W3C

Web Ontology Language (OWL)
Reference Version 1.0

W3C Working Draft 21 February 2003

This version:
http://www.w3.org/TR/2003/WD-owl-ref-20030221/
Latest version:
http://www.w3.org/TR/owl-ref/
Previous version:
http://www.w3.org/TR/2002/WD-owl-ref-20021112/
Editors:
Mike Dean
Guus Schreiber
Authors:
Frank van Harmelen
Jim Hendler
Ian Horrocks
Deborah L. McGuinness
Peter F. Patel-Schneider
Lynn Andrea Stein

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 is a W3C Working Draft for review by W3C members and other interested parties. It is a draft document and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use W3C Working Drafts as reference materials or to cite them as other than "work in progress." A list of current W3C Recommendations and other technical documents can be found at http://www.w3.org/TR/.

This Working Draft corresponds to the OWL Web Ontology Language 1.0 specification, which is being developed by the W3C Web Ontology Working Group. This document has been produced as part of the W3C Semantic Web Activity (Activity Statement) following the procedures set out for the W3C Process. The goals of the Web Ontology working group are discussed in the Web Ontology Working Group charter.

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

Comments on this document should be sent to public-webont-comments@w3.org, a mailing list with a public archive. General discussion of related technology is welcome in www-rdf-logic.

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 authors of this document were Dan Connolly, Frank van Harmelen, Jim Hendler, Ian Horrocks, Deborah McGuinness, Peter Patel-Schneider, and Lynn Andrea Stein. The sponsors of this document and its predecessor documents are also gratefully acknowledged.

Jeremy Carroll, Jim Hendler, Brian McBride and Peter Patel-Schneider provided substantive reviews and contributed text to this document. 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 members of this working group were .... (@@ include member list)

Contents


1. Introductory remarks

1.1 Purpose of this document

This document gives a systematic, compact and informal 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. 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 of example 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 machine-readable RDF Schema of OWL (included as Appendix B) and in the OWL Abstract Syntax and Semantics document [OWL AS&S]. The latter document also contains a precise definition of the meaning of the language constructs in the form of a model-theoretic semantics.

1.2 OWL Full/DL/Lite

As also discussed in the OWL Overview and OWL Guide documents, the OWL language provides two specific subsets that we believe will be of great 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 Description Logic (OWL DL) 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.

OWL Full and OWL DL support the same set of language constructs. Their difference lies in restrictions on the use of some of those 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 Abstract Syntax and Semantics document [OWL AS&S]. Section 8 "OWL Lite/DL/Full constructs" summarizes the differences between OWL Full and OWL DL.

OWL Lite is a sublanguage of OWL 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 was designed to extend the modeling capabilities of RDFS by adding some common features used in extending vocabularies and thesauri into ontologies. OWL Lite also 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 Abstract Syntax and Semantics document [OWL AS&S].

1.3 OWL syntax

An OWL ontology is represented as a set of RDF triples. As with any set of RDF triples, OWL triples can be represented in many different syntactic forms (as described in the RDF/XML Syntax Specification (Revised) [RDF/XML Syntax]). This document (as does the Guide document) uses some specific syntactic forms of RDF/XML for representing triples. However, the meaning of an OWL ontology is solely determined by the resulting set of triples. Thus, it is allowed to use any syntactic RDF forms, as long as these result in the same underlying set of RDF triples. Such other syntactic forms would then carry exactly the same prescribed meaning as the syntactic form used in this document.

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

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

The following RDF statement:

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

results in exactly the same set of RDF triples, and is therefore perfectly allowed.

1.4 OWL and RDF semantics

OWL is a vocabulary extension of RDF. Thus any RDF graph forms an OWL ontology. Further, the meaning given to an RDF graph by OWL includes the meaning given to the graph by RDF. OWL 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 Abstract Syntax and Semantics [OWL AS&S] specifies exactly which triples are assigned a specific meaning, and what this meaning is.

1.5 Annotations

@@ Explain use of annotations such as rdfs:comment, isDefinedBy. seeAlso, etc,

1.6 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 an illustration of the use of OWL language constructs. They do not form one consistent ontology. For such examples the reader is referred to the Guide document [OWL Guide].

