, but in fact describes a class
<code>A</code> that is a subclass of some anonymous instance of
<code>owl:Thing</code>. This is thus a use of class as instance and is
outside OWL DL. The desired effect of a subclass of
<code>owl:Thing</code> is obtained through:</p>

<pre class="code">
&lt;owl:Class rdf:about="#A"&gt;
  &lt;rdfs:subClassOf&gt;
    &lt;owl:Class rdf:about="http://www.w3.org/2002/07/owl#Thing"/&gt;
  &lt;/rdfs:subClassOf&gt;
&lt;/owl:Class&gt;
</pre>

<p>Be careful not to confuse <code>owl:Class</code> and
<code>rdfs:Class</code>. The following is <strong>not</strong> in DL
due to the fact that <code>c</code> is not given an appropriate
type.</p>

<pre class="code">
c rdf:type rdfs:Class
</pre>






<h3><a name="Notes" id="Notes"></a>Notes</h3>

<p>
<a name="1">[1]</a> Of course the necessity to type everything does
not apply to things from the OWL, RDF or RDFS namespaces.
</p>

<p>
<a name="2">[2]</a> Strictly speaking, if the property is defined as
being an <code>owl:TransitiveProperty</code>,
<code>owl:SymmetricProperty</code> or
<code>owl:InverseFunctionalProperty</code> then this is not
necessary. 
</p>

<p>
<a name="3">[3]</a> An exception here is that we can have:
</p>
<pre class="code">
x rdf:type rdfs:Class
x rdf:type owl:Class
</pre> 
<pre class="code">
p rdf:type rdf:Property
p rdf:type owl:ObjectProperty
</pre> 
<p>or</p>
<pre class="code">
q rdf:type rdf:Property
q rdf:type owl:DatatypeProperty
</pre> 
<p>In addition, for restrictions, we can have:</p>
<pre class="code">
x rdf:type owl:Restriction
x rdf:type rdfs:Class
x rdf:type owl:Class
</pre> 

<h2><a name="changes-since-PR" id="changes-since-PR"></a>Appendix F.
Change Log since PR</h2>

<ol>
<li>
Removed spurious endnote [4] in Appendix E.
</li>
<li>
Added rdfs:label element to AnnotationProperty and OntologyProperty in Appendix
B (RDF Schema of OWL) after comment from 
<a
href="http://lists.w3.org/Archives/Public/public-webont-comments/2003Dec/0024.html">Jacco van Ossenbruggen</a>. 
</li>
<li>
Fixed broken section reference plus corrected section reference style. 
</li>
<li>
Standardized reference section.
</li>
<li>
Editorial revision of requirement description for rdf:RDF element 
after comment from
<a href="http://lists.w3.org/Archives/Public/public-webont-comments/2004Jan/0017.html">Minsu Jang</a>.
</li>
<li>
Several editorial changes in response to a review by 
<a href="http://lists.w3.org/Archives/Public/public-webont-comments/2004Jan/0012.html">Lacy</a>. 
</li>
<li>
Added explanatory text to Sec. 7.1 about OWL DL constraints on the use of 
annotation properties, after 
some public comments (for example, see the comments by 
<a
href="http://lists.w3.org/Archives/Public/public-webont-comments/2004Jan/0006.html">Benjamin Nowack</a>. 
Added also a sentence to Sec. 7.2
to indicate that the same constraints hold for ontology properties. 
</li>
<li> 
Several small editorial corrections after final read-though by editor.
</li>
</ol>

<hr />

<h2><a id="References" name="References">References</a></h2>

<dl>

<dt><a name="ref-OWL-Overview" id="ref-OWL-Overview">[OWL Overview]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-owl-features-20040210/">OWL Web Ontology Language Overview</a></cite>, Deborah L. McGuinness and Frank van Harmelen, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-owl-features-20040210/ . <a href="http://www.w3.org/TR/owl-features/">Latest version</a> available at http://www.w3.org/TR/owl-features/ .</dd>

<dt><a name="ref-owl-guide" id="ref-owl-guide">[OWL Guide]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-owl-guide-20040210/">OWL Web Ontology Language Guide</a></cite>, Michael K. Smith, Chris Welty, and Deborah L. McGuinness, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-owl-guide-20040210/ . <a href="http://www.w3.org/TR/owl-guide/">Latest version</a> available at http://www.w3.org/TR/owl-guide/ .</dd>

