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OWL Web Ontology Language
Semantics and Abstract Syntax
W3C Recommendation 10 February 2004
New Version
Available: OWL 2
(Document Status Update, 12 November 2009)
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 OWL 2
Document Overview for an introduction to OWL 2 and a guide
to the OWL 2 document set.
- This version:
-
http://www.w3.org/TR/2004/REC-owl-semantics-20040210/
- Latest version:
-
http://www.w3.org/TR/owl-semantics/
- Previous version:
-
http://www.w3.org/TR/2003/PR-owl-semantics-20031215/
- Editors:
-
Peter F. Patel-Schneider,
Bell Labs Research, Lucent Technologies
Patrick Hayes,
IHMC, University of West Florida
Ian Horrocks,
Department of Computer Science, University of Manchester
Please refer to the errata
for this document, which may include some normative corrections.
This document is also available in this non-normative form: single HTML file.
See also translations.
Copyright © 2004
W3C®
(MIT, ERCIM, Keio), All Rights Reserved. W3C
liability,
trademark,
document
use and
software
licensing rules apply.
This description of OWL, the Web Ontology Language
being designed by the W3C Web Ontology Working Group,
contains a high-level abstract syntax for both OWL DL and OWL Lite,
sublanguages of OWL.
A model-theoretic semantics is given to provide a formal meaning for OWL
ontologies written in this abstract syntax.
A model-theoretic semantics in the form of an extension to the RDF
semantics is also given to provide a formal meaning for OWL ontologies
as RDF graphs (OWL Full).
A mapping from the abstract syntax to RDF graphs is given and
the two model theories are shown to have the same consequences on
OWL ontologies that can be written in the abstract syntax.
1. Introduction (Informative)
This document is one part of the specification of OWL, the Web Ontology
Language.
The OWL Overview
[OWL Overview]
describes each of the different documents in the specification
and how they fit together.
This document
contains several interrelated normative
specifications of the several
styles of OWL, the Web Ontology Language being produced by the
W3C Web Ontology Working Group
(WebOnt).
First, Section 2 contains
a high-level, abstract syntax for both
OWL Lite, a subset of OWL,
and OWL DL, a fuller style of using OWL
but one that still places some
limitations on how OWL ontologies are constructed.
Eliminating these limitations results in the full OWL language, called
OWL Full, which has the same syntax
as RDF.
The normative exchange syntax for OWL is
RDF/XML [RDF Syntax];
the OWL Reference document
[OWL Reference]
shows how the RDF syntax is used in OWL.
A mapping from the OWL abstract syntax to
RDF graphs
[RDF Concepts]
is, however, provided in Section 4.
This document contains two formal semantics for OWL.
One of these semantics, defined in
Section 3,
is a direct, standard model-theoretic semantics for
OWL ontologies written in the abstract syntax.
The other, defined in Section 5,
is a vocabulary extension of the RDF semantics
[RDF Semantics] that provides semantics
for OWL ontologies in the form of RDF graphs.
Two versions of this second semantics are provided, one that corresponds
more closely to the direct semantics (and is thus a semantics for OWL DL)
and one that can be used in cases where classes need to be treated as
individuals or other situations that cannot be handled in the abstract
syntax (and is thus a semantics for OWL Full). These two versions are
actually very close, only differing in how they divide up the domain of
discourse.
Appendix A
contains a proof that the direct and RDFS-compatible semantics have the same
consequences on OWL ontologies that correspond to abstract OWL
ontologies that separate OWL individuals, OWL classes, OWL properties,
and the RDF, RDFS, and OWL structural vocabulary.
Appendix A
also contains the sketch of a proof that the entailments in the
RDFS-compatible semantics for OWL Full include all the entailments in
the RDFS-compatible semantics for OWL DL.
Finally a few examples of the various concepts defined in the document are
presented in Appendix B.
This document is designed to be read by those interested in the
technical details of OWL. It is not particularly intended for the
casual reader, who should probably first read the OWL Guide
[OWL Guide]. Developers of parsers
and other syntactic tools for
OWL will be particularly interested in Sections
2 and 4.
Developers of reasoners and other semantic tools for OWL will be
particularly interested in Sections
3 and 5.
Appendix C. Changes from Last Call (Informative)
This appendix provides an informative account of the changes from the
last-call version of this document.
All substantive post-last call changes to the document, as well as some editorial
post-last-call changes, are indicated in the style of this appendix.
C.1 Substantive changes after Last Call
This section provides information on the post Last Call changes to the document that make
changes to the specification of OWL.
