SBVR — Projection position and reference scheme for variables

Doc: dtc/06-03-02
Date: March 2006
Version: Interim Convenience Document
Chapter: 9.1.1
Pages: 101
Nature: correction
Severity: minor

Description:

In the definition of 'variable' in 9.1.1, there are two Reference Schemes given for variables. The one for projection variables indicates that the scheme is a pair (projection, variable range concept).

In 9.1.2, the definition of 'projection position' says that it "distinguishes a variable", but it is not mentioned in the reference scheme in 9.1.1.

But 9.1.2 defines the 'projection position' to be the reference scheme for 'auxiliary variable'. Since an auxiliary variable could have the same range concept as the primary range variable for the projection, the reference scheme in 9.1.1 cannot be correct. The scheme given in 9.1.1 should be the same as that for auxiliary variable, and then it need not be restated for auxiliary variable.

Further, the reference scheme given for logical variables in 9.1.1 is:
"a quantification that introduces the variable and the set of each concept that is ranged over by the variable and whether the variable is unitary".

This is mostly unnecessary. The reference scheme is the quantification that introduces the variable, full stop. The scope of the quantification is the scope in which the variable refers to that one.

Now, since variables do not appear to be distinguished by type: logical variable vs. projection variable, it is difficult to manage incompatible reference schemes, when both kinds can appear in the logical formulation that is the selection criterion for a projection! So variables have to have either a common reference scheme or have distinguished subtypes with distinguished reference schemes.

Recommendation:

a. Define two subtypes of variable, 'logic variable' or 'quantified variable' in 9.1.1 and 'projection variable' (in lieu of 'auxiliary variable') in 9.1.2.

b. For the logic variable, the reference scheme should be: the quantification that introduces the variable.

c. For the projection variable, the reference scheme should be as given for 'auxiliary variable' in 9.1.2.

(I'm not sure this really solves the problem for parsing logical formulations that appear in projections.)

Clarify the use of reference schemes for semantic formulations in the introduction to Clause 9.
Fix the references schemes for 'variable' and 'auxiliary variable' so that they involve the complete structure (as is done for all parts of semantic formulations).