Information Modeling and Relational Databases by Terry Halpin

Author:Terry Halpin [Halpin, Terry; Morgan, Tony]
Language: eng
Format: epub
ISBN: 978-0-08-056873-7
Publisher: Elsevier Science
Published: 2008-11-14T16:00:00+00:00

Figure 10.62 The categorization relationship “is of:”.

For the first-order logic interpretation, all types are first-order, so instances of B are individuals, not types. We use lowercase letters (possibly subscripted) to range over individuals. For our higher-order logic interpretation, we use capital letters (in italics) to denote type variables of any order. The order (1, 2, 3, …) of any type is implicit, since it can be derived by inspecting the full schema. If it is desired to explicitly show the order of a type, a presuperscript may be used (e.g.,2B indicates that B is a second-order type).

Post-superscripts are typically used to denote arity, and postsubscripts are often used to distinguish variables of the same type. Ignoring the case of crossing metalevels, assign the order of a type to be 1, plus the number of relationships in a contiguous chain of zero or more categorization relationships that end at the type.

Using ∃1 for the “there exists exactly one” quantifier, we may now formalize the constraints on the categorization relationship in Figure 10.62(b), which has a mandatory and uniqueness constraint. The first-order formalization treats AccountType as a type of individuals.

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