- [10 April 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Apr/0046.html,
added owl:Class,
owl:Restriction,
owl:ObjectProperty,
owl:DatatypeProperty,
owl:AnnotationProperty,
owl:OntologyProperty,
owl:Ontology,
owl:AllDifferent,
owl:FunctionalProperty,
owl:InverseFunctionalProperty,
owl:SymmetricProperty, and
owl:TransitiveProperty
to CI
in Section 5.2. Some of these were
inferrable already.
- [10 April 2003]
Related to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Apr/0046.html,
added owl:distinctMembers
to RI
in Section 5.2.
- [15 April 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Apr/0064.html,
added owl:OntologyProperty
to the disallowed vocabulary
in disallowed OWL vocabulary
in Section 4.2.
- [5 May 2003]
Per a decision of the Web Ontology working group on 1 May 2003
to add owl:Nothing to OWL Lite,
recorded in
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0017.html,
changed the introduction of
owl:Nothing to so indicate.
The index for
owl:Nothing
was also updated.
- [9 May 2003]
To improve internal consistency, added optional
rdf:Property types for Annotation
Properties in
Section 4.1.
- [30 May 2003]
Per a decision of the Web Ontology working group on 29 May 2003 to
modify the mapping of EquivalentClasses,
recorded in
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0402.html
and in response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Apr/0003.html
and
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0052.html,
changed the mapping rule for
EquivalentClasses(d1 ... dn)
to
T(di) owl:equivalentTo T(dj) . for all <i,j> in G
where G is a set of pairs over {1,...,n} that if
interpreted as an undirected graph forms a connected graph
for {1,...,n}.
- [30 May 2003]
Per a decision of the Web Ontology working group on 29 May 2003 to
add axioms for ontology properties,
recorded in
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0402.html,
added axioms for ontology properties to the OWL Lite and OWL DL
abstract syntax in Sections 2.3.1.3.
and Section 2.3.2.4;
added direct semantics conditions for ontology property axioms
in Section 3.3; and
added a mapping for ontology property axioms
in Section 4.1.
Fixed the proofs of Lemma 2
and Lemma 3.
- [30 May 2003]
Per a decision of the Web Ontology working group on 29 May 2003 to
change the semantics for
owl:intersectionOf and related
resources from an intensional semantics to an extensional semantics,
recorded in
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0402.html,
modified the semantic conditions for
owl:intersectionOf,
owl:unionOf,
owl:complementOf, and
owl:oneOf
in Section 5.2.
No change needed to be made to the proof of
Lemma 1.
Fixed the proofs of
Lemma 4 and
Lemma 2.
- [2 June 2003]
In response to an observation by Jeremy Carroll in
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0004.html,
changed the mapping rule for anonymous individuals with no types
slightly in Section 4.1.
- [4 June 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0011.html,
the treatment of datatypes and rdfs:Literal has been slightly
changed in Section 2.3.1.3,
Section 2.3.2.3, and
Section 4.1.
- [4 June 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0050.html,
point owlsas-rdf-equivalent-class, modified the treatment of
ontology annotations in Section 3.4.
- [5 June 2003]
In response to a comment by Jeremy Carroll in
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0004.html,
the direct semantics has been modified to allow for domain elements
that are not OWL individuals. These domain elements are used to
provide meaning for annotations on classes, properties, and ontologies.
Changes have been made in
Section 3.1,
Section 3.2,
Section 3.3,
and
Appendix A.1.
- [6 June 2003]
Changed the treatment of datatypes to correspond with the
substantive post-last-call fixes and changes to the treatment of
datatypes in RDF.
Changes have been made in
Section 3.1 and
Appendix A.1.
- [26 June 2003]
Per a decision of the Web Ontology working group on 26 June 2003
to replace owl:sameIndividualAs with
owl:sameAs,
recorded in
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0364.html,
made changes to
Section 2.2,
Section 3.3,
Section 4.1,
Section 4.2,
Section 5.2, and
Appendix A.1.
- [30 June 2003]
Fixed a bug in the semantic conditions for
owl:hasValue
noticed by Jeremy Carroll, changing the conditions for the value
from a property to an individual or a data value
in Section 5.2.
- [23 July 2003]
In response to a substantive post-last-call change to the RDF semantics,
changing the if-and-only-if conditions for
rdfs:subClassOf and
rdfs:subPropertyOf to only-if
conditions,
added if-and-only-if conditions for
rdfs:subClassOf,
over OWL classes, and
rdfs:subPropertyOf,
over OWL individual-valued properties and
over OWL datatype properties,
to Section 5.2.
- [23 July 2003]
In response to a substantive change to the RDF syntax mapping to
triples, removing the typing triples for collections,
[applicable document unknown],
made typing of list resources optional in
Section 4.1.
Also modified an example in
Appendix B.1.
