W3C

Web Ontology Language (OWL)
Abstract Syntax and Semantics

W3C Working Draft 3 February 2003

This version:
http://www.w3.org/TR/2003/WD-owl-semantics-20030203/
Latest version:
http://www.w3.org/TR/owl-semantics/
Previous version:
http://www.w3.org/TR/2002/WD-owl-semantics-20021108/
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

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Copyright © 2003 W3C® (MIT, ERCIM, Keio), All Rights Reserved. W3C liability, trademark, document use and software licensing rules apply.

Abstract

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 model theory 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.

Status of this document

This is a W3C Web Ontology Working Group Working Draft produced 3 February 2003 as part of the W3C Semantic Web Activity (Activity Statement). It incorporates decisions made by the Working Group in designing the OWL Web Ontology Language. This is a public W3C Working Draft and may be updated, replaced, or obsoleted by other documents at any time. However, it is expected that this working draft is quite close to the Last Call version of the document. It is inappropriate to use W3C Working Drafts as reference material or to cite as other than "work in progress". A list of current W3C Recommendations and other technical documents can be found at http://www.w3.org/TR/.

There are no patent disclosures related to this work at the time of this writing.

Comments on this document are invited and should be sent to the public mailing list public-webont-comments@w3.org. An archive of comments is available at http://lists.w3.org/Archives/Public/public-webont-comments/ .

Table of contents

1. Introduction

This document contains several interrelated 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 model-theoretic semantics [RDF MT] 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. For such OWL ontologies the direct model theory is authoritative and the RDFS-compatible model theory is secondary. 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 particulary interested in Sections 3 and 5.

1.1. Differences from DAML+OIL

The language described in this document is very close to the DAML+OIL web ontology language [DAML+OIL]. The only substantive changes between OWL and DAML+OIL are

There are also a number of minor differences between OWL and DAML+OIL, including a number of changes to the names of the various constructs, as mentioned in Appendix A of the OWL Reference Description [OWL Reference].

Acknowledgments

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 DAM+OIL and thus in OWL are also present in the Ontology Inference Layer (OIL). Many of the other members of the W3C Web Ontology Working Group have had substantial input into this document.

Index of Vocabulary (Informative)

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.

Vocabulary Terms
Vocabulary Term Abstract OWL DL Syntax Abstract OWL Lite Syntax Direct Semantics Mapping to Triples RDFS-Compatible Semantics
owl:AllDifferent 4.1 5.2
owl:allValuesFrom 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:backwardCompatibleWith 2.1 2.1 4.1
owl:cardinality 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:Class 2.3.2.1 2.3.1.1 3.3 4.1 5.2
owl:complementOf 2.3.2.2 3.2 4.1 5.2
owl:DatatypeProperty 2.3.2.4 2.3.1.3 3.3 4.1 5.2
owl:DeprecatedClass
owl:DeprecatedProperty
owl:differentFrom 2.2 2.2 3.3 4.1 5.2
owl:disjointWith 2.3.2.1 3.3 4.1 5.2
owl:distinctMembers 4.1 5.2
owl:FunctionalProperty 2.3.2.4 2.3.1.3 3.3 4.1 5.2
owl:hasValue 2.3.2.3 3.2 4.1 5.2
owl:imports 2.1 2.1 3.4 4.1 5.3.1
owl:incompatibleWith 2.1 2.1 4.1
owl:intersectionOf 2.3.2.2 3.2 4.1 5.2
owl:InverseFunctionalProperty 2.3.2.4 2.3.1.3 3.3 4.1 5.2
owl:inverseOf 2.3.2.4 2.3.1.3 3.3 4.1 5.2
owl:maxCardinality 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:minCardinality 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:Nothing 2.1 3.2 4.1 5.2
owl:ObjectProperty 2.3.2.4 2.3.1.3 3.3 4.1 5.2
owl:oneOf 2.3.2.2 3.2 4.1 5.2
owl:onProperty 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:Ontology 2.1 2.1 3.4 4.1 5.2
owl:priorVersion 2.1 2.1 4.1
owl:Property 5.2
owl:Restriction 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:sameAs 5.2
owl:sameClassAs 2.3.2.1 2.3.1.1 3.3 4.1 5.2
owl:sameIndividualAs 2.2 2.2 3.3 4.1 5.2
owl:samePropertyAs 2.3.1.3 2.3.1.3 3.3 4.1 5.2
owl:someValuesFrom 2.3.2.3 2.3.1.2 3.2 4.1 5.2
owl:SymmetricProperty 2.3.2.4 2.3.1.3 3.3 4.1 4.2
owl:Thing 2.1 2.1 3.2 4.1 5.2
owl:TransitiveProperty 2.3.2.4 2.3.1.3 3.3 4.1 5.2
owl:unionOf 2.3.2.2 3.2 4.1 5.2
rdf:List 5.2
rdf:nil 5.2
rdf:type 2.2 2.2 3.3 4.1
rdfs:comment 2.1 2.1 4.1
rdfs:Datatype 5.2
rdfs:domain 2.3.2.4 2.3.1.3 3.3 4.1 5.2
rdfs:label 2.1 2.1 4.1
rdfs:Literal 5.2
rdfs:range 2.3.2.4 2.3.1.3 3.3 4.1 5.2
rdfs:subClassOf 2.3.2.1 2.3.1.1 3.3 4.1
rdfs:subPropertyOf 2.3.1.3 2.3.1.3 3.3 4.1

