amp-sidebar 6

In OWL properties define binary relations with the same semantics and characteristics as binary relations in First Order Logic.

There are two types of OWL properties for describing a domain: Object properties and Data properties.

Object properties have classes as their domain and range.

Data properties have classes as their domain and simple datatypes such as xsd:string or xsd:dateTime as their range.

In figure 3.3 the individual Michael is related to the individual USA by the property livesIn.

Consider all the individuals who are an instance of Person and also have the same relation, that each livesIn the USA.

This group is a set or OWL class such as USAResidents.

In OWL a class can be defined by describing the various properties and values that hold for all individuals in the class. Such definitions are called restrictions in OWL.

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 – that is, 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 (that is, 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 restrictions [6].

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 us 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.

The restrictions for a class are displayed and edited using the Class Description View shown in Figure 4.17.

The Class Description View holds most of the information used to describe a class.

The Class Description View is a powerful way of describing and defining classes. It is one of the most important differences between describing classes in OWL and in other models such as most object-oriented programming languages.

In other models there is no formal definition that describes why one class is a subclass of another, in OWL there is. Indeed, the OWL classifier can actually redefine the class hierarchy based on the logical restrictions defined by the user. We will see an example of this later in the tutorial.

---

[6] These have the same meaning as existential and universal quantification in First Order Logic.