2. Language structure

An OWL document consists of an optional ontology header and any number of class axioms, property axioms, and individual axioms. Please note that "axiom" is the formal term used in the AS&S 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 all RDF documents, the OWL code should be enclosed in a <rdf:RDF> begin and end tag. The document can contain standard XML entity and namespace declarations. For a typical XML header, see the wine.owl file, which contains the example wine ontology discussed in the Guide document.

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

Appendix B contains an RDF schema for the OWL language constructs. This schema defines the OWL language constructs in terms of RDF Schema classes and properties. This schema provides the basis for the RDF/XML syntax of OWL. Conventionally, classes have a leading uppercase character; properties a leading lowercase character. Thus, owl:Ontology is a class, and owl:imports is a property. Appendix C gives a tabular overview of all OWL language constructs in terms of the built-in OWL classes and properties (the latter with their domain and range).

@@ This file was always named "owl.owl". Does this mean that Appendix B should be extended to represent a "real" OWL ontology of OWL, using OWL constructs to define OWL constructs. For DAML+OIL the decision was made (?!) to limit this specification to RDF Schema constructs to avoid circular definitions (for example, using "onProperty" to define "onProperty"). We could also provide both an RDF schema and an OWL ontology of OWL.

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

2.1 OWL URI vocabulary and namespace

Certain URI references are reserved for use by OWL and may not be used for any purpose not sanctioned by the OWL specifications. Specifically, URI references with the following leading substring are reserved for the OWL vocabulary:

http://www.w3.org/2002/07/owl# (conventionally associated with namespace prefix owl:)

Used with the RDF/XML serialization, these URI prefix strings correspond to XML namespaces associated with the OWL vocabulary terms.

3. Ontology header

owl:Ontology

A ontology header component is represented with an instance of the class owl:Ontology, which typically identifies the containing document with a same-document reference [section 4.2 of RFC2396], and which may optionally contain, in any order, any number of import and/or versioning statements.

A sample ontology header could look like this:

<owl:Ontology rdf:about="">
  <owl:versionInfo>$Id: Overview.html,v 1.1 2003/02/21 23:05:17 henri Exp $
  </owl:versionInfo>
  <rdfs:comment>An example ontology</rdfs:comment>
  <owl:imports rdf:resource="http://www.w3.org/2002/07/owl"/>
</owl:Ontology>

The rdf:about="" refers to the current document. The following sections describe the various types of statements that are typically used within the header.

@@ domain/range constraints of the import and versioning properties should be checked

owl:imports

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. 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 namespaces only provide a mechanism for creating unique names, and do not actually include definitions in the way that owl:imports does. Similarly, owl:imports statements do not set up a shorthand notation for names. Therefore, it is common to have corresponding namespace definitions and owl:imports statements.

If an OWL Lite ontology imports an OWL DL or OWL Full ontology, it effectively becomes an OWL DL or OWL Full ontology. Similarly, an OWL DL ontology that imports a OWL Full ontology becomes an OWL Full ontology.

owl:versionInfo

An owl:versionInfo @@ statement generally contains 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.

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: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 is defined as a subproperty of owl:priorVersion, and thus has also no meaning in the model theoretic semantics other than that given by the RDF(S) model theory.

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 is defined as a subproperty of owl:priorVersion, and thus has also no meaning in the model theoretic semantics other than that given by the RDF(S) model theory.

4. 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.

@@ include example.@@ cite Martin and Odell,Ch. 2

When in this document we use wording such as "a class of individuals ..", this should be read as the "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 (the same holds for properties).

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.

4.1 Class descriptions

A class description is the term used in this document (and in the OWL Abstract Syntax and Semantics) for the basic building blocks of class axioms (informally called class definitions in the Overview and Guide documents). 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 describes a class through a name. The other five types of class descriptions define an anonymous class, respectively a class that contains exactly the enumerated individuals (2nd type), a class of all individuals which satisfy the property restriction (3rd type), or a class that satisfies boolean combinations of such descriptions (4th, 5th and 6th type). Intersection, union and complement can be respectively seen as the logical AND, OR and NOT operators. These three 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 instance of owl:Class, a subclass of rdfs:Class:

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

This will assert the triple "Human rdf:type owl:Class .".

