7.3.21 GeneralizationSet

*Generalizations

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    PackageableElement (from Kernel ) on page 111

*Description

   Each Generalization is a binary relationship that relates a specific Classifier to a more general Classifier (i.e., from a class to its superclasses). Each GeneralizationSet defines a particular set of Generalization relationships that describe the way in which a general Classifier (or superclass) may be divided using specific subtypes. For example, a GeneralizationSet could define a partitioning of the class Person into two subclasses: Male Person and Female Person. Here, the GeneralizationSet would associate two instances of Generalization. Both instances would have Person as the general classifier; however, one Generalization would involve Male Person as the specific Classifier and the other would involve Female Person as the specific classifier. In other words, the class Person can here be said to be partitioned into two subclasses: Male Person and Female Person. Person could also be divided into North American Person, Asian Person, European Person, or something else. This collection of subsets would define a different GeneralizationSet that would associate with three other Generalization relationships. All three would have Person as the general Classifier; only the specific classifiers would differ (i.e., North American Person, Asian Person, and European Person).

*Attributes

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   • isCovering : Boolean Indicates (via the associated Generalizations) whether or not the set of specific Classifiers are covering for a particular general classifier. When isCovering is true, every instance of a particular general Classifier is also an instance of at least one of its specific Classifiers for the GeneralizationSet . When isCovering is false, there are one or more instances of the particular general Classifier that are not instances of at least one of its specific Classifiers defined for the GeneralizationSet . For example, Person could have two Generalization relationships each with a different specific Classifier: Male Person and Female Person. This GeneralizationSet would be covering because every instance of Person would be an instance of Male Person or Female Person. In contrast, Person could have a three Generalization relationship involving three specific Classifiers: North American Person, Asian Person, and European Person. This GeneralizationSet would not be covering because there are instances of Person for which these three specific Classifiers do not apply. The first example, then, could be read: any Person would be specialized as either being a Male Person or a Female Person— and nothing else; the second could be read: any Person would be specialized as being North American Person, Asian Person, European Person, or something else. Default value is false.

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   • isDisjoint : Boolean Indicates whether or not the set of specific Classifiers in a Generalization relationship have instance in common. If isDisjoint is true, the specific Classifiers for a particular GeneralizationSet have no members in common; that is, their intersection is empty. If isDisjoint is false, the specific Classifiers in a particular GeneralizationSet have one or more members in common; that is, their intersection is not empty. For example, Person could have two Generalization relationships, each with the different specific Classifier: Manager or Staff. This would be disjoint because every instance of Person must either be a Manager or Staff. In contrast, Person could have two Generalization relationships involving two specific (and non-covering) Classifiers: Sales Person and Manager. This GeneralizationSet would not be disjoint because there are instances of Person that can be a Sales Person and a Manager. Default value is false.

*Associations

• generalization : Generalization [*] Designates the instances of Generalization that are members of a given GeneralizationSet (see constraint [1] below).

• powertype : Classifier [0..1] Designates the Classifier that is defined as the power type for the associated GeneralizationSet (see constraint [2] below).

*Constraints

   [1] Every Generalization associated with a particular GeneralizationSet must have the same general Classifier.

   generalization->collect(g | g.general)->asSet()->size() <= 1

   [2] The Classifier that maps to a GeneralizationSet may neither be a specific nor a general Classifier in any of the Generalization relationships defined for that GeneralizationSet . In other words, a power type may not be an instance of itself nor may its instances be its subclasses.

*Semantics

   The generalizationSet association designates the collection of subsets to which the Generalization link belongs. All of the Generalization links that share a given general Classifier are divided into subsets (e.g., partitions or overlapping subset groups) using the generalizationSet association. Each collection of subsets represents an orthogonal dimension of specialization of the general Classifier.

   As mentioned above, in essence, a power type is a class whose instances are subclasses of another class. Power types, then, are metaclasses with an extra twist: the instances can also be subclasses. The powertype association relates a classifier to the instances of that classifier, which are the specific classifiers identified for a GeneralizationSet . For example, the Bank Account Type classifier could associate with a GeneralizationSet that has Generalizations with specific classifiers of Checking Account and Savings Account. Here, then, Checking Account and Savings Account are instances of Bank Account Type. Furthermore, if the Generalization relationship has a general classifier of Bank Account, then Checking Account and Savings Account are also subclasses of Bank Account. Therefore, Checking Account and Savings Account are both instances of Bank Account Type and subclasses of Bank Account. (For more explanation and examples see Examples on page 79.)

*Notation

   The notation to express the grouping of Generalizations into GeneralizationSet s was presented in the Notation section of Generalization, above. To indicate whether or not a generalization set is covering and disjoint, each set should be labeled with one of the constraints indicated below.

   {complete, disjoint} -Indicates the generalization set is covering and its specific Classifiers have no common instances.

   {incomplete, disjoint} -Indicates the generalization set is not covering and its specific Classifiers have no common instances*. {complete, overlapping} -Indicates the generalization set is covering and its specific Classifiers do share common instances. {incomplete, overlapping} -Indicates the generalization set is not covering and its specific Classifiers do share common instances.

   * default is {incomplete, disjoint}

   Figure 7.45 - Generalization set constraint notation

   Graphically, the GeneralizationSet constraints are placed next to the sets, whether the common arrowhead notation is employed of the dashed line, as illustrated below..

   (a) GeneralizationSet constraint when sharing common generalization arrowhead.

   {Generalization Set constraint-3} {Generalization Set constraint-4}

   Power type specification is indicated by placing the name of the powertype Classifier—preceded by a colon—next to the GeneralizationSet graphically containing the specific classifiers that are the instances of the power type. The illustration below indicates how this would appear for both the shared arrowhead and the dashed-line notation for GeneralizationSet s.

   SpecificClassifier-3

   (a) Power type specification when sharing common generalization arrowhead

   (b) Power type specification using dashed-line notation

   Figure 7.47 - Power type notation

*Examples

   In the illustration below, the Person class can be specialized as either a Female Person or a Male Person. Because this GeneralizationSet is partitioned (i.e., is constrained to be complete and disjoint), each instance of Person must either be a Female Person or a Male Person; that is, it must be one or the other and not both. (Therefore, Person is an abstract class because a Person object may not exist without being either a Female Person or a Male Person.) Furthermore, a Person object can be specialized as an Employee. The generalization set here is expressed as {incomplete, disjoint}, which means that instances of Persons can be subset as Employees or some other unnamed collection that consists of all non-Employee instances. In other words, Persons can either be an Employee or in the complement of Employee, and not both. Taken together, the diagram indicates that a Person may be 1) either a Male Person or Female Person, and 2) an Employee or not. When expressed in this manner, it is possible to partition the instances of a classifier using a disjunctive normal form (DNF).