W3C

OWL Web Ontology Language
Reference

W3C Proposed Recommendation 9 December 2003

Editor's Draft document - no W3C status at this time. Please review the Candidate Recommendation Document

This version:
http://www.w3.org/TR/2003/PR-owl-ref-20031209/
Latest version:
http://www.w3.org/TR/owl-ref/
Previous version:
http://www.w3.org/TR/2003/CR-owl-ref-20030818/
Editors:
Mike Dean, BBN Technologies
Guus Schreiber, Free University Amsterdam
Authors:
Sean Bechhofer, University of Manchester
Frank van Harmelen, Free University Amsterdam
Jim Hendler, University of Maryland
Ian Horrocks, University of Manchester
Deborah L. McGuinness, Stanford University
Peter F. Patel-Schneider, Bell Labs Research, Lucent Technologies
Lynn Andrea Stein, Franklin W. Olin College of Engineering

Abstract

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.

Status of this document

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 W3C technical reports index at http://www.w3.org/TR/.

Publication as a Proposed Recommendation does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than "work in progress".

This draft is one of six parts of the Proposed Recommendation (PR) for OWL, the Web Ontology Language. It has been developed by the Web Ontology Working Group as part of the W3C Semantic Web Activity (Activity Statement, Group Charter) for publication on 9 December 2003.

The design of OWL expressed in earlier versions of these documents has been widely reviewed and satisfies the Working Group's technical requirements. The Working Group has addressed all comments received, making changes as necessary. During Candidate Recommendation, many implementations were reported, covering among them all features of the language. Changes to this document since the Candidate Recommendation version (if any) are detailed in the change log.

The Working Group now hopes for review and, where appropriate, endorsement of OWL by Consortium members, prior to possible advancement to Recommendation status. Everyone with comments is welcome to send them to public-webont-comments@w3.org (archive) by 8 January 2004. General discussion of related technology is welcome at www-rdf-logic@w3.org (archive).

The W3C maintains a list of any patent disclosures related to this work.

Acknowledgments

Parts of this document are derived from the DAML+OIL (March 2001) Reference Description [DAML+OIL] which was submitted as part of the DAML+OIL W3C Note . The sponsors of this document and its predecessor documents are gratefully acknowledged.

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.

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-Francois Baget, James Barnette, Sean Bechhofer, Jonathan Borden, Stephen Buswell, Jeremy Carroll, Dan Connolly, Peter Crowther, Jonathan Dale, Jos De Roo, David De Roure, Mike Dean, Larry Eshelman, Jerome Euzenat, Tim Finin, Nicholas Gibbins, Sandro Hawke, Patrick Hayes, Jeff Heflin, Ziv Hellman, James Hendler, Bernard Horan, Masahiro Hori, Ian Horrocks, Jane Hunter, Ruediger Klein, Natasha Kravtsova, Ora Lassila, Deborah McGuinness, Enrico Motta, Leo Obrst, Mehrdad Omidvari, Martin Pike, Marwan Sabbouh, Guus Schreiber, Noboru Shimizu, Michael Smith, John Stanton, Lynn Andrea Stein, Herman ter Horst, Lynne R. Thompson, David Trastour, Frank van Harmelen, Bernard Vatant, Raphael Volz, Evan Wallace, Christopher Welty, Charles White, Frederik Brysse, Francesco Iannuzzelli, Massimo Marchiori, Laurent Olivry, Michael Sintek, John Yanosy.

Contents


1. Introduction

1.1 Purpose of this document

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.

This document is one component of the description of OWL, the Web Ontology Language, being produced by the W3C Web Ontology Working Group. The Document Roadmap 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 [OWL Overview], and subsequently the OWL Guide [OWL Guide] for a more narrative description and examples of the use of the language.

This document assumes the reader is familiar with the basic concepts of RDF [RDF Concepts] and has a working knowledge of the RDF/XML syntax [RDF/XML Syntax] and of RDF Schema [RDF Schema].

The normative reference on the precise syntax of the OWL language constructs can be found in the OWL Semantics and Abstract Syntax document [OWL S&AS]. 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.

Use cases and requirements for the OWL language are described in the OWL requirements document [OWL Use Cases and Requirements]. Test cases for OWL tools (e.g., entailment tests, consistency tests) are specified in the Test document [OWL Test Cases] .

1.2 OWL Full/DL/Lite

As also discussed in the OWL Overview document [OWL Overview], and subsequently the OWL Guide [OWL Guide], 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.

NOTE: RDF documents will generally be in OWL Full, unless they are specifically constructed to be in OWL DL or Lite.

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 [OWL S&AS]. Sect. 8.2 OWL DL summarizes the differences between OWL Full and OWL DL.

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 Section 8.3 "OWL Lite constructs". 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 [OWL S&AS].

NOTE: RDF users upgrading to OWL should be aware that OWL Lite is not 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 (e.g., 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 (e.g., reasoning support) outweigh the DL/Lite restrictions on the use of OWL and RDF constructs.

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. Sec. 8.3.provides a summary of these additional OWL Lite restrictions.

1.3 OWL syntax

An OWL ontology is an RDF graph [RDF Concepts], 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) [RDF/XML Syntax]). 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.

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

<owl:Class rdf:ID="Continent"/> 

The following RDF/XML syntax:

<rdf:Description rdf:about="#Continent">
  <rdf:type rdf:resource="http://www.w3.org/2002/07/owl#Class"/>
</rdf:Description> 

encodes the same set of RDF triples, and therefore would convey the same meaning.

1.4 OWL and RDF semantics

OWL is a vocabulary extension of RDF [RDF Semantics]. 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 [OWL S&AS] specifies exactly which triples are assigned a specific meaning, and what this meaning is.

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.

1.5 A note about the examples

For readability purposes the examples in this document assume the XML entities &rdf;, &rdfs;, &owl; and &xsd; (for XML Schema datatypes) are defined in the same way as in Appendix B. The same assumption holds for the corresponding namespaces rdf:, rdfs:, owl: and xsd:.

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 [OWL Guide].

1.6 Data Aggregation and Privacy

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 owl:sameAs can be used to state that seemingly different individuals are actually the same. Similarly, owl:InverseFunctionalProperty can be used to link individuals together. For example, if a property such as SocialSecurityNumber is an owl:InverseFunctionalProperty, 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 aggregation can be used to determine facts that are not directly represented in any one source.

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 SAML and P3P

1.7 Appendices to this document

This document has a set of appendices containing additional information.

Links in this document that are attached to definitions of language constructs provide access to the OWL Semantics and Abstract Syntax [OWL S&AS]. Appendix A contains a systematic set of links for each language construct to the corresponding sections in the Guide and the S&AS documents.

Appendix B 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, owl:Ontology is a class, and owl:imports is a property.

NOTE: The RDF Schema file for OWL is not expected to be imported explicitly (i.e., with owl:imports) 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.

Appendix C 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).

For readers familiar with DAML+OIL, Appendix D lists many of the changes between DAML+OIL and OWL.

Finally, Appendix E provides a set of practical guidelines for specifying OWL DL ontologies in RDF.

2. OWL document

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.

2.1 Content

An OWL document consists of optional ontology headers (generally at most one) plus any number of class axioms, property axioms, and facts about individuals. Please note that "axiom" is the formal term used in the S&AS document. These axioms are somewhat more informally called "definitions" in the Guide and Overview documents.

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.

As with any RDF document, the OWL code should be subelements of an rdf:RDF 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 [OWL Guide].

2.2 OWL built-in vocabulary

The built-in vocabulary for OWL all comes from the OWL namespace

http://www.w3.org/2002/07/owl#

conventionally associated with the namespace name owl. 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.

2.3 MIME type

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 application/rdf+xml [RDF Concepts], or alternatively the XML MIME type application/xml.

As file extension, we recommend to use either .rdf or .owl.