C.2 Editorial changes after Last Call
This section provides information on post Last Call editorial changes to the document,
i.e., changes that do not affect the specification of OWL.
- [9 April 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0023.html,
point 2, changed ``most information about properties'' to
``most information concerning properties''
in Section 2.3.
- [14 April 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0029.html,
point 1, added
``Because there is no standard way to go from a URI reference to an XML
Schema datatype in an XML Schema, there is no standard way to use
user-defined XML Schema datatypes in OWL.''
to the discussion of allowable XML Schema datatypes in
Section 2.
- [14 April 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0029.html,
point 2.1, added
``(The property rdf:type is added to the annotation properties so as
to provide a meaning for deprecation, see
below.)'' after
``ER provides meaning for URI references that are used as
OWL properties.'' in
Section 3.1.
- [14 April 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0029.html,
point 2.3, added ``A datatype theory must contain datatypes for
xsd:string and
xsd:integer. It may contain datatypes
for the other
built-in XML Schema
datatypes that are suitable for use in OWL. It may also
contain other datatypes, but there is no provision in the OWL
syntax for conveying what these datatypes are.'' just after the
definition of a datatype theory in
Section 3.1.
- [14 April 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0029.html,
point 2.5, added ``annotations'' the the list of things that EC is
extended to in
Section 3.2.
- [9 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0050.html,
point owlsas-rdf-datatype-denotation, removed the phrase ``as in RDF''
from
Section 2.1.
- [9 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0050.html,
point owlsas-rdf-equivalent-class, added an explanation of why one
might admit EquivalentClasses with only
one description in
Section 2.3.2.1.
- [9 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0050.html,
added ``, for n>=1 '' in the semantic condition for
multi-restrictions in
Section 3.2.
- [9 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0050.html,
changed to ``include class identifiers and restrictions''
in Section 2.3.2.2
and ``Elements of the OWL vocabulary that construct descriptions''
in Section 5.2.
- [13 May 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0180.html,
the links in the table of contents for
in Appendix A
were fixed.
- [14 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0030.html,
added a new paragraph to the beginning of
Section 4.
- [14 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0057.html,
made some changes to the wording on OWL ontologies in the abstract
syntax near the beginning of
Section 2.1.
- [14 May 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0057.html,
added anchors to the transformations in
Section 4.1.
- [14 May 2003]
In response to some discussion about ontology names
changed the discussion of the purpose of ontology names in
Section 2.1.
- [22 May 2003]
In response to a message from Jeff Heflin,
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0302.html,
added a comment to the effect tools should determine entailment
between imports closures in
Section 5.3 and
Section 5.4.
(Removed on 27 May 2003.)
- [22 May 2003]
Changed ``consistent with the Web'' to ``imports closed''
Section 5.3 and
Appendix A.
- [26 May 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0335.html,
changed several `if' to `iff' in definitions in
Section 3.4,
Section 5.3, and
Section 5.4.
This is editorial as
complete definitions are often written using `if'.
- [30 May 2003]
Fixed a typographical error in the proof of
Lemma 4.
- [4 June 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0029.html,
points 2.2 and 2.3, the status of
rdfs:Literal and
rdf:XMLLiteral has been clarified in
Section 2,
Section 2.1, and
Section 4.2.
- [19 June 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0257.html,
changed to note after the proof of
Theorem 2
in Appendix A.2
to note that the converse of the theorem is not true.
- [19 June 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003May/0055.html,
changed some explanatory text concerning the transformation to
triples in Section 4.1.
- [19 June 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jun/0264.html,
added introductory material about the other WebOnt documents to
Section 1.
- [24 June 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003May/0069.html,
added note about correspondence to existing DLs to
Section 2.
- [22 July 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Jul/0011.html and
http://lists.w3.org/Archives/Public/public-webont-comments/2003Jul/0041.html,
changed several uses of ``object'' to ``individual'' or ``individual-valued'' in
Section 2 and
Section 5.2 and made other editorial
changes to Section 5.2.
- [23 July 2003]
To remove any reference to tools, made wording changes in
Section 3.1 and
Section 2.1, concerning the treatment
of datatypes.
- [25 July 2003]
In response to
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0064.html,
added explicit tagging of the informative or normative nature of
all sections.
- [25 July 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jul/0296.html,
removed a comment about the relationship between the two model
theories from
Section 1.
- [6 August 2003]
In response to
http://lists.w3.org/Archives/Public/www-webont-wg/2003Jul/0015.html,
changed owl:IndividualProperty
to owl:ObjectProperty in
Appendix A.2.