<dt><a name="ref-owl-abstract-syntax" id="ref-owl-abstract-syntax">[OWL Semantics and Abstract Syntax]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-owl-semantics-20040210/">OWL Web Ontology Language Semantics and Abstract Syntax</a></cite>, Peter F. Patel-Schneider, Patrick Hayes, and Ian Horrocks, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-owl-semantics-20040210/ . <a href="http://www.w3.org/TR/owl-semantics/">Latest version</a> available at http://www.w3.org/TR/owl-semantics/ .</dd>

<dt><a name="ref-owl-test" id="ref-owl-test">[OWL Test]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-owl-test-20040210/">OWL Web Ontology Language Test Cases</a></cite>, Jeremy J. Carroll and Jos De Roo, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-owl-test-20040210/ . <a href="http://www.w3.org/TR/owl-test/">Latest version</a> available at http://www.w3.org/TR/owl-test/ .</dd>

<dt><a name="ref-owl-requirements" id="ref-owl-requirements">[OWL Requirements]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-webont-req-20040210/">OWL Web Ontology Language Use Cases and Requirements</a></cite>, Jeff Heflin, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-webont-req-20040210/ . <a href="http://www.w3.org/TR/webont-req/">Latest version</a> available at http://www.w3.org/TR/webont-req/ .</dd>

<dt><a name="ref-rdf-concepts" id="ref-rdf-concepts">[RDF Concepts]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/">Resource Description Framework (RDF): Concepts and Abstract Syntax</a></cite>, Graham Klyne and Jeremy J. Carroll, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/ . <a href="http://www.w3.org/TR/rdf-concepts/">Latest version</a> available at http://www.w3.org/TR/rdf-concepts/ .</dd>

<dt><a name="ref-rdf-syntax" id="ref-rdf-syntax">[RDF Syntax]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/">RDF/XML Syntax Specification (Revised)</a></cite>, Dave Beckett, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/ . <a href="http://www.w3.org/TR/rdf-syntax-grammar/">Latest version</a> available at http://www.w3.org/TR/rdf-syntax-grammar/ .</dd>

<dt><a name="ref-RDF-Semantics" id="ref-RDF-Semantics">[RDF Semantics]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-rdf-mt-20040210/">RDF Semantics</a></cite>, Pat Hayes, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-mt-20040210/ . <a href="http://www.w3.org/TR/rdf-mt/">Latest version</a> available at http://www.w3.org/TR/rdf-mt/ .</dd>

<dt><a name="ref-rdf-vocabulary" id="ref-rdf-vocabulary">[RDF Vocabulary]</a></dt>
<dd><cite><a href="http://www.w3.org/TR/2004/REC-rdf-schema-20040210/">RDF Vocabulary Description Language 1.0: RDF Schema</a></cite>, Dan Brickley and R. V. Guha, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-schema-20040210/ . <a href="http://www.w3.org/TR/rdf-schema/">Latest version</a> available at http://www.w3.org/TR/rdf-schema/ .</dd>

<dt><a id="ref-daml">[DAML+OIL]</a></dt>
<dd>
<cite>
<a href="http://www.w3.org/TR/2001/NOTE-daml+oil-reference-20011218">
DAML+OIL (March 2001) Reference Description</a></cite>.
Dan Connolly, Frank van Harmelen, Ian Horrocks, 
Deborah L. McGuinness, Peter F. Patel-Schneider, and Lynn Andrea Stein.
W3C Note 18 December 2001.
<a href="http://www.w3.org/TR/daml+oil-reference">Latest version</a>
is available at 
<code>http://www.w3.org/TR/daml+oil-reference</code>.
</dd>

<dt><a id="ref-xml-schema2" name="ref-xml-schema2"></a>[XML-SCHEMA2]
</dt>
<dd><cite><a href="http://www.w3.org/TR/xmlschema-2/">XML Schema
Part 2: Datatypes - W3C Recommendation</a></cite>, World Wide Web
Consortium, 2 May 2001.
</dd>

</dl>

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