SBVR — Quantification definitions

Doc: dtc/06-03-02
Date: March 2006
Version: Interim Convenience Document
Chapter: 9.1.1.7
Pages:
Nature: Editorial
Severity: minor

Description:

In 9.1.1.7, the model of quantification shows it to be a kind of logical formulation that MAY (0..1) scope over a logical formulation. A quantification has to "scope over" something. And it binds a variable in that something. The definition does not reflect this requirement.
Further, iIf a quantification doesn't 'scope over' a logical formulation, it isn't itself a logical formulation. A logical formulation represents a proposition that is true or false.

If necessary, define logical quantification with the well-defined properties and define some other kind of quantification for whatever else a quantification may "scope over".

Recommendation:

In the entry for 'quantification'
a. Modify the definition of quantification to read:
logical formulation that applies a logical quantification operator to a free variable in the logical formulation that the quantification scopes over.

b. Add a Note
Note: the variable must be free in the logical formulation scoped over. The quantification binds that variable in the resulting logical formulation.

c. Modify Necessity (3) to read:
Necessity: Each quantification scopes over exactly one logical formulation.
(Not "at most one".)

In the entry 'logical formulation restricts quantification', At the end of the Note, add:
The logical formulation represented by the quantification is logically equivalent to scoping over the conjunction of the logical formulation that restricts the logical quantification with the logical formulation it scopes over."

In the entry 'universal quantification', replace the text of Definition with:
quantification that is true if the logical formulation it scopes over is true for all admissible referents of the variable, and false in any other case.

In the entry 'existential quantification', replace the text of Definition with:
quantification that is true if the logical formulation it scopes over is true for any admissible referent(s) of the variable, and false only if it is true for no admissible referent.

Add Note: An existential quantification is equivalent to an at least n quantification where n=1.

Make the definitions of the different kinds of quantification more precise. Add notes for clarity.