3. Classes

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 class extension. The individuals in the class extension are called the instances 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.

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 ...".

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.

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.

3.1 Class descriptions

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.

OWL distinguishes six types of class descriptions:

  1. a class identifier (a URI reference)
  2. an exhaustive enumeration of individuals that together form the instances of a class
  3. a property restriction
  4. the intersection of two or more class descriptions
  5. the union of two or more class descriptions
  6. the complement of a class description

The first type is special in the sense that it describes a class through a class name (syntactically represented as a URI reference). The other five types of class descriptions describe an anonymous class by placing constraints on the class extension.

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.

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

<owl:Class rdf:ID="Human"/>

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

NOTE: In OWL Lite and OWL DL, owl:Class (or owl:Restrictions, see further) must be used for all class descriptions.

NOTE: owl:Class is defined as a subclass of rdfs:Class. 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 owl:Class and rdfs:Class are equivalent in OWL Full.

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 rdf:type property whose value is owl:Class.

NOTE: If one provides an RDF identifier for class descriptions of the enumerattion, 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 Section 3.2.3 for details.

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.

Two OWL class identifiers are predefined, namely the classes owl:Thing and owl:Nothing. The class extension of owl:Thing is the set of all individuals. The class extension of owl:Nothing is the empty set. Consequently, every OWL class is a subclass of owl:Thing and owl:Nothing is a subclass of every class (for the meaning of the subclass relation, see the section on rdfs:subClassOf).

3.1.1 Enumeration

A class description of the "enumeration" kind is defined with the owl:oneOf property. This value of this built-in OWL property must be a list of individuals that are the instances of the class. This enables a class to be described by exhaustively enumerating its instances. The class extension of a class described with owl:oneOf contains exactly the enumerated individuals, no more, no less. The list of individuals is typically represented with the help of the RDF construct rdf:parseType="Collection", 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:

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

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

In the section on datatypes we will see another use of the owl:oneOf construct, namely to define an enumeration of data values.

NOTE: Enumeration is not part of OWL Lite

3.1.2 Property restrictions

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.

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

A cardinality constraint puts constraints on the number of values a property can take, in the context of this particular class description. For example, we might want to say that for a soccer team the hasPlayer property has 11 values. For a basketball team the same property would have only 5 values.

OWL also supports a limited set of constructs for defining global property cardinality, namely owl:FunctionalProperty and owl:InverseFunctionalProperty (see the section on properties).

Property restrictions have the following general form:

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

The class owl:Restriction is defined as a subclass of owl:Class. A restriction class should have exactly one triple linking the restriction to a particular property, using the owl:onProperty property. The restriction class should also have exactly one triple that represents the value constraint c.q. cardinality constraint on the property under consideration, e.g., that the cardinality of the property is exactly 1.

Property restrictions can be applied both to datatype properties (properties for which the value is a data literal) and object properties (properties for which the value is an individual). For more information about this distinction, see the section on properties.

3.1.2.1 Value constraints
3.1.2.1.1 owl:allValuesFrom

The value constraint owl:allValuesFrom is a built-in OWL property that links a restriction class to either a class description or a data range. A restriction containing an owl:allValuesFrom 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.

A simple example:

<owl:Restriction>
  <owl:onProperty rdf:resource="#hasParent" />
  <owl:allValuesFrom rdf:resource="#Human"  />
</owl:Restriction>

This example describes an anonymous OWL class of all individuals for which the hasParent property only has values of class Human. 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.

NOTE: In OWL Lite the only type of class description allowed as object of owl:allValuesFrom is a class name.

An owl:allValuesFrom 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 owl:allValuesFrom with the universal quantifier means that an owl:allValuesFrom 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 owl:allValuesFrom constraint demands that all values of P should be of type T, and if no such values exist, the constraint is trivially true.

3.1.2.1.2 owl:someValuesFrom

The value constraint owl:someValuesFrom is a built-in OWL property that links a restriction class to a class description or a data range. A restriction containing an owl:someValuesFrom 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.

The following example defines a class of individuals which have at least one parent who is a physician:

<owl:Restriction>
  <owl:onProperty rdf:resource="#hasParent" />
  <owl:someValuesFrom rdf:resource="#Physician" />
</owl:Restriction>

The owl:someValuesFrom 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.

NOTE: In OWL Lite the only type of class description allowed as object of owl:someValuesFrom is a class name.

3.1.2.1.3 owl:hasValue

The value constraint owl:hasValue is a built-in OWL property that links a restriction class to a value V, which can be either an individual or a data value. A restriction containing a owl:hasValue constraint describes a class of all individuals for which the property concerned has at least one value semantically equal to V (it may have other values as well).

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 owl:sameAs).

NOTE: the value constraint owl:hasValue is not included in OWL Lite.

The following example describes the class of individuals who have the individual referred to as Clinton as their parent:

<owl:Restriction>
  <owl:onProperty rdf:resource="#hasParent" />
  <owl:hasValue rdf:resource="#Clinton" />
</owl:Restriction>
3.1.2.2 Cardinality constraints

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.

NOTE: OWL Lite includes the use of all three types of cardinality constraints, but only when used with the values "0" or "1".

3.1.2.2.1 owl:maxCardinality

The cardinality constraint owl:maxCardinality 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 nonNegativeInteger. A restriction containing an owl:maxCardinality constraint describes a class of all individuals that have at most 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 rdf:datatype attribute.

The following example describes a class of individuals that have at most two parents:

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

RDF datatyping is discussed in more detail in Section "6. Datatypes".

3.1.2.2.2 owl:minCardinality

The cardinality constraint owl:minCardinality 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 nonNegativeInteger. A restriction containing an owl:minCardinality constraint describes a class of all individuals that have at least 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 rdf:datatype attribute.

The following example describes a class of individuals that have at least two parents:

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

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

3.1.2.2.3 owl:cardinality

The cardinality constraint owl:cardinality is a built-in OWL property that links a restriction class to a data value belonging to the range of the XML Schema datatype nonNegativeInteger. A restriction containing an owl:cardinality constraint describes a class of all individuals that have exactly 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 rdf:datatype attribute.

This construct is in fact redundant as it can always be replaced by a pair of matching owl:minCardinality and owl:maxCardinality constraints with the same value. It is included as a convenient shorthand for the user.

The following example describes a class of individuals that have exactly two parents:

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

3.1.3 Intersection, union and complement

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).

3.1.3.1 owl:intersectionOf

The owl:intersectionOf property links a class to a list of class descriptions. An owl:intersectionOf 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.

An example:

<owl:Class>
  <owl:intersectionOf rdf:parseType="Collection">
    <owl:Class>
      <owl:oneOf rdf:parseType="Collection">
        <owl:Thing rdf:about="#Tosca" />
        <owl:Thing rdf:about="#Salome" />
      </owl:oneOf>
    </owl:Class>
    <owl:Class>
      <owl:oneOf rdf:parseType="Collection">
        <owl:Thing rdf:about="#Turandot" />
        <owl:Thing rdf:about="#Tosca" />
      </owl:oneOf>
    </owl:Class>
  </owl:intersectionOf>
</owl:Class>

In this example the value of owl:intersectionOf 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 Tosca. as this is the only individual that is common to both enumerations.

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 Sec. 6 "Individuals" one can find OWL language constructs for making constraints about equality and difference of individuals.

NOTE: In this example we use enumerations to make clear what the meaning is of this language construct. See the OWL Guide [OWL Guide] for more typical examples.

NOTE: OWL Lite is restricted in its use of owl:intersectionOf. This is discussed later in this document, see Section 3.2.3

owl:intersectionOf can be viewed as being analogous to logical conjunction.

3.1.3.2 owl:unionOf

The owl:unionOf property links a class to a list of class descriptions. An owl:unionOf 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.