- [6 August 2003]
In response to
Section 2.1, concerning the treatment
http://lists.w3.org/Archives/Public/public-webont-comments/2003Apr/0064.html,
added quotes around
rdfs:Literal
to indicate that it is a terminal, not a non-terminal, in
Section 2.3.1.3 and
Section 2.3.2.3.
C.3 Substantive changes after Candidate Recommendation
This section provides information on the post Candidate Recommendation
changes to the document that make changes to the specification of OWL.
C.4 Editorial changes after Candidate Recommendation
This section provides information on post Candidate Recommendation editorial changes to the document,
i.e., changes that do not affect the specification of OWL.
C.5 Changes since Proposed Recommendation
This section provides information on post Proposed Recommendation changes to the document.
The following table provides pointers to information about each
element of the OWL vocabulary, as well as some elements of the RDF and RDFS
vocabularies.
The first column points to the vocabulary element's major definition
in the abstract syntax of Section 2.
The second column points to the vocabulary element's major definition
in the OWL Lite abstract syntax.
The third column points to the vocabularly element's major definition
in the direct semantics of Section 3.
The fourth column points to the major piece of the translation from
the abstract syntax to triples for the vocabulary element
Section 4.
The fifth column points to the vocabularly element's major definition
in the RDFS-compatible semantics of Section 5.
The
Joint US/EU ad hoc Agent Markup Language Committee
developed DAML+OIL, which is the direct precursor to OWL.
Many of the ideas in DAML+OIL and thus in OWL are also present in the
Ontology Inference Layer (OIL).
This document is the result of extensive discussions within the
Web Ontology Working Group
as a whole. The participants in this working group included:
Yasser alSafadi,
Jean-François 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,
Jérôme 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,
Rüdiger 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.
- [RDF Concepts]
- Resource
Description Framework (RDF): Concepts and Abstract Syntax,
Graham Klyne and Jeremy J. Carroll, Editors, W3C Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/ . Latest version available
at http://www.w3.org/TR/rdf-concepts/ .
- [RDF Semantics]
- RDF
Semantics, Patrick Hayes, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-mt-20040210/
. Latest version available
at http://www.w3.org/TR/rdf-mt/ .
- [RDF Syntax]
- RDF/XML
Syntax Specification (Revised), Dave Beckett, Editor, W3C
Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/ . Latest version
available at http://www.w3.org/TR/rdf-syntax-grammar/ .
- [RDF Tests]
- RDF
Test Cases, Jan Grant and Dave Beckett, Editors, W3C
Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-testcases-20040210/ . Latest version
available at http://www.w3.org/TR/rdf-testcases/ .
- [XML]
-
Extensible Markup Language (XML) 1.0 (Second Edition).
Tim Bray, Jean Paoli, C. M. Sperberg-McQueen, and Eve Maler, eds.
W3C Recommendation 6 October 2000.
Latest version is available at
http://www.w3.org/TR/REC-xml.
- [XML Schema Datatypes]
-
XML Schema Part 2: Datatypes..
Paul V. Biron and Ashok Malhotra, eds.
W3C Recommendation 02 May 2001.
Latest version is available at
http://www.w3.org/TR/xmlschema-2/.
- [DAML+OIL]
-
DAML+OIL (March 2001) Reference Description.
Dan Connolly, Frank van Harmelen, Ian Horrocks,
Deborah L. McGuinness, Peter F. Patel-Schneider, and Lynn Andrea Stein.
W3C Note 18 December 2001.
Latest version is available at
http://www.w3.org/TR/daml+oil-reference.
- [OWL Guide]
- OWL Web
Ontology Language Guide, 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/ . Latest version available at
http://www.w3.org/TR/owl-guide/ .
- [OWL Issues]
-
Web Ontology Issue Status.
Michael K. Smith, ed.
27 June 2003.
- [OWL
Overview]
- OWL Web
Ontology Language Overview, Deborah L. McGuinness and Frank
van Harmelen, Editors, W3C Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-owl-features-20040210/ . Latest version available
at http://www.w3.org/TR/owl-features/ .
- [OWL
Reference]
- OWL Web
Ontology Language Reference, Mike Dean and Guus Schreiber,
Editors, W3C Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-owl-ref-20040210/ . Latest version available at
http://www.w3.org/TR/owl-ref/ .
- [RDF Syntax]
- RDF/XML
Syntax Specification (Revised), Dave Beckett, Editor, W3C
Recommendation, 10 February 2004,
http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/ . Latest version
available at http://www.w3.org/TR/rdf-syntax-grammar/ .
- [RDF
Vocabulary]
- RDF
Vocabulary Description Language 1.0: RDF Schema, Dan
Brickley and R. V. Guha, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-schema-20040210/ . Latest version available
at http://www.w3.org/TR/rdf-schema/ .