The other five forms of class descriptions are represented as anonymous instances of owl:Class (a blank node with the rdf:type owl:Class) and includes certain statements about properties of this anonymous class.

NOTE: If one uses the syntactic form of class descriptions of type 2-6, but with a class identifier, OWL treats this as a specific kind of class axiom. See Section 4.2 for details.

NOTE: Class descriptions of type 1 can always be used as a stand-alone class axiom (see Section 4.2). OWL DL allows the use of class descriptions of type 2-6 only within particular types of class axioms (see Sections 4.2 and 8.2). OWL Full does not impose such a restriction: every class description is in itself a valid OWL Full class axiom.

Class descriptions of type 2-6 are discussed in more detail in the following subsections.

Two OWL class names are predefined, namely the classes owl:Thing and owl:Nothing. The class extension of owl:Thing is the set of all individuals in the domain of discourse. The class extension of owl:Nothing is the empty set. Consequently, every 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).

NOTE: owl:Nothing is not included in OWL Lite.

4.1.1 Enumeration

A class description of the "enumeration" type is defined with the owl:oneOf property, which points to a list of individuals that are the instances of the class. This enables us to define a class by exhaustively enumerating its instances. The class extension of the class defined 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 owl:oneOf statement 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>

A statement of the form <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.

4.1.2 Property restrictions

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

A value restriction puts constraints on the value range of the property when applied to this particular class description. For example, we might want to say that for the class Region the value of the property adjacentTo should also be a Region. Note the difference with the RDF Schema construct rdfs:range, which applies to all situations in which the property is used.

A cardinality restriction 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 the owl:FunctionalProperty and the owl:InverseFunctionalProperty definitions (see the section on properties).

Property restrictions have the following general format:

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

The class owl:Restriction is defined as a subclass of owl:Class. A restriction class should have exactly one statement linking the restriction to a particular property, using the owl:onProperty property. The restriction class should also have exactly one statement that represents the value restriction c.q. cardinality restriction 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 range value is a data literal) and object properties (properties for which the range value is an individual). For more information about this distinction, see the section on properties.

4.1.2.1 Value restrictions
owl:allValuesFrom

An owl:allValuesFrom restriction is a property that links a restriction class to either a class description or a data range. A restriction containing an owl:allValuesFrom statement s used to describe a class of all individuals for which all range 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 range values of class "Human". Note that this class description does not state that the property always has range values of this class; just that this is true for individuals of the anonymous restriction class.

An owl:allValuesFrom restriction is analogous to the universal (for-all) quantifier of Predicate logic - for each instance of the class or datatype that is being defined, every range value for P must fulfill the restriction. Also notice that the correspondence of owl:allValuesFrom with the universal quantifier means that an owl:allValuesFrom restriction 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 restriction demands that all values of P belong to class P, and if no such values exist, the restriction is trivially true.

owl:someValuesFrom

The value restriction owl:someValuesFrom is a property that links a restriction class to a class description or a data range. A restriction containing an owl:someValuesFrom statement 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 restriction 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 restriction.

owl:hasValue

An owl:hasValue restriction is a 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 statement 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:sameIndividualAs).

NOTE: the value restriction 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>
4.1.2.2 Cardinality restrictions
The default cardinality of properties is "any". 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 restrictions, but only when used with the range values "0" or "1".

owl:maxCardinality

An owl:maxCardinality property links a restriction class to a data value belonging to the range of the XML Schema datatype nonNegativeInteger. A restriction containing an owl:maxCardinality statement describes a class of all individuals that have at most N distinct range values (individuals or data values) for the property concerned, where N is the range value of the cardinality statement. Syntactically, the cardinality statement 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 "7. Datatypes".

owl:minCardinality

An owl:minCardinality property links a restriction class to a data value belonging to the range of the XML Schema datatype nonNegativeInteger. A restriction containing an owl:minCardinality statement describes a class of all individuals that have at least N distinct range values (individuals or data values) for the property concerned, where N is the range value of the cardinality statement. Syntactically, the cardinality statement 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>
owl:cardinality

An owl:cardinality property links a restriction class to a data value belonging to the range of the XML Schema datatype nonNegativeInteger. A restriction containing an owl:cardinality statement describes a class of all individuals that have exactly N distinct range values (individuals or data values) for the property concerned, where N is the range value of the cardinality statement. Syntactically, the cardinality statement 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 restrictions 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>

4.1.3 Intersection, union and complement

The three forms 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).

