Ontology: Fundamentals and Languages ◾ 51
2.8.3.3.3 Enumeration
A class description of enumeration denes an anonymous class that contains exactly
the enumerated individuals. It is dened with the owl:oneOf property that points
to a list of individuals that serve as instances of the class. It is essential to describe
the complete set of members and subelements for each member. In the example
below, the class owl:ing is used but more particular classes could be used too.
<owl:IndianSubcontinent>
<owl:oneOf rdf:parseType=”Collection”>
<owl:Thing rdf:about=”#India”/>
<owl:Thing rdf:about=“#Bangala Desh”/>
<owl:Thing rdf:about=”#Pakistan”/>
</owl:oneOf>
</owl:IndianSubcontinent>
2.8.3.3.4 Property Restrictions
A local property restriction denes an anonymous class of all individuals that sat-
isfy the restriction:
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:ID=”hasRoom”/>
</owl:onProperty>
<owl:someValuesFrom>
<owl:Class rdf:ID=”Guestroom”/>
</owl:someValuesFrom>
</owl:Restriction>
OWL distinguishes two kinds of restrictions.
2.8.3.3.4.1 Value Restrictions—A value restriction puts constraints on the
value range of a property when applied to this particular class description. e
three types of value restrictions are:
owl:allValuesFrom
owl:someValuesFrom
owl:hasValue
An owl:allValuesFrom restriction property links a restriction class to either a class
description or a data range:
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about=”#hasRoom”/>
52 ◾ Rajendra Akerkar
</owl:onProperty>
<owl:allValuesFrom>
<owl:Class>
<owl:unionOf rdf:parseType=”Collection”>
<owl:Class rdf:about=”#Guestroom”/>
<owl:Class rdf:ID=”ConferenceRoom”/>
</owl:unionOf>
</owl:Class>
</owl:allValuesFrom>
</owl:Restriction>
An owl:allValuesFrom restriction is analogous to the universal (for-all) quanti-
er of predicate logic. Similarly, the value restriction owl:someValuesFrom is a
property that links a restriction class to a class description or a data range. e
owl:someValuesFrom restriction is analogous to the existential quantier of predi-
cate logic. Also, the owl:hasValue restriction is a property that links a restriction
class to a value V that may be an individual or data value.
2.8.3.3.4.2 Cardinality Restrictions—OWL provides three constructs for
restricting the cardinality of properties locally within a class context:
owl:maxCardinality
owl:minCardinality
owl:cardinality
A restriction containing an owl:maxCardinality statement describes a class of all
individuals that have at most specied distinct range values (individuals or data
values) for the property concerned. e following example describes a class of indi-
viduals that have at most two activities:
<owl:Restriction>
<owl:onProperty rdf:resource=”#has_Activities” />
<owl:maxCardinality rdf:datatype=”&xsd;nonNegativeInteger
”> 2
</owl:maxCardinality>
</owl:Restriction>
A restriction containing an owl:minCardinality statement describes a class of all
individuals that have at least specied distinct range values (individuals or data
values) for the property concerned. e following example describes a class of indi-
viduals that have at least two activities:
<owl:Restriction>
<owl:onProperty rdf:resource=”#has_Activities” />
<owl:minCardinality rdf:datatype=”&xsd;nonNegative
Integer”> 2
</owl:minCardinality>
</owl:Restriction>
Ontology: Fundamentals and Languages ◾ 53
A restriction containing an owl:cardinality statement describes a class of all indi-
viduals that have exactly specied distinct range values (individuals or data values)
for the property concerned. e example given below describes a class of individu-
als that have exactly two activities:
<owl:Restriction>
<owl:onProperty rdf:resource=”#has_Activities” />
<owl:cardinality rdf:datatype=”&xsd;nonNegative
Integer”>2
</owl:cardinality>
</owl:Restriction>
2.8.3.3.5 Operators
e three operators in OWL are given standard set operator names: intersection,
union, and complement. ese operators can be used to dene Boolean combi-
nations of classes and may be dened in OWL. owl:intersectionOf describes the
class extension containing precisely those individuals that are members of the class
extension of all class descriptions in the range list:
<owl:Class>
<owl:intersectionOf rdf:parseType=”Collection”>
<owl:Class rdf:about=“#GuestRoom”/>
<owl:Class rdf:about=“#ConferenceRoom”/>
</owl:intersectionOf>
</owl:Class>
owl:intersectionOf can be viewed as analogous to a logical conjunction. owl:unionOf
is analogous to logical disjunction:
<owl:Class>
<owl:unionOf rdf:parseType=”Collection”>
<owl:Class rdf:about=”#Event”/>
<owl:Class rdf:about=”#Infrastructure”/>
</owl:unionOf>
</owl:Class>
owl:complementOf means items do NOT belong to. Here owl:complementOf is
analogous to logical negation, but restricted to individuals only. e statement
Neither GuestRoom Nor ConferenceRoom could be written as:
<owl:Class>
<owl:complementOf>
<owl:Class>
<owl:unionOf
rdf:parseType=”Collection”>
<owl:Class
54 ◾ Rajendra Akerkar
rdf:about=”#GuestRoom”/>
<owl:Class
rdf:about=”#ConferenceRoom”/>
</owl:unionOf>
</owl:Class>
</owl:complementOf>
</owl:Class>
Note that every Boolean operator takes one or more classes as operands. Such classes
may be named classes or complex classes formed from descriptions.
