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CHAPTER 12 ANALYSIS MODELING 305

FIGURE 12.4
Relationships
Book Bookstore

(a) A basic connection between objects

Orders

Displays
Stocks
Book Bookstore
Sells

Returns
(b) Relationships between objects

The relationships orders, displays, stocks, sells, and returns define the relevant con-
nections between book and bookstore. Figure 12.4b illustrates these object/rela-
tionship pairs graphically.
It is important to note that object/relationship pairs are bidirectional. That is, they
can be read in either direction. A bookstore orders books or books are ordered by a
bookstore. 2

12.3.2 Cardinality and Modality
The elements of data modeling—data objects, attributes, and relationships— provide
the basis for understanding the information domain of a problem. However, addi-
tional information related to these basic elements must also be understood.
We have defined a set of objects and represented the object/relationship pairs that
bind them. But a simple pair that states: object X relates to object Y does not pro-
vide enough information for software engineering purposes. We must understand
how many occurrences of object X are related to how many occurrences of object
Y. This leads to a data modeling concept called cardinality.

Cardinality. The data model must be capable of representing the number of occur-
rences objects in a given relationship. Tillmann [TIL93] defines the cardinality of an
object/relationship pair in the following manner:

2 To avoid ambiguity, the manner in which a relationship is labeled must be considered. For exam-
ple, if context is not considered for a bidirectional relation, Figure 12.4b could be misinterpreted
to mean that books order bookstores. In such cases, rephrasing is necessary.