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 range 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 range of the intersection statement is a list of two class description, 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 the section on individuals one can find OWL language constructs for making statements about equality and difference of individuals.

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

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 range 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).

owl:unionOf is analogous to logical disjunction.

owl:complementOf

An owl:complementOf property links a class to precisely one class description. The owl:complementOf statement defines a class for which the class extension contains exactly those individuals that do not belong to the class extension of the range class. owl:complementOf is analogous to logical negation, but restricted to individuals only.

As an example of the use of complement, the expression "neither meat nor fish" could be written as:

<owl:Class>
  <owl:complementOf>
    <owl:Class>
      <owl:unionOf rdf:parseType="Collection">
        <owl:Class rdf:about="#Meat"/>
        <owl:Class rdf:about="#Fish"/>
      </owl:unionOf>
    </owl:Class>
  </owl:complementOf>
</owl:Class>

@@ Reconsider example, Peter said it was incorrect

Note that arbitrarily complex combinations of these set-operator class descriptions can be formed.

4.2 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.

NOTE: In OWL Full every type of class description is also a valid class axiom. OWL DL and OWL Lite impose restrictions on the ways in which class descriptions of type 2-6 can be used to form class axioms.

For example, the following class axiom declares the URI reference "Human" to be 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 such definitions:

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 the section Axioms for complete classes without using owl:equivalentClass).

rdfs:subClassOf

The property rfs:subClassOf 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 description 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: OWL DL only allows a class identifier to be the domain value of an rdfs:subClassOf statement. OWL Lite has the additional restriction that only class identifiers or property restrictions are allowed as range values.

Class axioms can also use the other types of class descriptions, such as property restrictions, enumerations, intersections, unions and complements. 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.

@@ mention of the use of rdf:about versus rdf:ID ??

A final point about the previous two examples is that multiple subclass axioms for the same class define in fact an intersection: the class at the lefthand side should be a subclass of both class descriptions. Thus, the following two class axioms are semantically equivalent:

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

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

The use of intersection (and union and complement) leads to nested class descriptions. Another form of nested class descriptions can occur when defining property restrictions with the owl:allValuesFrom or owl:someValuesFrom constructs, because these may point to a 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 restriction, it could actually have both values).

More examples can be found in the Guide document and in the corresponding wine.owl file. 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 operettas are exactly those musical works that have a librettist and are not operas, we would need to use the owl:equivalentClass construct.

owl:equivalentClass

A class axiom may contain (multiple) owl:equivalentClass @@ statements. The property owl:equivalentClass links a class description to another class description. The meaning of such a class axiom is that the two classes 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 (or its synonym owl:sameIndividualAs, see the section on individuals). As this requires treating classes as individuals, class equality can only be expressed in OWL Full.

owl:equivalentClass is also 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="DaPonteperaOfMozart">
  <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 domain and range values of an owl:equivalentClass statement. In OWL Lite only class identifiers and property restrictions are allowed as domain and range values.

NOTE: Although in principle different types of class descriptions are allowed as the lefthand-side (domain value) of an equivalentClass statement, in practice it usually is some class identifier. The is also true for the examples in this section.

It is possible to have multiple equivalentClass axioms about the same class. However, this requires great 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 denotes indeed the same set of individuals 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 equal (and thus has the same meaning as "A equivalentClass B"). Such subClassOf "cycles" are explicitly allowed. As OWL should be usable in a distributed environment, this may be a useful feature.

Axioms for complete classes without using owl:equivalentClass

OWL allows users to define class axioms by giving a name to classes 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:complenentOf. 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 range values of intersectionOf should be class identifiers and/or property restrictions. Thus, "complete class" axioms using enumeration, complement and union are not allowed in OWL Lite.

