What semantic meaning does the copula 'be' have in its specifying use?

The Cambridge Grammar of the English Language (Page 252) says:

It may be that the be of [Kim is fond of animals] should be regarded as semantically empty, serving the purely syntactic function of carrying the tense inflection, which has to be associated with a verb: note in this connection that translation equivalents in a good number of languages contain no verb. However, there are undoubtedly constructions where be does express a semantic predicate (e.g. in The chief culprit was Kim: see §5.5), and we will simplify by assuming that it does in all cases.

The copula be (is) of Kim is fond of animals is in the ascriptive use in that it ascribes to Kim the property of being fond of animals. By contrast, in The chief culprit was Kim, the copula be (was) is in the specifying use in that it specifies who the chief culprit was.

In the above excerpt, CGEL seems to be saying that the copula be in the ascriptive use has no meaning ("semantically empty") whereas that in the specifying use does have some meaning ("does express a semantic predicate").

Assuming this is what CGEL is saying, what semantic meaning does the copula be have in its specifying use (that the ascriptive be doesn’t have)?