References

Normative References

[RDF Concepts]
Resource Description Framework (RDF): Concepts and Abstract Syntax. Graham Klyne and Jeremy J. Carroll, eds. W3C Working Draft 23 January 2003. Latest version is available at http://www.w3.org/TR/rdf-concepts/.
[RDF MT]
RDF Semantics. Patrick Hayes, ed. W3C Working Draft 23 January 2003. Latest version is available at http://www.w3.org/TR/rdf-mt/.
[RDF Syntax]
RDF/XML Syntax Specification (Revised) Dave Beckett, ed. W3C Working Draft 23 January 2003. Latest version is available at http://www.w3.org/TR/rdf-syntax-grammar/.
[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 2000. Latest version is available at http://www.w3.org/TR/xmlschema-2/.

Other References

[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 Features]
Feature Synopsis for OWL Lite and OWL. Deborah L. McGuinness and Frank van Harmelen. W3C Working Draft 29 July 2002. Latest version is available at http://www.w3.org/TR/owl-features/.
[OWL Issues]
Web Ontology Issue Status. Michael K. Smith, ed. 18 December 2002.
[OWL Guide]
OWL Web Ontology Language (OWL) Guide Version 1.0. Michael K. Smith, Deborah McGuinness, Raphael Volz, and Chris Welty. W3C Working Draft 4 November 2002. Latest version is available at http://www.w3.org/TR/owl-guide/.
[OWL Reference]
OWL Web Ontology Language 1.0 Reference. Mike Dean, Dan Connolly, Frank van Harmelen, James Hendler, Ian Horrocks, Deborah L. McGuinness, Peter F. Patel-Schneider, and Lynn Andrea Stein. W3C Working Draft 12 November 2002. Latest version is available at http://www.w3.org/TR/owl-ref/.
[RDFMS]
Resource Description Framework (RDF) Model and Syntax Specification. Ora Lassila and Ralph R. Swick, eds. W3C Recommendation 22 February 1999. Latest version is available at http://www.w3.org/TR/REC-rdf-syntax/.
[RDF Schema]
RDF Vocabulary Description Language 1.0: RDF Schema. Dan Brickley and R. V. Guha, eds. W3C Working Draft 23 January 2003. Latest version is available at http://www.w3.org/TR/rdf-schema/.
[RDF Tests]
RDF Test Cases. Jan Grant and Dave Beckett, eds. W3C Working Draft 23 January 2003. Latest version is available at http://www.w3.org/TR/rdf-testcases/.