2.8.3.3.6 Properties
A property is a binary relationship between individuals or between individu-
als and data values. Properties let us assert general facts about the members of
classes and specic facts about individuals. Every property has a domain and a
range. A domain is a set of individuals to which the property can be applied; a
range is a set of individuals that the property may have as values. rdfs:domain
links a property to a class description that asserts that the domain values of the
property must belong to the class extension of the class description. Both the
domain and range of a property are global restrictions. A restriction is stated
on a property and not only on a property when it is associated with a specic
class. Both the domain and range of a property may be used to infer the type of
individual. For a property, one can dene multiple rdfs:domain statements that
will be interpreted as a conjunction. Further, a domain can be a disjunction of
multiple classes (owl:unionOf ).
<owl:ObjectProperty rdf:ID=”hasTimePeriond”>
<rdfs:comment
rdf:datatype=”http://www.w3.org/2001/XMLSchema#string”
>This property links an individual representing a date
period.</rdfs:comment>
<rdfs:range rdf:resource=”#TimePeriod”/>
<rdfs:domain>
<owl:Class>
<owl:unionOf rdf:parseType=”Collection”>
<owl:Class rdf:about=”#OpeningHours”/>
<owl:Class rdf:about=”#Event”/>
</owl:unionOf>
</owl:Class>
</rdfs:domain>
</owl:ObjectProperty>
An rdfs:range links a property to either a class description or a data range. It asserts
that the range values of the property must belong to the class extension of the class
Ontology: Fundamentals and Languages ◾ 55
description or to data values in the specied data range. As with rdfs:domain, con-
junctions of multiple rdfs:range statements are allowed, and dierent combinations
of class descriptions such as owl:unionOf can be used.
2.8.3.3.7 Datatypes
OWL allows two types of data range specications:
◾ User dened XML schema datatypes such as xsd:string, xsd:integer,
xsd:positiveInteger
◾ Enumerated datatypes that make use of the owl:oneOf construct; the range value
of owl:oneOf is a list of literals
Most XML schema datatypes are supported by OWL 2 DL. Additionally, OWL
2 introduced some new datatypes and now supports owl:boolean, owl:string,
xsd:integer, xsd:dateTime, xsd:hexBinary, and a number of datatypes derived from
them by placing various restrictions on them. In addition, xsd:decimal, xsd:double,
and xsd:oat will most likely be complemented with owl:real (it is interpreted as
the set of all real numbers). OWL 2 also provides a datatype restriction construct
allowing new datatypes to be dened by restricting the built-in datatypes in vari-
ous ways.
2.8.3.3.7.1 Individual and Axiom—An individual is a member of some dened
classes. Two dierent names of individuals do not mean that the names refer to dif-
ferent individuals. Remember that OWL does not support multidened datatypes.
Individual ordering is not important for dening individuals. e denition of a
specic individual can be divided into various parts in an ontology. Every indi-
vidual in the OWL world is a member of the class owl:ing:
< owl:Thing rdf:ID=“Accommodation“/>
Accommodation ∈Thing
An individual can be a member of a specic class:
<Camping rdf:ID=“Accommodation“/>
Accommodation ∈ Camping
An individual may be a member of more than one class:
<owl:Individual rdf:about=”#Accommodation”>
<rdf:type>
<owl:Class rdf:about=”#Camping”/>
</rdf:type>
<rdf:type>
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