Practical Guidelines for Supertype and Subtype Modeling - High-Performance Web Databases: Design, Development, and Deployment - page 316

(e.g., X,Y) in R. Basic set theory does not, however, support the intersec-
tion of two sets of a different degree (e.g., [X] versus [X,Y]).

The definition of a detail subset may require the data modeler to exten-
sively rethink the original superset definitions. This problem is inherent in
basic sets-how to determine that the criteria for including a member in a set
is complete and unambiguous for all occurrences. Godel's incompleteness
theorem proves that no definition of a set is absolutely complete. The chal-
lenge is to provide a definition that is complete for all practical purposes.

ENTITY SETS

Membership in each set defined by an entity is determined by the unique
attributes of the entity (i.e., algebraic variables) and the values that those
attributes can take on (i.e., their domains). A subtype entity defines a subset
of the set that is defined by the supertype entity. All the rigor and rules of set
theory apply and all the inherent problems remain. Practical guidelines
must be set up to ensure that subtype entities defined within project data
models serve appropriate purposes and define useful entity subsets.

Arbitrary and indiscriminate subtype modeling leads to endless discus-
sions that add little or no value to the project and may be counterproduc-
tive. Set theory illustrates that all sets have an infinite number of subsets,
most of which contain no members. Subtype entity proliferation in a model
without defined goals for the entities leads to cluttered model diagrams
that may hide relevant business detail from the analyst. If the analyst exam-
ines the uses that subtype modeling serves, practical guidelines can be
established to define when subtype modeling is appropriate and predict
what impact entity subtypes may have on the application and data archi-
tectures of targeted application systems.

SUPERTYPE AND SUBTYPE MODELING

When subtype entities are included in the data model, several asser-
tions are made that are less generic than those that are a part of set theory.
Specifically, to claim that ENTITY

is to assert not
just that the former describes a subset of the latter, but that each instance
of the subtype entity corresponds to the same real world object as the cor-
responding instance of the supertype entity. This translates into a specific
relationship description between the supertype and subtype entities (see
Exhibit 1). Each instance of the subtype entity is one and the same with an

is a subtype of ENTITY

1 0

Exhibit 20-1. Generic supertype and subtype definition.