SBVR — Meaning of noun concept formulation

Doc: dtc/06-03-02
Date: March 2006
Version: Interim Convenience Document
Chapter: 9.1.1.9
Pages:
Nature: Editorial
Severity: minor

Description:

In clause 9.1.1.9, 'noun concept formulation', the definition is
"projecting formulation of a referent noun concept whose intension is formulated in a particular projection"

a. It is not clear in this definition what 'referent noun concept' is being referred to.
b. 'projecting formulation' as a GeneralConcept has no semantics. Use 'logical formulation'?
c. This apparently means that the noun concept is defined to be the set that is the projection, which is the extension, not the intension. (I suppose the intension is "is a member of that set".) The problem here is that while a projection has the form of an intensional definition, it has the semantics of an extensional definition. Perhaps the problem is that this use of the projection syntax does not have the same semantics as other uses.
d. This definition provides no indication as to the role of the bindable target (from 'projecting formulation'). The thing being defined is a noun concept – not a variable, although perhaps a constant – so the bindable target must enter into the definition, but the note says there is some "understood reference".
e. This definition is only a 'logical formulation' if the noun concept is treated as a classifying predicate, like an instantiation formulation. And in that case, the bindable target would be the thing whose referent is to be tested for membership in the projection set.
f. In the closed form, one possible interpretation of this construct is that it is a test for whether the bindable target is a member of the projection set. If that is the case, it would certainly be helpful to the reader to say exactly that, at least in a Note.
g. One possible 'open form' would apparently define a function of the bindable target whose result is the closed projection that corresponds to the substitution of the bindable target for the (sole?) free variable in the projection, but that is not a logical formulation in that its meaning is not a proposition.
h. Of itself, the open form does not define a noun concept. There must be a further requirement that all free variables in the projection are bound in the context in which the would-be noun concept is 'defined'. And what this means is that a noun concept formulation is only well-defined when it is closed by substitution. All of this should be part of the definition and not of some attached Note.
i. Another possible interpretation is that this really was intended to represent the definition of a term to refer to a noun concept defined by an intensional formulation. In that case, the 'bindable target' should be a constant (text?) whose referent is being defined, the noun concept formulation should introduce a single variable, and the intensional definiens should be a logical formulation with exactly one free variable, and that variable corresponds to the variable introduced. No projection ("set") is involved.

"Note: A noun concept formulation is satisfied for each referent that is a noun concept defined by the projection."
Whatever this was supposed to mean, it is wrong. A noun concept formulation is satisfied if the referent of the bindable target is actually in the set defined by the projection.

The Examples are strangely phrased. E.g. in the 2nd example, the noun concept formulation is: 'the distance that is the reading of the rental car's odometer', and anything that satisfies that formulation IS a distance, because 'distance' is the concept over which odometer-reading(?car) projects.
The 'distance concept' is in the formulation, but the referents are individual distances.

see above