@@ Guideline about explicit vs. implicit form of complete classes??

owl:disjointWith

A class axiom may also contain (multiple) owl:disjointWith statements. The construct owl:disjointWith is a property with a class description as domain and range. Each owl:disjointWith statement asserts that the class extensions of the two class description 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 DL does not put any constraints on the types of class descriptions that can be used as domain and range values of an owl:disjointWith statement. OWL Lite does not allow the use of owl:disjointWith.

5. Properties

OWL distinguishes between two types of properties:

An object property is defined with the help of an owl:ObjectProperty class. A datatype property is defined through an owl:DatatypeProperty class. 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 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 properties. 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 the range values should be individuals.

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

In the next subsections, these property-related language constructs 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).

5.1 RDF Schema property 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.

rdfs:subPropertyOf

A rdfs:subPropertyOf statement 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 statements can be applied to both datatype properties and object properties.

NOTE: In OWL DL the domain and range value of a subproperty statement should be either both datatype properties or both object properties.

rdfs:domain

For a property one can define (multiple) rdfs:domain statements. Syntactically, rdfs:domain is a property that links a property (some instance of the class rdf:Property) to a class description. An rdfs:domain statement asserts that the domain values of this property must belong to the class extension of the class description.

Multiple rdfs:domain statements 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>

The rdfs:domain restrictions are global, meaning that they cannot be used for an individual for which the class is not explicitly included in the domain restriction. Because of this feature, rdfs:domain statements should be used with care.

NOTE: In OWL Lite the range value of a rdfs:domain statement may only contain class identifiers or property restrictions.

rdfs:range

For a property one can define (multiple) rdfs:range statements. Syntactically, rdfs:range is a 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 statement asserts that the range 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 restrictions described in the section on class descriptions, rdfs:range restrictions are global. Value restrictions 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 range value of a rdfs:range statement may only contain class identifiers or property restrictions.

5.2 Relations to other properties

owl:equivalentProperty

The owl:equivalentProperty @@ construct can be used to state that two properties have the same property extension. Syntactically, owl:equivalentProperty is a property with as both domain and range an instance of rdf:Property.

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 statements can only be made in OWL Full.

An example of two equivalent properties:

@@ include example of equivalent properties

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 property that takes instances of owl:ObjectProperty as domain and range values. A statement 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 class 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>

@@ make a note that in OWL Full it is allowed to apply inverseOf to datatype properties (as they are a subclass of object properties in OWL Full). Is there is a test case for this?!

5.3 Global cardinality restrictions on properties

owl:FunctionalProperty

OWL defines the class owl:FunctionalProperty as a special subclass of the RDF class rdf:Property. This asserts that the property can only have one (unique) value y for each instance x, i.e. there cannot be two distinct range values y1 and y2 such that the pairs (x,y1) and (x,y2) are both instances of this property. This corresponds to the notion of "optional" value encountered in many data-modelling notations.

There are two typical syntactic variations for writing down functional properties:

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

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

The only difference between the two examples is that the second property axiom gives rise to one additional triple, namely that the property "husband" is an object property. As always, there are other syntactic variations. For example, the second 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" />

owl:InverseFunctionalProperty

The construct owl:InverseFunctionalProperty is also a subclass of the OWL class owl:ObjectProperty. If a property is declared to be inverse-functional, the a range value uniquely determines the domain value (some individual). More formally, if we state that P is an owl:InverseFunctionalProperty, then this asserts that a range 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.

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="hasSocialSecurityNumber">
  <rdfs:domain rdf:resource="Person"/>
</owl:InverseFunctionalProperty>

This example states that a social security number should uniquely identify a human individual (whether that is really always true is another matter). Inverse-functional properties resemble the notion of a key in databases.

Notice that owl:FunctionalProperty and owl:InverseFunctionalProperty specify global cardinality restrictions. 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.

5.4 Logical characteristics of properties

owl:TransitiveProperty

The OWL property class owl:TransitiveProperty is a subclass of owl:ObjectProperty. 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. 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 "Chianti Classico", "Tuscany" and "Italy" are regions, and "Chianti Classico" is a subregion of "Tuscany", and "Tuscany" is a subregion of "Italy", then "Chianti Classico" 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>

owl:SymmetricProperty

The OWL property class owl:SymmetricProperty is, like owl:TransitiveProperty, a subclass of owl:ObjectProperty. 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.

