Feature Synopsis of the OWL Ontology Language

Peter F. Patel-Schneider
Ian Horrocks
Frank van Harmelen


The OWL Web Ontology Language is being designed by the W3C Web Ontology Working Group as a revision of the DAML+OIL web ontology language. This description of OWL is at a high level, ignoring the details of concrete syntax and precise semantics, and in a more user-friendly fashion than the RDF syntax of DAML+OIL.

Table of contents

  1. Introduction
    1. Differences from DAML+OIL
  2. Ontologies
  3. Axioms
    1. Class Axioms
    2. Property Axioms
    3. Descriptions
    4. Restrictions
  4. Facts

1. Introduction

The W3C Web Ontology Working Group (WebOnt) is tasked with producing a web ontology language extending the reach of XML, RDF, and RDF Schema. This language, called OWL, will be based on the DAML+OIL web ontology language.

A number of problems have been discovered in the design of DAML+OIL, mostly having to do with its relationship with the changes to RDF being undertaken by the W3C RDF Core Working Group.

This document contains a high-level description of the features that will be in OWL, in the form of abstract constructs and informal descriptions of the meaning of these constructs. It is being produced so that WebOnt can continue its work in advance of the resolution of the issues related to the problems in DAML+OIL.

An overview of the language that abstracts from concrete syntax facilities access to and evaluation of the languages. In this overview a high-level abstract syntax is used to make the language features easier to see as it is more compact than an XML- or RDF-based concrete syntax would be. This particular abstract syntax has a frame-like style, where a collection of information about a class or property is given in one large syntactic construct, instead of being divided into a number of atomic chunks (as in most Description Logics) or even being divided into even more triples (as in DAML+OIL), again for ease of readability. The syntax used here is rather informal, even for an abstract syntax - in general the arguments of a construct should be considered to be unordered where the order would not affect the meaning of the construction.

This abstract syntax does not have to worry about any of the problems induced by the RDF triple model, including non-closed and ill-formed lists and restrictions. No parsetype extensions are needed for readability, and issues of coordination with the RDF Core WG are not active at this level of syntax. Layering issues can also be safely ignored.

1.1. Differences from DAML+OIL

The abstract syntax here can be viewed as an abstract syntax for DAML+OIL. It can easily be transformed into DAML+OIL. The only substantive changes from DAML+OIL are

Readers should assume that anything that can be stated in this abstract syntax will end up in OWL, and in a manner maximally compatible with DAML+OIL. There are also a number of minor differences, including a number of changes to the names of the various constructs. These naming changes may indicate potential changes to the preferred names in the concrete syntax for OWL, but the intent of WebOnt is to maintain the DAML+OIL names to the maximum extent reasonable.

2. Ontologies

An OWL ontology is a sequence of axioms and facts, plus inclusion references to other ontologies, which are considered to be included in the ontology. OWL ontologies are web documents, and can be referenced by means of a URI. Ontologies also have a non-logical component (not yet specified) that can be used to record authorship, and other non-logical information to be associated with a ontology.

<ontology> ::= Ontology ( [<authorship-etc>] {<directive>} )

<authorship-etc> ::= ...

<directive> ::= <include>
<directive> ::= <axiom>
<directive> ::= <fact>

<include> ::= Include ( < URI > )

Ontologies incorporate information about classes, properties, and individuals, each of which can have an ID which is a qualified name. (Actually, IDs may be end up being URI references.) Ontologies can also reference XML Schema datatypes, by means of a qualified name for the datatype.

<datatypeID>             ::= <QName>
<classID>                ::= <QName>
<individualID>           ::= <QName>
<datavaluedPropertyID>         ::= <QName>
<individualvaluedPropertyID>   ::= <QName>

If a qualified name is a datatype, i.e., if there is a datatype definition retrievable using the qualified name, then that qualified name cannot be used as the ID for a class. However, a qualified name can be the ID of a class or datatype as well as the ID of a property as well as the ID of an individual.

The meaning of OWL constructs will be defined in a separate document, but some indications of this meaning will be given here. The meaning of OWL will be given via a model-theoretic semantics, which will be an extension of the model theory for RDF. In this model theory there is a domain of discourse, consisting of resources, which is disjoint from the set of XML Schema data values. Individual IDs are used to refer to these resources, and typed data literals are used to refer to the XML Schema data values.

Datatypes then refer to the set of XML Schema data values that is the value space for the datatype and classes refer to sets of individuals. Properties relate individuals to other information. Properties are divided into two disjoint groups, data-valued properties and individual-valued properties. Elements of the first group of properties relate individuals to data values, elements of the second group relate individuals to other individuals.

3. Axioms

Axioms are used to associate class and property IDs with either partial or complete specifications of their characteristics, and to give other logical information about classes and properties. These used to be called definitions, but they are not all definitions in the common sense of the term, as has been made evident in several discussions in the WG, and thus a more-neutral name has been chosen.

The abstract syntax used here for classes is meant to look somewhat like the syntax used in some frame systems. Each class axiom contains a collection of more-general classes; a collection of local property restrictions, in the form of restriction constructs; and a collection of descriptions. The restriction construct gives the local range of a property, how many values are permitted, and a collection of required values. Descriptions are used to specify boolean combinations of restrictions and other descriptions as well as construct sets of individuals. Classes can also be specified by enumeration or be made the same or disjoint.

Properties can be the equivalent to or subproperties of others; can be made functional, inverse functional, or transitive; and can be given global domains and ranges. However, most information about properties is more naturally expressed in restrictions, which allow local cardinality and range information to be specified.

3.1 Class Axioms

The following axiom states that a class is exactly equivalent to the conjunction of a collection of superclasses, property restrictions, and descriptions.

