30 
 
The following are some examples of classes of individuals that we might want to define via property 
restrictions: 
• The class of individuals with at least one hasChild relation. 
• The class of individuals with 2 or more hasChild relations. 
• The class of individuals that have at least one hasTopping relationship to individuals that are 
members of MozzarellaTopping – i.e. the class of things that have at least a mozzarella 
topping. 
• The class of individuals that are Pizzas and only have hasTopping relations to instances of the 
class VegetableTopping (i.e., VegetarianPizza). 
In OWL we can describe all of the above classes using restrictions. OWL restrictions fall into three main 
categories: 
1. Quantifier restrictions. These describe that a property must have some or all values that are of a 
particular class.  
2. Cardinality restrictions. These describe the number of individuals that must be related to a class 
by a specific property.  
3. hasValue restrictions. These describe specific values that a property must have.  
We will initially use quantifier restrictions. Quantifier restrictions can be further categorized as existential 
restrictions and universal restrictions6. Both types of restrictions will be illustrated with examples in this 
tutorial.  
• Existential restrictions describe classes of individuals that participate in at least one relation along 
a specified property. For example, the class of individuals who have at least one (or some) 
hasTopping relation to instances of VegetableTopping. In OWL the keyword some is used 
to denote existential restrictions.  
• Universal restrictions describe classes of individuals that for a given property only have relations 
along a property to individuals that are members of a specific class. For example, the class of 
individuals that only have hasTopping relations to instances of the class VegetableTopping. 
In OWL they keyword only is used for universal restrictions.  
 
Let’s take a closer look at an example of an existential restriction. The restriction hasTopping some 
MozzarellaTopping is an existential restriction (as indicated by the some keyword), which restricts the 
hasTopping property, and has a filler MozzarellaTopping. This restriction describes the class of 
individuals that have at least one hasTopping relationship to an individual that is a member of the class 
MozzarellaTopping.  
 
 
 
 
 
6 These have the same meaning as existential and universal quantification in First Order Logic.  
A restriction always describes a class. Sometimes (as we will soon see) it can be a defined class. 
Other times it may be an anonymous class. In all cases the class contains all of the individuals 
that satisfy the restriction, i.e., all of the individuals that have the relationships required to be a 
member of the class. In section 9.2 one of our SPARQL queries will return several anonymous 
classes.