An example:

<owl:Class>
  <owl:unionOf rdf:parseType="Collection">
    <owl:Class>
      <owl:oneOf rdf:parseType="Collection">
        <owl:Thing rdf:about="#Tosca" />
        <owl:Thing rdf:about="#Salome" />
      </owl:oneOf>
    </owl:Class>
    <owl:Class>
      <owl:oneOf rdf:parseType="Collection">
        <owl:Thing rdf:about="#Turandot" />
        <owl:Thing rdf:about="#Tosca" />
      </owl:oneOf>
    </owl:Class>
  </owl:unionOf>
</owl:Class>

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

NOTE: owl:unionOf is not part of OWL Lite.

owl:unionOf is analogous to logical disjunction.

3.1.3.3 owl:complementOf

An owl:complementOf property links a class to precisely one class description. An owl:complementOf statement describes a class for which the class extension contains exactly those individuals that do not belong to the class extension of the class description that is the object of the statement. owl:complementOf is analogous to logical negation: the class extension consists of those individuals that are NOT members of the class extension of the complement class.

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

<owl:Class>
  <owl:complementOf>
    <owl:Class rdf:about="#Meat"/>
  </owl:complementOf>
</owl:Class>

The extension of this class description contains all individuals that do not belong to the class Meat.

NOTE: owl:complementOf is not part of OWL Lite.

3.2 Class axioms

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 owl:Class with a class identifier.

For example, the following class axiom declares the URI reference #Human to be the name of an OWL class:

<owl:Class rdf:ID="Human"/>

This is correct OWL, but does not tell us very much about the class Human. 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:

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.

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 owl:equivalentClass statement, so these will be discussed right after that subsection (see Section 3.2.3 Axioms for complete classes without using owl:equivalentClass).

3.2.1 rdfs:subClassOf

AXIOM SCHEMA: class description rdfs:subClassOf class description

The rdfs:subClassOf construct is defined as part of RDF Schema [RDF Schema]. Its meaning in OWL is exactly the same: if the class description C1 is defined as a subclass of class description C2, than 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).

An example:

<owl:Class rdf:ID="Opera">
  <rdfs:subClassOf rdf:resource="#MusicalWork" />
</owl:Class>

This class axiom declares a subclass relation between two OWL classes that are described through their names (Opera and MusicalWork). 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.

NOTE: In OWL Lite the subject of an rdfs:subClassOf statement must be a class identifier. The object must be either a class identifier or a property restriction.

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

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

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

Class axioms can get more complex when class descriptions are nested. For example, property restrictions with an owl:allValuesFrom or owl:someValuesFrom statement may point to any class description. Consider the following example:

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

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

More examples can be found in the Guide document [OWL Guide]. 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 and sufficient conditions OWL provides the owl:equivalentClass construct. As a stepping stone to such axioms, consider the following example:

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

This class axiom states that an operetta is a musical work, that has a 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 exactly those musical works that have a librettist but are not operas, we would need to use the owl:equivalentClass construct.

3.2.2 owl:equivalentClass

AXIOM SCHEMA: class description owl:equivalentClass class description

A class axiom may contain (multiple) owl:equivalentClass statements. owl:equivalentClass 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).

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

<owl:Class rdf:about="#US_President">
  <equivalentClass rdf:resource="#PrincipalResidentOfWhiteHouse"/>
</owl:Class>

NOTE: The use of owl:equivalentClass 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 owl:sameAs construct. As this requires treating classes as individuals, class equality can only be expressed in OWL Full.

Axioms with owl:equivalentClass 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:

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

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.

NOTE: OWL DL does not put any constraints on the types of class descriptions that can be used as subject and object of an owl:equivalentClass statement. In OWL Lite only class identifiers and property restrictions are allowed as subject and object.

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.

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:

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

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.

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.

3.2.3 Axioms for complete classes without using owl:equivalentClass

AXIOM SCHEMA: named class description of type 2 (with owl:oneOf) or type 4-6 (with owl:intersectionOf, owl:unionOf or owl:complementOf

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:

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

This class axiom should be interpreted as follows: the class extension of the class DaPonteOperaOfMozart is exactly defined by the enumeration.

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

<owl:Class rdf:ID="LivingBeing">
  <owl:unionOf rdf:parseType="Collection">
    <owl:Class rdf:about="#Plant"/>
    <owl:Class rdf:about="#Animal"/>
  </owl:unionOf>
</owl:Class>

This class axiom states that the class extension of LivingBeing exactly corresponds to the union of the class extensions of Plant and Animal.

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

3.2.4 owl:disjointWith

AXIOM SCHEMA: class description owl:disjointWith class description

A class axiom may also contain (multiple) owl:disjointWith statements. owl:disjointWith is a built-in OWL property with a class description as domain and range. Each owl:disjointWith statement asserts that the class extensions of the two class descriptions involved have no individuals in common. Like axioms with rdfs:subClassOf, declaring two classes to be disjoint is a partial definition: it imposes a necessary but not sufficient condition on the class.

This is a popular example of class disjointness:

<owl:Class rdf:about="Man">
  <owl:disjointWith rdf:resource="#Woman"/>
</owl:Class>

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:

<owl:Class rdf:about="MusicDrama">
  <owl:equivalentClass>
    <owl:Class>
      <owl:unionOf rdf:parseType="Collection">
        <owl:Class rdf:about="#Opera"/>
        <owl:Class rdf:about="#Operetta"/>
        <owl:Class rdf:about="#Musical"/>
      </owl:unionOf>
    </owl:Class>
  </owl:equivalentClass>
</owl:Class>

<owl:Class rdf:about="#Opera">
  <rdfs:subClassOf rdf:resource="#MusicDrama"/>
</owl:Class>

<owl:Class rdf:about="#Operetta">
  <rdfs:subClassOf rdf:resource="#MusicDrama"/>
  <owl:disjointWith rdf:resource="#Opera"/>
</owl:Class>

<owl:Class rdf:about="#Musical">
  <rdfs:subClassOf rdf:resource="#MusicDrama"/>
  <owl:disjointWith rdf:resource="#Opera"/>
  <owl:disjointWith rdf:resource="#Operetta"/>
</owl:Class>

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

NOTE: OWL Lite does not allow the use of owl:disjointWith.

4. Properties

OWL distinguishes between two main categories of properties that an ontology builder may want to define:

NOTE: OWL also has the notion of annotation properties (owl:AnnotationProperty) and ontology properties (owl:OntologyProperty). These are needed in OWL DL for semantic reasons. See Sec. 7 and the OWL Semantics and Abstract Syntax document [OWL S&AS].

An object property are defined as an instance of the built-in OWL class owl:ObjectProperty. A datatype property is defined as an instance of the built-in OWL class owl:DatatypeProperty. Both owl:ObjectProperty and owl:DatatypeProperty are subclasses of the RDF class rdf:Property (see Appendix B).

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 owl:ObjectProperty is equivalent to rdf:Property In practice, this mainly has consequences for the use of owl:InverseFunctionalProperty. See also the OWL Full characterization in Section 8.1.

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

<owl:ObjectProperty rdf:ID="hasParent"/>

This defines a property with the restriction that its values should be individuals.

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

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

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).

4.1 RDF Schema constructs

The constructs in this section are discussed in detail in the RDF Schema document [RDF Schema]. The description in this section provides a synopsis of these constructs and provides some OWL-specific aspects and examples.

4.1.1 rdfs:subPropertyOf

A rdfs:subPropertyOf 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).

An example:

<owl:ObjectProperty rdf:ID="hasMother">
  <rdfs:subPropertyOf rdf:resource="#hasParent"/>
</owl:ObjectProperty>

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".

Subproperty axioms can be applied to both datatype properties and object properties.

NOTE: In OWL DL the subject and object of a subproperty statement must be either both datatype properties or both object properties.