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>

Symmetric properties should have identical domains and ranges to make sense

@@ Is this a hard constraint in OWL??

6. Individuals

6.1 Individual axioms ("facts")

Individual axioms (also called "facts") are statements about individuals, indicating class membership and statements about relevant properties. 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>

These axioms include a number of statements about the opera Tosca, composed by Giacomo Puccini. The opera has three libretto writers. The property premiereDate links an opera to a 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 example below. The example defines some facts about an anonymous instance of the class Measurement, a quantitative observation for which facts such as the observed subject, 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, phenomenon weight for the subject Jane Doe. The measured value 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].

6.2 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 making statements about the identity of individuals:

owl:sameAs and owl:sameIndividualAs

The property owl:sameAs has as its domain and range 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 historical reasons, OWL also supports owl:sameIndividualAs as a synonym with exactly the same meaning.

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:

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

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 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.

owl:differentFrom

An owl:differentFrom property links an individual to another 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 operas, which are all different individuals.

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. The owl:AllDifferent construct is a special OWL class, for which the property owl:distinctMembers is defined, which links an instance of owl:Different 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="#Tools"/>
    <Opera rdf:about="#Turandot"/>
    <Opera rdf:about="#Salome"/>
  </owl:distinctMembers>
</owl:AllDifferent>

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

@@ Include example of how to add to this list?!

7. 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 two types of data range specifications:

7.1 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. A typed literal needs to have an RDF attribute rdf:datatype of which the value should be a URI reference to an XML Schema datatype. Note that even if the range of a property is declared to be of a certain datatype, RDF still requires a rdf:datatype attribute in a statement about this property, otherwise it is treated as a plain literal. 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>

The datatype dateTime is defined by XML Schema.

The OWL Guide document [OWL Guide] contains a table of frequently-used data types. For a full listing, see the XML Schema documentation [XML Schema Datatypes].

@@ Discuss use of XMLLiteral, QName as datatypes

7.2 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 range value of owl:oneOf is a list of literals. Unfortunately, we cannot use the rdf:parseType="Collection" idiom for specifying this 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.

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>
    <rdfs:Class>
      <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>
    </rdfs:Class>
  </rdfs:range>
</owl:DatatypeProperty>

NOTE: Enumerated datatypes are not part of OWL Lite.

@@ What should be the class of the enumerated datatype? It cannot be rdfs:Datatype, because that should be an XML Schema datatype. For the moment, we used rdfs:Class (as AS&S does), but this may puzzle people. The alternative is to define a class owl:Datatype.

8. OWL Full, OWL DL and OWL Lite

In the introduction we briefly discussed the three sublanguages of OWL. In this section an informal specification is given of the differences between the three "species" of OWL. A formal account of the differences is given in the Abstract Syntax and Semantics document [OWL AS&S].

8.1 OWL Full

OWL Full is not actually a sublanguage. OWL Full contains all the OWL language constructs and provides free, unconstrained mixing of OWL and RDF. The construct 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). 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 to also be part of the individual domain. 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). Although from the semantics point of view it is not forbidden in OWL Full to declare datatype properties to be inverse, transitive, or symmetric, in practice this does not make much sense (RDF does not allow data values as the subject of a statement). However, for inverse-functional properties this does make sense and such a definition is thus explicitly allowed in OWL Full.

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.

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:

The last constraint implies that all classes and properties that one refers to are explicitly defined in the same ontology as OWL classes or properties, respectively. For example, if the ontology contains the following component:

<owl:Class rdf:ID="C1">
  <rdfs:subClassOf rdf:about="#C2" />
</owl:Class>

then the ontology should also contain a owl:Class axiom for "C2".

An OWL DL ontology that imports a OWL Full ontology becomes an OWL Full ontology.

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 restriction 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.

