A reference property (such as chair in the example shown in Figure 8.1 above) can be modeled in a UML class diagram in the form of an association end owned by its domain class, which is visualized with the help of a small filled circle (also called a "dot"). This requires to connect the domain class and the range class of the reference property with an association line, place an ownership dot at the end of this line at the range class side, and annotate this association end with the property name and with a multiplicity symbol, as shown in Figure 8.2 below for the case of our example. In this way we get a unidirectional association, the source class of which is the property's domain and the target class of which is the property's range.

The fact that an association end is owned by the class at the other end, as visually expressed by the association end ownership dot at the association end chair in the example shown in Figure 8.2 below, implies that the association end represents a reference property. In the example of Figure 8.2, the represented reference property is Committee::chair having ClubMember as range. Such an association, with only one association end ownership dot, is unidirectional in the sense that it allows `navigation´ (object access) in one direction only: from the class at the opposite side of the dot (the source class) to the class where the dot is placed (the target class).

Figure 8.2. An association end with a "dot"

Thus, the two diagrams shown in Figure 8.1 and Figure 8.2 express essentially equivalent models. When a reference property, like chair in Figure 8.1, is modeled by an association end with a "dot", then the property's multiplicity is attached to the association end. Since in a design model, all association ends need to have a multiplicity, we also have to define a multiplicity for the other end at the side of the Committee class, which represents the inverse of the property. This multiplicity (of the inverse property) is not available in the original property description in the model shown in Figure 8.1, so it has to be added according to the intended semantics of the association. It can be obtained by answering the question "is it mandatory that any ClubMember is the chair of a Committee?" for finding the minimum cardinality and the question "can a ClubMember be the chair of more than one Committee?" for finding the maximum cardinality.

When the value of a property is a set of values from its range, the property is non-functional and its multiplicity is either 0..* or n..* where n > 0. Instead of 0..*, which means "neither mandatory nor functional", we can simply write the asterisk symbol *. The association shown in Figure 8.2 assigns at most one object of type ClubMember as chair to an object of type Committee. Consequently, it's an example of a functional association.

An overview about the different cases of functionality of an association is provided in the following table:

Notice that the directionality and the functionality type of an association are independent of each other. So, a unidirectional association can be either functional (one-to-one or many-to-one), or non-functional (one-to-many or many-to-many).