As always, the SF used when the auxiliary is stressed. He ˈwill /ˈwɪl/ have it his way. Note that in tags it is the auxiliary rather than the personal pronoun that carries the stress: I’m supposed to know this, am I? /ˈæm aɪ/ (*/əm ˈaɪ/).
There is, however, a second situation in which auxiliaries must be given their SF. Consider the following sentence: I think we can do it today, but I don’t think we can do it tomorrow. In such a sentence it is normal for the second occurrence of do it to be deleted (left out). You should observe that when this is done, the auxiliary, which must remain, has its SF: I think we can /kən/ do it today, but I don’t think we can /kæn/ tomorrow. We call the place where the words do it have been deleted a deletion site, and the rule can be phrased as follows:
The auxiliary has its SF immediately before a deletion site.
In the following examples the deletion sites are marked { DS}:
We could /kəd/ all give a little help. At least I could /kʊd/ { DS}, and I suppose Elsie could /kʊd/ { DS}, and Len could /kʊd/ on weekends…
Mary won’t believe this, but perhaps John will /wɪl/ { DS}.
In the following example the deletion site does not immediately follow the auxiliary, which therefore has its WF:
John doesn’t believe it. Do /də/ you { DS}?
When be is a copula, the deletion rule applies to the subject complement (also called the nominal part of the predicate):
Is he the captain? I thought you were /wɜr/ { DS}.
Summarizing: auxiliaries have their SF when they are stressed or when they occur immediately before a deletion site. In sentence-initial position, the SF may also be used.