The Cambridge Grammar of the English Language (Page 266) defines the ascriptive and specifying uses of be as follows:
[45] i His daughter is very bright/a highly intelligent woman. [ascriptive]
ii The chief culprit was Kim. [specifying]
In the ascriptive use, PC denotes a property and characteristically has the form of an AdjP or a non-referential NP; the subject is most often referential and the clause ascribes the property to the subject-referent. Thus [i], for example, ascribes to his daughter the property of being very bright or being a highly intelligent woman. The specifying use defines a variable and specifies its value. We might represent [ii] therefore as “The x such that x was the chief culprit was: Kim”; it serves to specify, or identify, who the chief culprit was. We will refer to the semantic roles joined by be as theme and property in the ascriptive case, and as variable and value in the specifying case.
In which use is the following sentence?
(1) One of the most successful pop singers is Adele.
At first, it seems to be in the specifying use, but I was wondering if we could represent (1) as “The x such that x was one of the most successful pop singers was: Adele”, which doesn't really make sense because there could be one of the most successful pop singers other than Adele.
Is (1) really in the specifying use?