8.3 OWL Lite

OWL Lite abides to all the restrictions OWL DL puts on the use of the OWL language constructs. In addition, OWL Lite puts the following restrictions on the use of the OWL vocabulary:

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, value and cardinality restrictions. In addition, OWL Lite allows properties to be made optional or required (using the cardinality features).

If an OWL Lite ontology imports an OWL DL or OWL Full ontology, it effectively becomes an OWL DL resp. OWL Full ontology.

OWL Lite is constrained to be a subset of OWL DL, thus assuring it retains the desirable reasoning features of that sublanguage. In addition, 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 databases, markup tools, or other non-reasoning tools. The Web Ontology Working Group has not designed a specific such subset or provided a name for it.

9. Class and property deprecation

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. Once again, 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:DeprecatedClass>

<owl:Class rdf:ID="Automobile">
  <owl:equivalentClass rdf:resource="#Car"/>
  <!-- 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:Class>

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

<owl:ObjectProperty rdf:ID="drives">
  <owl:inverseOf rdf:resource="#hasDriver"/>
</owl:ObjectProperty>

Appendix A. Index of all language elements

[OWL Reference]
(this document)
[OWL Abstract Syntax]
(normative)
[OWL Guide]
(examples)
owl:AllDifferent owl:AllDifferent owl:AllDifferent
owl:allValuesFrom owl:allValuesFrom owl:allValuesFrom
owl:backwardCompatibleWith owl:backwardCompatibleWith owl:backwardCompatibleWith
owl:cardinality owl:cardinality owl:cardinality
owl:Class owl:Class owl:Class
owl:complementOf owl:complementOf owl:complementOf
rdfs:Datatype
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
rdfs:domain
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:priorVersion owl:priorVersion owl:priorVersion
rdf:Property @@
rdfs:range
owl:Restriction owl:Restriction owl:Restriction
owl:sameAs owl:sameAs owl:sameAs
owl:equivalentClass owl:equivalentClass @@ owl:equivalentClass
owl:sameIndividualAs owl:sameIndividualAs owl:sameIndividualAs
owl:equivalentProperty owl:equivalentProperty @@ owl:equivalentProperty
owl:someValuesFrom owl:someValuesFrom owl:someValuesFrom
rdfs:subClassOf
rdfs:subPropertyOf
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 @@ owl:versionInfo @@

Appendix B. RDF Schema of OWL

<?xml version="1.0"?>
<!DOCTYPE owl [
     <!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
  xml:base  ="http://www.w3.org/2002/07/owl"
  xmlns     ="&owl;"
  xmlns:owl ="&owl;"
  xmlns:rdf ="&rdf;"
  xmlns:rdfs="&rdfs;"
  xmlns:dc  ="http://purl.org/dc/elements/1.1/"
>

<Ontology rdf:about="">
  <versionInfo>owl.owl,v 1.21</versionInfo>
  <imports rdf:resource="http://www.w3.org/2000/01/rdf-schema"/>
  <dc:title>OWL Web Ontology Language</dc:title>
  <dc:creator>W3C Web Ontology (WebOnt) Working Group</dc:creator>
  <dc:subject>OWL; Web Ontology Language; Semantic Web</dc:subject>
  <dc:description>Classes and properties for the OWL Web Ontology 
    Language specified in RDF Schema
  </dc:description>
  <dc:publisher>W3C</dc:publisher>
  <dc:date>Jan 15, 2003</dc:date>
  <dc:format>text/xml</dc:format>
  <dc:language>en</dc:language>
  <dc:identifier>http://www.w3.org/2002/07/owl</dc:identifier>
</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="sameIndividualAs">
  <rdfs:label>sameIndividualAs</rdfs:label>
  <rdfs:domain rdf:resource="#Thing"/>
  <rdfs:range rdf:resource="#Thing"/>
</rdf:Property>

<rdf:Property rdf:ID="sameAs"> 
  <rdfs:label>sameAs</rdfs:label>
  <EquivalentProperty rdf:resource="#sameIndividualAs"/>
</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="#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="&rdf;Property"/>
</rdfs:Class>

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

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

<rdf:Property rdf:ID="versionInfo">
  <rdfs:label>versionInfo</rdfs:label>
  <rdfs:domain rdf:resource="#Ontology"/>
</rdf:Property>