4.1.2 rdfs:domain

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

Multiple rdfs:domain axioms are allowed and should be interpreted as a conjunction: these restrict the domain of the property to those individuals that belong to the intersection 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 owl:unionOf form. For example, if we want to say that the domain of the property hasBankAccount can be either a Person or a Corporation, we would need to say something like this:

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

NOTE: In OWL Lite the value of rdfs:domain must be a class identifier.

4.1.3 rdfs:range

For a property one can define (multiple) rdfs:range axioms. Syntactically, rdfs:range is a built-in property that links a property (some instance of the class rdf:Property) to to either a class description or a data range. An rdfs:range 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.

Multiple range restrictions are interpreted as stating that the range of the property is the intersection 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 rdfs:domain, multiple alternative ranges can be specified by using a class description of the owl:unionOf form (see the previous subsection).

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

NOTE: In OWL Lite the only type of class description allowed as object of rdfs:range is a class name.

4.2 Relations to other properties

4.2.1 owl:equivalentProperty

The owl:equivalentProperty construct can be used to state that two properties have the same property extension. Syntactically, owl:equivalentProperty is a built-in OWL property with rdf:Property as both its domain and range.

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 owl:sameAs construct. As this requires that properties are treated as individuals, such axioms are only allowed in OWL Full.

4.2.2 owl:inverseOf

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 owl:inverseOf construct can be used to define such an inverse relation between properties.

Syntactically, owl:inverseOf is a built-in OWL property with owl:ObjectProperty as its domain and range. An axiom of the form P1 owl:inverseOf P2 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, owl:inverseOf is a symmetric property.

An example:

<owl:ObjectProperty rdf:ID="hasChild">
  <owl:inverseOf rdf:resource="#hasParent"/>
</owl:ObjectProperty>

4.3 Global cardinality constraints on properties

4.3.1 owl:FunctionalProperty

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 owl:FunctionalProperty as a special subclass of the RDF class rdf:Property.

The following axiom states that the husband property is functional, i.e., a person can have at most one husband (a good example of culture dependence of ontologies):

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

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

<owl:ObjectProperty rdf:ID="husband">
  <rdfs:domain rdf:resource="#Woman" />
  <rdfs:range  rdf:resource="#Man" />
</owl:ObjectProperty>

<owl:FunctionalProperty rdf:about="#husband" />

4.3.2 owl:InverseFunctionalProperty

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 owl:InverseFunctionalProperty, 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.

Syntactically, an inverse-functional property axiom is specified by declaring the property to be an instance of the built-in OWL class owl:InverseFunctionalProperty, which is a subclass of the OWL class owl:ObjectProperty.

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 Sections 8.1 and 8.2.

A typical example of an inverse-functional property:

<owl:InverseFunctionalProperty rdf:ID="biologicalMotherOf">
  <rdfs:domain rdf:resource="#Woman"/>
  <rdfs:range rdf:resource="#Human"/>
</owl:InverseFunctionalProperty>

This example states that for each object of biologicalMotherOf 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.

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.

Notice that owl:FunctionalProperty and owl:InverseFunctionalProperty 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 property restrictions. The latter are class descriptions and are only enforced on the property when applied to that class.

4.4 Logical characteristics of properties

4.4.1 owl:TransitiveProperty

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.

Syntactically, a property is defined as being transitive by making it an instance of the the built-in OWL class owl:TransitiveProperty, which is defined as a subclass of owl:ObjectProperty.

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

<owl:TransitiveProperty rdf:ID="subRegionOf">
  <rdfs:domain rdf:resource="#Region"/>
  <rdfs:range  rdf:resource="#Region"/>
</owl:TransitiveProperty>

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

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

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

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.

4.4.2 owl:SymmetricProperty

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 owl:SymmetricProperty, a subclass of owl:ObjectProperty.

A popular example of a symmetric property is the friendOf relation:

<owl:SymmetricProperty rdf:ID="friendOf">
  <rdfs:domain rdf:resource="#Human"/>
  <rdfs:range  rdf:resource="#Human"/>
</owl:SymmetricProperty>

The domain and range of a symmetric property are the same.

5. Individuals

Individuals are defined with individual axioms (also called "facts"). We discuss two types of facts:

  1. Facts about class membership and property values of individuals
  2. Facts about individual identity

5.1 Class membership and property values

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 Opera:

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

This example includes a number of facts about the individual Tosca, an instance of the class Opera. Tosca is composed by Giacomo Puccini. The opera has three libretto writers. The property premiereDate links an opera to a typed literal with as datatype the XML Schema datatype date. The XML schema document on datatypes [XML Schema Datatypes] contains the relevant information about syntax and semantics of this datatype.

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 Measurement, a quantitative observation for which facts such as the subject under observation, the observed phenomenon, the observed value, and the observation time are listed:

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

This individual axiom contains two anonymous individuals, namely some Measurement and some Quantity. In natural language, for the subject Jane Doe the measured value of the phenomenon Weight 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, float and dateTime are XML Schema datatypes, the syntactic and semantic details of which can be found in the relevant XML Schema documentation [XML Schema Datatypes].

5.2 Individual identity

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.

OWL provides three constructs for stating facts about the identity of individuals:

5.2.1 owl:sameAs

The built-in OWL property owl:sameAs links an individual to an individual. Such an owl:sameAs statement indicates that two URI references actually refer to the same thing: the individuals have the same "identity".

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:

<rdf:Description rdf:about="#William_Jefferson_Clinton">
  <owl:sameAs rdf:resource="#BillClinton"/>
</rdf:Description>

The owl:sameAs 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.

In OWL Full, where a class can be treated as instances of (meta)classes, we can use the owl:sameAs construct to define class equality, thus indicating that two concepts have the same intensional meaning. An example:

<owl:Class rdf:ID="FootballTeam">
  <owl:sameAs rdf:resource="http://sports.org/US#SoccerTeam"/>
</owl:Class>

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 owl:Class. This allows us to state that the class FootballTeam in some European sports ontology denotes the same concept as the class SoccerTeam in some American sports ontology. Note the difference with the statement:

<footballTeam owl:equivalentClass us:soccerTeam />

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

NOTE: For details of comparison of URI references, see the section on RDF URI references in the RDF Concepts document.

5.2.2 owl:differentFrom

The built-in OWL owl:differentFrom property links an individual to an individual. An owl:differentFrom statement indicates that two URI references refer to different individuals.

An example:

<Opera rdf:ID="Don_Giovanni"/>

<Opera rdf:ID="Nozze_di_Figaro">
  <owl:differentFrom rdf:resource="#Don_Giovanni"/>
</Opera>

<Opera rdf:ID="Cosi_fan_tutte">
  <owl:differentFrom rdf:resource="#Don_Giovanni"/>
  <owl:differentFrom rdf:resource="#Nozze_di_Figaro"/>
</Opera>
This states that there are three different operas.

5.2.3 owl:AllDifferent

For ontologies in which the unique-names assumption holds, the use of owl:differentFrom 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 owl:AllDifferent. owl:AllDifferent is a special built-in OWL class, for which the property owl:distinctMembers is defined, which links an instance of owl:AllDifferent 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.

An example:

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

This states that these six URI references all point to different operas.

NOTE: owl:distinctMembers is a special syntactical construct added for convenience and should always be used with an owl:AllDifferent individual as its subject.

6. Datatypes

In a number of places in this document we have seen the notion of a data range for specifying a range of data values. OWL allows three types of data range specifications:

The minimal level of tool support for datatypes is discussed in Sec. 6.3.

6.1 RDF Datatypes

OWL makes use of the RDF datatyping scheme, which provides a mechanism for referring to XML Schema datatypes [XML Schema Datatypes]. For a detailed description the reader is referred to the RDF documents, e.g., [RDF Concepts]. For the convenience of the reader, we provide here a synopsis of the use of RDF datatypes.