<axiom> ::= EquivalentClass( <classID> {<description>} )

The next axiom is the same, except that the class is an unspecified subclass of the conjunction.

<axiom> ::= SubClass( <classID> {<description>} )

It is also possible to define a class as exactly consisting of a certain set of individuals, as follows. This is just an abbreviation for making a class equivalent to a set.

<axiom> ::= EnumeratedClass( <classID> {<individualID>} )

Finally, it is possible to require that a collection of descriptions have the same members, or to be pairwise disjoint, or that one description is a subclass of another. Note that the last two of these constructs generalize the first two class constructs just above.

<axiom> ::= DisjointClasses( <description> {<description>} )
<axiom> ::= EquivalentClasses( <description> {<description>} )
<axiom> ::= SubClassOf( <description>  <description> )

3.2 Property Axioms

Properties are also specified using a frame-like syntax. Properties are divided into data-valued properties, which relate individuals to data values, like integers, and individual-valued properties, which relate individuals to other individuals. Properties can be given superproperties, allowing the construction of property hierarchy. Individual properties cannot be superproperties of data properties.

Properties can also be given domains and ranges. A domain for a property specifies which individuals are potential subjects of statements that have the property as verb, just as in RDF. The domains of properties are descriptions. Properties can have multiple domains, in which case only individuals that belong to all of the domains are potential subjects. A range for a property specifies which individuals or data values can be objects of the property. Again, properties can have multiple ranges, in which case only individuals or data values that belong to all of the ranges are potential objects. Ranges for individual-valued properties are descriptions; ranges for data-valued properties are datatypes or sets of data values.

Data-valued properties can be specified as functional, i.e., there is at most one relationship for that property between a given individual and a data value. Individual-valued properties can be specified as functional, inverse functional, or one-to-one. Individual-valued properties can be specified to be the inverse of another property. Finally, individual-valued properties can be specified as transitive. Individual-valued properties that are transitive, or that have transitive sub-properties, may not have cardinality conditions expressed on them, either in restrictions or by being functional, inverse functional, or one-to-one. This is necessary in order to maintain the decidability of the language.

<axiom> ::= DataProperty ( <datavaluedPropertyID> {super=<datavaluedPropertyID>}
                           {domain=<description>} {range=<dataRange>}
			   [Functional] )

<axiom> ::= IndividualProperty 
	( <individualvaluedPropertyID> {super=<individualvaluedPropertyID>}
	  {domain=<description>} {range=<description>} 
	  [inverseOf=<individualvaluedPropertyID>] [Symmetric] 
	  [Functional | InverseFunctional | OneToOne | Transitive] )

A dataRange, i.e., the range of a data-valued property, is either a datatype or a set of data values, which consist of a datatype and the lexical representation of a data value in that datatype.

<dataRange> ::= <datatypeID>
<dataRange> ::= OneOf({<dataLiteral>} )
<dataLiteral> ::= <datatypeID>  <lexical-form>

The following axioms make several properties be the same, or make one property be a sub-property of another.

<axiom> ::= EquivalentProperties( <datavaluedPropertyID>  {<datavaluedPropertyID>} )
<axiom> ::= SubPropertyOf( <datavaluedPropertyID>  <datavaluedPropertyID> )
<axiom> ::= EquivalentProperties( <individualvaluedPropertyID>  {<individualvaluedPropertyID>} )
<axiom> ::= SubPropertyOf( <individualvaluedPropertyID>  <individualvaluedPropertyID> )

3.3 Descriptions

Descriptions include class IDs and the restriction constructor. Descriptions can also be boolean combinations of other descriptions, and sets of individuals.

<description> ::= <classID>
                | <restriction>
		| UnionOf( <description> {<description>} )
		| IntersectionOf( <description> {<description>} )
		| ComplementOf( <description> )
		| OneOf({<individualID>} )

3.4 Restrictions

Restrictions provide constraints on properties. The localRange part of a restriction makes the constraint that all values of the property for object in the class must belong to the specified class or data range. Each required part makes the constraint that there must be at least one value for the property that belongs to the specified class or datatype range. Each value part makes the constraint that the individual or data value must be a value for the property. The cardinality part says how many distinct values there are for the property for each individual in the class. Properties that are transitive, or that have transitive sub-properties, may not have cardinality conditions expressed on them in restrictions.

<restriction> ::= restriction( <datavaluedPropertyID> [localRange=<dataRange>]
			       {required=<dataRange>} {value=<dataLiteral>}
			       [cardinality=<cardinality>] )
<restriction> ::= restriction( <individualvaluedPropertyID> [localRange=<description>]
                               {required=<description>} {value=<individualID>}
			       [cardinality=<cardinality>] )
<cardinality> ::= atleast( <positive-integer> )
 		| atmost( <non-negative-integer> )
                | atleast( <positive-integer> ) atmost( <non-negative-integer> )
		| exactly( <non-negative-integer> )

4. Facts

Facts state information about particular individuals in the form of a class that the individual belongs to plus properties and values. Individuals can either be given an individualID or be anonymous (blank nodes in RDF terms). The syntax here is set up to mirror the normal RDF/XML syntax.

<fact> ::= <individualFact> 
<individualFact> ::= Individual( [<individualID>] {type=<classID>}
                       {<propertyValue>} )
<propertyValue> ::= ( <individualvaluedPropertyID>  <individualFact> )
                  | ( <individualvaluedPropertyID>  <individualID> )
                  | ( <datavaluedPropertyID>  <dataLiteral> )

Facts can be used to make individual IDs denote the same individual, or pairwise-distinct individuals.

<fact> ::= SameIndividual( <individualID> {<individualID>} )
<fact> ::= DifferentIndividuals( <individualID> {<individualID>} )