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

<rdf:Property rdf:ID="backwardCompatibleWith">
  <rdfs:label>backwardCompatibleWith</rdfs:label>
  <rdfs:subPropertyOf rdf:resource="#priorVersion"/>
</rdf:Property>

<rdf:Property rdf:ID="incompatibleWith">
  <rdfs:label>incompatibleWith</rdfs:label>
  <rdfs:subPropertyOf rdf:resource="#priorVersion" />
</rdf:Property>

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

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

</rdf:RDF>

Appendix C. OWL Quick Reference

Classes defined by OWL:
rdfs:Class
owl:AllDifferent
owl:Class
owl:DatatypeProperty
owl:DeprecatedClass
owl:DeprecatedProperty
owl:FunctionalProperty
owl:InverseFunctionalProperty
owl:Nothing
owl:ObjectProperty
owl:Ontology
owl:Restriction
owl:SymmetricProperty
owl:Thing

Properties defined by OWL:
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: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:sameIndividualAs 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 namespace was changed to http://www.w3.org/2002/07/owl.
  2. Various updates to RDF and RDF Schema from the RDF Core Working Group were incorporated, including
  3. Qualified restrictions were removed from the language, resulting in the removal of the following properties:
  4. 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:sameClassAs owl:equivalentClass
    daml:samePropertyAs owl:equivalentProperty
    daml:toClass owl:allValuesFrom
    daml:UnambiguousProperty owl:InverseFunctionalProperty
    daml:UniqueProperty owl:FunctionalProperty
  5. owl:SymmetricProperty was added.
  6. An owl:DatatypeProperty may be an owl:InverseFunctionalProperty in OWL Full.
  7. Synonyms for RDF and RDF Schema classes and properties were removed from the language, resulting in the removal of:
  8. daml:disjointUnionOf was removed from the language, since it can be effected using owl:unionOf or rdfs:subClassOf and owl:disjointWith.
  9. daml:equivalentTo was renamed to owl:sameAs, and is no longer a superproperty of owl:equivalentClass, owl:equivalentProperty, and owl:sameIndividualAs
  10. The following properties and classes were added to support versioning:
  11. owl:AllDifferent and owl:distinctMembers were added to address the Unique Names Assumption.

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 Abstract Syntax]
Web Ontology Language (OWL) Abstract Syntax and Semantics. Peter F. Patel-Schneider, Patrick Hayes, and Ian Horrocks, eds. W3C Working Draft 3 February 2003. Latest version is available at http://www.w3.org/TR/owl-semantics/. Editor's draft is available at http://www-db.research.bell-labs.com/user/pfps/owl/semantics/.
[OWL Overview]
Web Ontology Language (OWL Lite and OWL) Feature Synopsis Version 1.0. Deborah L. McGuinness and Frank van Harmelen, eds. W3C Working Draft 29 Jul 2002. Latest version is available at http://www.w3.org/TR/owl-features/. Editor's draft is available at http://www.ksl.stanford.edu/people/dlm/webont/OWLOverview.htm.
[OWL Guide]
Web Ontology Language (OWL) Guide Version 1.0. Michael K. Smith, Christopher Welty, Raphael Volz, and Deborah McGuinness. W3C Working Draft 4 November 2002. Latest version is available at http://www.w3.org/TR/owl-guide/. Editor's draft is available at http://www.w3.org/2001/sw/WebOnt/guide-src/Guide.html.
[OWL Requirements]
Web Ontology Language (OWL) Use Cases and Requirements. Jeff Heflin, ed. W3C Working Draft 3 February 2003. Latest version is available at http://www.w3.org/TR/webont-req/.
[OWL Test Cases]
Web Ontology Language (OWL) Test Cases. Jeremy J. Carroll and Jos De Roo, eds. W3C Working Draft 24 October 2002. 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 Working Draft 23 January 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 Working Draft 23 January 2003. Latest version is available at http://www.w3.org/TR/rdf-schema/.
[RDF Semantics]
RDF Semantics. Patrick Hayes, ed. W3C Working Draft 23 January 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 Working Draft 23 January 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.