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

The RDF Semantics document [RDF Semantics, Section 5]. recommends use of the following simple built-in XML Schema datatypes.

NOTE: It is not illegal, although not recommended, for applications to define their own datatypes by defining an instance of rdfs:Datatype. Such datatypes are "unrecognized", but are treated in a similar fashion as "unsupported datatypes" (see Sect. 6.3 for details about how these should be treated by OWL tools).

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 Measurement example:

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

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

6.2 Enumerated datatype

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 owl:oneOf construct, that is also used for describing an enumerated class. In the case of an enumerated datatype, the subject of owl:oneOf is a blank node of class owl:DataRange and the object is a list of literals. Unfortunately, we cannot use the rdf:parseType="Collection" 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 rdf:first, rdf:rest and rdf:nil.

NOTE: Enumerated datatypes are not part of OWL Lite.

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

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

6.3 Support for datatype reasoning

Tools may vary in terms of support for datatype reasoning. As a minimum, tools must support datatype reasoning for the XML Schema datatypes xsd:string and xsd:integer. 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.

7. Annotations, ontology header, imports and version information

7.1 Annotations

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:

Five annotation properties are predefined by OWL, namely:

Here is an example of legal use of an annotation property in OWL DL:

<owl:AnnotationProperty rdf:about="&dc;creator"/>

<owl:Class rdf:about="MusicalWork">
  <rdfs:label>Musical work</rdfs:label>
  <dc:creator>N.N.</dc:creator>
</owl:Class>

The example assumes &dc; and dc: point respectively to the Dublin Core URI and namespace. Thus, using Dublin Core annotations 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 [OWL S&AS] for details).

NOTE: The use of owl:AnnotationProperty is not needed in OWL Full.

7.2 Ontology header

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

<owl:Ontology rdf:about="">
  <owl:versionInfo> ... </owl:versionInfo>
  <rdfs:comment>...</rdfs:comment>
  <owl:imports rdf:resource="..."/>
</owl:Ontology>

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

  <owl:Ontology rdf:about="">

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

A sample ontology header could look like this:

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

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

NOTE: The ontology-import construct owl:imports and the ontology-versioning constructs owl:priorVersion, owl:backwardCompatibleWith and owl:incompatibleWith are defined in the OWL vocabulary as instances of the OWL built-in class owl:OntologyProperty. Instances of owl:OntologyProperty must have the class owl:Ontology as their domain and range. It is permitted to define other instances of owl:OntologyProperty.

7.3 Importing an ontology

An owl:imports 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, owl:imports is a property with the class owl:Ontology as its domain and range.

The owl:imports statements are transitive, that is, if ontology A imports B, and B imports C, then A imports both B and C.

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.

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.

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.

NOTE: owl:imports is an instance of owl:OntologyProperty.

7.4 Version information

7.4.1 owl:versionInfo

An owl:versionInfo 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.

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 owl:versionInfo statement to an OWL class.

NOTE: owl:versionInfo is an instance of owl:AnnotationProperty.

7.4.2 owl:priorVersion

An owl:priorVersion 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.

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

NOTE: owl:priorVersion is an instance of owl:OntologyProperty.

7.4.3 owl:backwardCompatibleWith

An owl:backwardCompatibleWith 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 owl:imports statements to refer to the URL of the new version). If owl:backwardCompatibleWith is not declared for two versions, then compatibility should not be assumed.

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

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

NOTE: owl:backwardCompatibleWith is an instance of owl:OntologyProperty.

7.4.4 owl:incompatibleWith

An owl:incompatibleWith 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.

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

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

NOTE: owl:backwardCompatibleWith is an instance of owl:OntologyProperty.

7.4.5 owl:DeprecatedClass and owl:DeprecatedProperty

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 owl:DeprecatedClass or owl:DeprecatedProperty, where owl:DeprecatedClass is a subclass of rdfs:Class and owl:DeprecatedProperty is a subclass of rdf:Property. 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.

An example of deprecation is:

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

<owl:DeprecatedClass rdf:ID="Car">
  <rdfs:comment>Automobile is now preferred</rdfs:comment>
  <owl:equivalentClass rdf:resource="#Automobile"/>
  <!-- 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 -->        
</owl:DeprecatedClass>

<owl:Class rdf:ID="Automobile" />

<owl:DeprecatedProperty rdf:ID="hasDriver">
  <rdfs:comment>inverse property drives is now preferred</rdfs:comment>
  <owl:inverseOf rdf:resource="#drives" />
</owl:DeprecatedProperty>

<owl:ObjectProperty rdf:ID="drives" />

8. OWL Full, OWL DL and OWL Lite

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 [OWL S&AS].

8.1 OWL Full

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 owl:Class is equivalent to rdfs:Class. This is different from OWL DL and OWL Lite, where owl:Class is a proper subclass of rdfs:Class (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 (e.g., an instance of the class AirplaneType).

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 (owl:Thing is equivalent to rdfs:Resource). This means that object properties and datatype properties are not disjoint. In OWL Full owl:ObjectProperty is equivalent to rdf:Property. The consequence is that datatype properties are effectively a subclass of object properties. (Note: the fact that owl:ObjectProperty and owl:DatatypeProperty are both subclasses of rdf:Property is not inconsistent with this).

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 below) that OWL DL and OWL Lite can provide for reasoning systems.

NOTE: RDF documents will generally be in OWL Full, unless they are specifically constructed to be in OWL DL or Lite.

NOTE: Thus, in OWL Full owl:Thing is equivalent to rdfs:Resource, owl:Class is equivalent to rdfs:Class, and owl:ObjectProperty is equivalent to rdf:Property,

8.2 OWL DL

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:

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.

NOTE: Appendix E provides a set of practical guidelines for specifying OWL DL ontologies in RDF.

8.3 OWL Lite

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:

OWL Lite also requires that:

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.

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.

Appendix A. Index of all language elements

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 [RDF Schema].

[OWL Reference]
(this document)
[OWL Semantics]
(normative)
[OWL Guide]
(examples)
owl:AllDifferent owl:AllDifferent owl:AllDifferent
owl:allValuesFrom owl:allValuesFrom owl:allValuesFrom
owl:AnnotationProperty owl:AnnotationProperty
owl:backwardCompatibleWith owl:backwardCompatibleWith owl:backwardCompatibleWith
owl:cardinality owl:cardinality owl:cardinality
owl:Class owl:Class owl:Class
owl:complementOf owl:complementOf owl:complementOf
owl:DataRange owl:DataRange
owl:DatatypeProperty owl:DatatypeProperty owl:DatatypeProperty
owl:DeprecatedClass owl:DeprecatedClass owl:DeprecatedClass
owl:DeprecatedProperty owl:DeprecatedProperty owl:DeprecatedProperty
owl:differentFrom owl:differentFrom owl:differentFrom
owl:disjointWith owl:disjointWith owl:disjointWith
owl:distinctMembers owl:distinctMembers owl:distinctMembers
owl:equivalentClass owl:equivalentClass owl:equivalentClass
owl:equivalentProperty owl:equivalentProperty owl:equivalentProperty
owl:FunctionalProperty owl:FunctionalProperty owl:FunctionalProperty
owl:hasValue owl:hasValue owl:hasValue
owl:imports owl:imports owl:imports
owl:incompatibleWith owl:incompatibleWith owl:incompatibleWith
owl:intersectionOf owl:intersectionOf owl:intersectionOf
owl:InverseFunctionalProperty owl:InverseFunctionalProperty owl:InverseFunctionalProperty
owl:inverseOf owl:inverseOf owl:inverseOf
owl:maxCardinality owl:maxCardinality owl:maxCardinality
owl:minCardinality owl:minCardinality owl:minCardinality
owl:Nothing owl:Nothing owl:Nothing
owl:ObjectProperty owl:ObjectProperty owl:ObjectProperty
owl:oneOf owl:oneOf owl:oneOf
owl:onProperty owl:onProperty owl:onProperty
owl:Ontology owl:Ontology owl:Ontology
owl:OntologyProperty owl:OntologyProperty
owl:priorVersion owl:priorVersion owl:priorVersion
owl:Restriction owl:Restriction owl:Restriction
owl:sameAs owl:sameAs owl:sameAs
owl:someValuesFrom owl:someValuesFrom owl:someValuesFrom
owl:SymmetricProperty owl:SymmetricProperty owl:SymmetricProperty
owl:Thing owl:Thing owl:Thing
owl:TransitiveProperty owl:TransitiveProperty owl:TransitiveProperty
owl:unionOf owl:unionOf owl:unionOf
owl:versionInfo owl:versionInfo

Appendix B. RDF Schema of OWL

See Sec. 1.7 for a description of the purpose of this appendix. The RDF/XML version of this appendix can be found at http://www.w3.org/2002/07/owl

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

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

<Ontology rdf:about="">
  <imports rdf:resource="http://www.w3.org/2000/01/rdf-schema"/>
  <rdfs:isDefinedBy rdf:resource="http://www.w3.org/TR/2003/PR-owl-semantics-20031209/" />
  <rdfs:isDefinedBy rdf:resource="http://www.w3.org/TR/2003/PR-owl-test-20031209/" />
  <rdfs:isDefinedBy rdf:resource="http://www.w3.org/TR/2003/PR-owl-features-20031209/" />
  <rdfs:comment>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. 
  </rdfs:comment>
  <versionInfo>9 December 2003</versionInfo>
</Ontology>

<rdfs:Class rdf:ID="Class">
  <rdfs:label>Class</rdfs:label>
  <rdfs:subClassOf rdf:resource="&rdfs;Class"/>
</rdfs:Class>

<Class rdf:ID="Thing">
  <rdfs:label>Thing</rdfs:label>
  <unionOf rdf:parseType="Collection">
    <Class rdf:about="#Nothing"/>
    <Class>
      <complementOf rdf:resource="#Nothing"/>
    </Class>
  </unionOf>
</Class>

<Class rdf:ID="Nothing">
  <rdfs:label>Nothing</rdfs:label>
  <complementOf rdf:resource="#Thing"/>
</Class>

<rdf:Property rdf:ID="equivalentClass">
  <rdfs:label>equivalentClass</rdfs:label>
  <rdfs:subPropertyOf rdf:resource="&rdfs;subClassOf"/>
  <rdfs:domain rdf:resource="#Class"/>
  <rdfs:range rdf:resource="#Class"/>
</rdf:Property>

<rdf:Property rdf:ID="disjointWith">
  <rdfs:label>disjointWith</rdfs:label>
  <rdfs:domain rdf:resource="#Class"/>
  <rdfs:range rdf:resource="#Class"/>
</rdf:Property>

<rdf:Property rdf:ID="equivalentProperty">
  <rdfs:label>equivalentProperty</rdfs:label>
  <rdfs:subPropertyOf rdf:resource="&rdfs;subPropertyOf"/>
</rdf:Property>

<rdf:Property rdf:ID="sameAs"> 
  <rdfs:label>sameAs</rdfs:label>
  <rdfs:domain rdf:resource="#Thing"/>
  <rdfs:range rdf:resource="#Thing"/>
</rdf:Property>

<rdf:Property rdf:ID="differentFrom">
  <rdfs:label>differentFrom</rdfs:label>
  <rdfs:domain rdf:resource="#Thing"/>
  <rdfs:range rdf:resource="#Thing"/>
</rdf:Property>

<rdfs:Class rdf:ID="AllDifferent">
  <rdfs:label>AllDifferent</rdfs:label>
</rdfs:Class>

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

<rdf:Property rdf:ID="intersectionOf">
  <rdfs:label>intersectionOf</rdfs:label>
  <rdfs:domain rdf:resource="#Class"/>
  <rdfs:range rdf:resource="&rdf;List"/>
</rdf:Property>

<rdf:Property rdf:ID="complementOf">
  <rdfs:label>complementOf</rdfs:label>
  <rdfs:domain rdf:resource="#Class"/>
  <rdfs:range rdf:resource="#Class"/>
</rdf:Property>

<rdf:Property rdf:ID="oneOf">
  <rdfs:label>oneOf</rdfs:label>
  <rdfs:domain rdf:resource="&rdfs;Class"/>
  <rdfs:range rdf:resource="&rdf;List"/>
</rdf:Property>

<rdfs:Class rdf:ID="Restriction">
  <rdfs:label>Restriction</rdfs:label>
  <rdfs:subClassOf rdf:resource="#Class"/>
</rdfs:Class>

<rdf:Property rdf:ID="onProperty">
  <rdfs:label>onProperty</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
  <rdfs:range rdf:resource="&rdf;Property"/>
</rdf:Property>

<rdf:Property rdf:ID="allValuesFrom">
  <rdfs:label>allValuesFrom</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
  <rdfs:range rdf:resource="&rdfs;Class"/>
</rdf:Property>

<rdf:Property rdf:ID="hasValue">
  <rdfs:label>hasValue</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
</rdf:Property>

<rdf:Property rdf:ID="someValuesFrom">
  <rdfs:label>someValuesFrom</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
  <rdfs:range rdf:resource="&rdfs;Class"/>
</rdf:Property>

<rdf:Property rdf:ID="minCardinality">
  <rdfs:label>minCardinality</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
  <rdfs:range rdf:resource="&xsd;nonNegativeInteger"/>
</rdf:Property>

<rdf:Property rdf:ID="maxCardinality">
  <rdfs:label>maxCardinality</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
  <rdfs:range rdf:resource="&xsd;nonNegativeInteger"/>
</rdf:Property>

<rdf:Property rdf:ID="cardinality">
  <rdfs:label>cardinality</rdfs:label>
  <rdfs:domain rdf:resource="#Restriction"/>
  <rdfs:range rdf:resource="&xsd;nonNegativeInteger"/>
</rdf:Property>

<rdfs:Class rdf:ID="ObjectProperty">
  <rdfs:label>ObjectProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="&rdf;Property"/>
</rdfs:Class>

<rdfs:Class rdf:ID="DatatypeProperty">
  <rdfs:label>DatatypeProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="&rdf;Property"/>
</rdfs:Class>

<rdf:Property rdf:ID="inverseOf">
  <rdfs:label>inverseOf</rdfs:label>
  <rdfs:domain rdf:resource="#ObjectProperty"/>
  <rdfs:range rdf:resource="#ObjectProperty"/>
</rdf:Property>

<rdfs:Class rdf:ID="TransitiveProperty">
  <rdfs:label>TransitiveProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="#ObjectProperty"/>
</rdfs:Class>

<rdfs:Class rdf:ID="SymmetricProperty">
  <rdfs:label>SymmetricProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="#ObjectProperty"/>
</rdfs:Class>

<rdfs:Class rdf:ID="FunctionalProperty">
  <rdfs:label>FunctionalProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="&rdf;Property"/>
</rdfs:Class>

<rdfs:Class rdf:ID="InverseFunctionalProperty">
  <rdfs:label>InverseFunctionalProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="&owl;ObjectProperty"/>
</rdfs:Class>

<rdfs:Class rdf:ID="AnnotationProperty">
  <rdfs:subClassOf rdf:resource="&rdf;Property"/>
</rdfs:Class>

<AnnotationProperty rdf:about="&rdfs;label"/>
<AnnotationProperty rdf:about="&rdfs;comment"/>
<AnnotationProperty rdf:about="&rdfs;seeAlso"/>
<AnnotationProperty rdf:about="&rdfs;isDefinedBy"/>

<rdfs:Class rdf:ID="Ontology">
  <rdfs:label>Ontology</rdfs:label>
</rdfs:Class>

<rdfs:Class rdf:ID="OntologyProperty">
  <rdfs:subClassOf rdf:resource="&rdf;Property"/>
</rdfs:Class>

<rdf:Property rdf:ID="imports">
  <rdfs:label>imports</rdfs:label>
  <rdf:type rdf:resource="#OntologyProperty"/>
  <rdfs:domain rdf:resource="#Ontology"/>
  <rdfs:range rdf:resource="#Ontology"/>
</rdf:Property>

<rdf:Property rdf:ID="versionInfo">
  <rdfs:label>versionInfo</rdfs:label>
  <rdf:type rdf:resource="#AnnotationProperty"/>
</rdf:Property>

<rdf:Property rdf:ID="priorVersion">
  <rdfs:label>priorVersion</rdfs:label>
  <rdf:type rdf:resource="#OntologyProperty"/>
  <rdfs:domain rdf:resource="#Ontology"/>
  <rdfs:range rdf:resource="#Ontology"/>
</rdf:Property>

<rdf:Property rdf:ID="backwardCompatibleWith">
  <rdfs:label>backwardCompatibleWitesh</rdfs:label>
  <rdf:type rdf:resource="#OntologyProperty"/>
  <rdfs:domain rdf:resource="#Ontology"/>
  <rdfs:range rdf:resource="#Ontology"/>
</rdf:Property>

<rdf:Property rdf:ID="incompatibleWith">
  <rdfs:label>incompatibleWith</rdfs:label>
  <rdf:type rdf:resource="#OntologyProperty"/>
  <rdfs:domain rdf:resource="#Ontology"/>
  <rdfs:range rdf:resource="#Ontology"/>
</rdf:Property>

<rdfs:Class rdf:ID="DeprecatedClass">
  <rdfs:label>DeprecatedClass</rdfs:label>
  <rdfs:subClassOf rdf:resource="&rdfs;Class"/>
</rdfs:Class>

<rdfs:Class rdf:ID="DeprecatedProperty">
  <rdfs:label>DeprecatedProperty</rdfs:label>
  <rdfs:subClassOf rdf:resource="&rdf;Property"/>
</rdfs:Class>

<rdfs:Class rdf:ID="DataRange">
  <rdfs:label>DataRange</rdfs:label>
</rdfs:Class>

</rdf:RDF>


Appendix C. OWL Quick Reference

Classes in the OWL vocabulary:

rdfs:Class
owl:AllDifferent
owl:AnnotationProperty
owl:Class
owl:DataRange
owl:DatatypeProperty
owl:DeprecatedClass
owl:DeprecatedProperty
owl:FunctionalProperty
owl:InverseFunctionalProperty
owl:Nothing
owl:ObjectProperty
owl:Ontology
owl:OntologyProperty
owl:Restriction
owl:SymmetricProperty
owl:Thing
owl:TransitiveProperty

Properties in the OWL vocabulary:

rdf:Property rdfs:domain rdfs:range
owl:allValuesFrom owl:Restriction rdfs:Class
owl:backwardCompatibleWith owl:Ontology owl:Ontology
owl:cardinality owl:Restriction xsd:nonNegativeInteger
owl:complementOf owl:Class owl:Class
owl:differentFrom owl:Thing owl:Thing
owl:disjointWith owl:Class owl:Class
owl:distinctMembers owl:AllDifferent rdf:List
owl:equivalentClass owl:Class owl:Class
owl:equivalentProperty rdf:Property rdf:Property
owl:hasValue owl:Restriction
owl:imports owl:Ontology owl:Ontology
owl:incompatibleWith owl:Ontology owl:Ontology
owl:intersectionOf owl:Class rdf:List
owl:inverseOf owl:ObjectProperty owl:ObjectProperty
owl:maxCardinality owl:Restriction xsd:nonNegativeInteger
owl:minCardinality owl:Restriction xsd:nonNegativeInteger
owl:oneOf owl:Class rdf:List
owl:onProperty owl:Restriction rdf:Property
owl:priorVersion owl:Ontology owl:Ontology
owl:sameAs owl:Thing owl:Thing
owl:someValuesFrom owl:Restriction rdfs:Class
owl:unionOf owl:Class rdf:List
owl:versionInfo

Appendix D. Changes from DAML+OIL

This section summarizes the changes from DAML+OIL [DAML+OIL] to OWL.

  1. The semantics have changed significantly. With respect to the three sublanguages, the DAML+OIL semantics are closest to the OWL DL semantics.
  2. The namespace was changed to http://www.w3.org/2002/07/owl.
  3. Various updates to RDF and RDF Schema from the RDF Core Working Group were incorporated, including
  4. Qualified restrictions were removed from the language, resulting in the removal of the following properties:
  5. Various properties and classes were renamed, as shown in the following table:
    DAML+OIL OWL
    daml:differentIndividualFrom owl:differentFrom
    daml:equivalentTo owl:sameAs
    daml:sameClassAs owl:equivalentClass
    daml:samePropertyAs owl:equivalentProperty
    daml:hasClass owl:someValuesFrom
    daml:toClass owl:allValuesFrom
    daml:UnambiguousProperty owl:InverseFunctionalProperty
    daml:UniqueProperty owl:FunctionalProperty
  6. owl:SymmetricProperty was added.
  7. An owl:DatatypeProperty may be an owl:InverseFunctionalProperty in OWL Full.
  8. Synonyms for RDF and RDF Schema classes and properties were removed from the language, resulting in the removal of:
  9. daml:disjointUnionOf was removed from the language, since it can be effected using owl:unionOf or rdfs:subClassOf and owl:disjointWith.
  10. daml:equivalentTo was renamed to owl:sameAs, and is no longer a superproperty of owl:equivalentClass and owl:equivalentProperty,
  11. The following properties and classes were added to support versioning:
  12. owl:AllDifferent and owl:distinctMembers were added to address the Unique Names Assumption.

Appendix E. Rules of Thumb for OWL DL ontologies

The OWL Abstract Syntax and Semantics document [OWL S&AS] provides a characterization of OWL ontologies in terms of an abstract syntax, along with a mapping to RDF triples.

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&AS, but instead gives some general pointers — 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.

Don't mess with the vocabulary

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

Provide Explicit Typing

Everything should have a type1. If any URI reference x is used where a class is expected, the graph should contain a triple stating that

x rdf:type owl:Class

Similarly, if a property p is used where an object property is expected then there should be a triple2

p rdf:type owl:ObjectProperty

If a property q is used where a data property is expected then there should be a triple

q rdf:type owl:DatatypeProperty

If a property o is used where an ontology property is expected then it should either be one of the built in ontology properties (owl:imports, owl:priorVersion, owl:backwardCompatibleWith, and owl:incompatibleWith) or there should be a triple:

o rdf:type owl:OntologyProperty

If a property a is used where an annotation property is expected then it should either be one of the built in annotation properties (owl:versionInfo, rdfs:label, rdfs:comment, rdfs:seeAlso, and rdfs:isDefinedBy) or there should be a triple:

a rdf:type owl:AnnotationProperty

Any individuals that occur in the ontology should have at least one type specified, i.e. for an individual i, there must be a triple:

i rdf:type c

where c is an owl:Class or owl:Restriction.

Keep names separate

URI references for classes, properties (object, datatype, ontology and annotation) and individuals should be disjoint. Thus we cannot have things like:

x rdf:type owl:Class
x rdf:type owl:ObjectProperty

In particular, this means that we cannot use classes as instances, i.e.

x rdf:type owl:Class
y rdf:type owl:Class
x rdf:type y

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

x rdf:type owl:Class

then x should not appear as the subject of any other triple with predicate rdf:type.3

Restrictions

If a node x has rdf:type owl:Restriction then the following should be the case:

Class axioms

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

x rdfs:subClassOf y

then the graph must contain one of:

x rdf:type owl:Class

or

x rdf:type owl:Restriction.

and one of

y rdf:type owl:Class

or

y rdf:type owl:Restriction.

Property axioms

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

p owl:equivalentProperty q

then the graph must contain either:

p rdf:type owl:ObjectProperty
q rdf:type owl:ObjectProperty.

or

p rdf:type owl:DatatypeProperty
q rdf:type owl:DatatypeProperty.

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

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

Both the subject and object of an owl:inverseOf triple must have type owl:ObjectProperty.

Individual axioms

For any triples with predicate owl:sameAs4 or owl:differentFrom, the subject and object must be individuals.

Note that relating two classes via owl:sameAs is a very different thing to relating them via owl:equivalentClass. The former says that the two objects are in fact the same, is actually an example of class as instance, 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.

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

If a node x has rdf:type owl:AllDifferent, then the following should be the case:

Boolean class expressions

Boolean Operators (and, or, not) are represented in OWL using owl:intersectionOf, owl:unionOf and owl:complementOf.

The subject of an owl:complementOf triple must be an owl:Class, the object must be either an owl:Class or owl:Restriction.

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

<owl:Class>
 <owl:intersectionOf rdf:parseType="Collection">
  <owl:Class rdf:about="x"/>
  <owl:Class rdf:about="y"/>
 </owl:intersectionOf>
</owl:Class>

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

Enumerations

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

Ontology and Annotation Properties

The subject and object of any triple with an ontology predicate should be an ontology, e.g. a node x such that there is a triple:

x rdf:type owl:Ontology

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.

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

Annotation and ontology properties themselves should be typed, and should not appear as the subject or object of triples other than as the subject of a triple with predicate rdf:type or an annotation property.

Avoid structure sharing

In general, the S&AS description of OWL does not permit structure sharing 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:

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

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

Avoid orphan blank nodes

In general, blank nodes occurring in the graph either represent unnamed individuals, or should be exactly one of the following:

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

Ground facts

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 owl:ObjectProperty or owl:DatatypeProperty. The subject of any such triple must be an individual (which should be typed). The object can either be a reference to an individual (if the property is an owl:ObjectProperty) or a data literal (if the property is an owl:DatatypeProperty).

OWL Lite

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:

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

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

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

Miscellaneous

Be careful of the use of owl:Thing. For example, the following OWL-RDF fragment:

<owl:Class rdf:about="#A">
  <rdfs:subClassOf>
    <owl:Thing/>
  </rdfs:subClassOf>
</owl:Class>

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

<owl:Class rdf:about="#A">
  <rdfs:subClassOf>
    <owl:Class rdf:about="http://www.w3.org/2002/07/owl#Thing"/>
  </rdfs:subClassOf>
</owl:Class>

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

c rdf:type rdfs:Class

Notes

[1] Of course the necessity to type everything does not apply to things from the OWL, RDF or RDFS namespaces.

[2] Strictly speaking, if the property is defined as being an owl:TransitiveProperty, owl:SymmetricProperty or owl:InverseFunctionalProperty then this is not necessary.

[3] An exception here is that we can have:

x rdf:type rdfs:Class
x rdf:type owl:Class
p rdf:type rdf:Property
p rdf:type owl:ObjectProperty

or

q rdf:type rdf:Property
q rdf:type owl:DatatypeProperty

In addition, for restrictions, we can have:

x rdf:type owl:Restriction
x rdf:type rdfs:Class
x rdf:type owl:Class

[4] Or owl:sameAs.

Appendix F. Change Log

This section summarizes recent changes to this document. It will be removed in the final version.

Changes since the Candidate Recommendation version:

  1. Added this new list of changes
  2. Fixed typo in response to comments by Benjamin Nowack
  3. Replaced text as suggested in comments by Susan Lesch
  4. Revised note in Sec. 3.1. to exclude named owl:Restriction to be axioms for complete classes after comments from Benhamin Nowack.
  5. Adapted owl.rdf after comments from Dave Beckett (Aug 19).
  6. Removed enumeration example after comments from Olivier Corby.
  7. Error corrected: changed "sub" into "super" in DL constraint on transitive properties in Sec. 4.4.1

Changes between the Last Call version and the Candidate Recommendation version:

  1. change to Sec. 8.3 after comment from Qu
  2. changes to Sec. 1, Sec. 7 and the appendices after several comments from Patel-Schneider: 24 April 24 April 24 April 24 April
  3. owl:Nothing is now in OWL Lite, per Minutes telecon May 1, 2003
  4. changes to Appendix D suggested in Language Ref Appendix D editorial comments
  5. "For historical reasons" deleted in Sec. 5.2, owl:sameAs after comment on Guide.
  6. Added forward reference to datatype support in intro Sec. 6 plus changed "should" to "must" in Sec. 6.3 after comment from Connolly.
  7. Changed superclass of InverseFunctionalProperty to owl:ObjectProperty after comment from Finin.
  8. Updated RDF/XML version of Appendix B as separate owl.owl file and included link to this file after comment from Dave Beckett
  9. Several changes in response to comments by Lacy Lee
  10. Several changes in response to comments by the RDFCore Working Group
  11. Included Appendix E "Rules of Thumb for OWL DL ontologies" in response to comments about a readable description of OWL DL as RDF graphs. .
  12. Several small changes after comments from Brian McBride
  13. Revised description of purpose of Appendix B after comments from Dave Beckett
  14. Changed link in Sec. 6 for RDF datatype details to point to RDF Semantics document after a comment from Brian McBride
  15. Revised Sec. 7.3 on imports after comments from Jennifer Golbeck and Dave Beckett
  16. Revised Sec. 1.6 on privacy after comments from Rigo Wenning
  17. Revised Sec. 7.2 on ontology documents after comments from the RDFCore WG
  18. Added paragraph in the Introduction about the set of OWL documents after in response to the review by the QA WG
  19. Changes reflecting the new resolution on issue 4.6 to use owl:sameAs as the only term for equality of individuals.
  20. Revised Appendix D (daml:item) after comments from Bijan Parsia.

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 Use Cases and Requirements]
OWL Web Ontology Language Use Cases and Requirements. Jeff Heflin, ed. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/webont-req/.
[OWL Overview]
OWL Web Ontology Language Overview. Deborah L. McGuinness and Frank van Harmelen, eds. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/owl-features/.
[OWL Guide]
OWL Web Ontology Language Guide. Michael K. Smith, Christopher Welty, Raphael Volz, and Deborah McGuinness. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/owl-guide/.
[OWL S&AS]
OWL Web Ontology Language Semantics and Abstract Syntax. Peter F. Patel-Schneider, Patrick Hayes, and Ian Horrocks, eds. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/owl-semantics/.
[OWL Test Cases]
OWL Web Ontology Language Test Cases. Jeremy J. Carroll and Jos De Roo, eds. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/owl-test/.
[RDF Concepts]
Resource Description Framework (RDF): Concepts and Abstract Syntax. Graham Klyne and Jeremy J. Carroll, eds. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/rdf-concepts/.
[RDF Schema]
RDF Vocabulary Description Language 1.0: RDF Schema. Dan Brickley and R.V. Guha, eds. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/rdf-schema/.
[RDF Semantics]
RDF Semantics. Patrick Hayes, ed. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/rdf-mt/.
[RDF/XML Syntax]
RDF/XML Syntax Specification (Revised). Dave Beckett, ed. W3C Proposed Recommendation 9 December 2003. Latest version is available at http://www.w3.org/TR/rdf-syntax-grammar/.
[XML-SCHEMA2]
XML Schema Part 2: Datatypes - W3C Recommendation, World Wide Web Consortium, 2 May 2001.