General information
Consider the below sentence.
Terry seems to be annoyed.
In this sentence, the verb 'seem' is a raising verb: it raises the argument in 'Terry' out of a lower clause ('It seems that Terry is annoyed', with 'Terry' here being the subject of the extraposed/complement clause) to become the subject of a higher clause ('Terry seems to be annoyed', with 'Terry' here being the subject of the seem clause).
Syntactically, 'Terry' is the subject of seem; however, thematically, 'Terry' is the subject of be annoyed. The verb seem gives the sentence a modal interpretation, but other than that, it is semantically empty.
It is possible for raising verbs such as seem to take a complement headed by the auxiliary 'have'. In these cases, the perfect 'have' changes the temporal interpretation of the clauses.
He appears to have become mad.
She seemed to have done a great deal of work.
Typically (and according to CGEL), the present perfect locates some event or state (whose time we shall denote Tr, the time referred to) as anterior to a specific time (the time of orientation, To) which is usually simultaneous with the time of utterance (Td, or deictic time).
She has now finished her project.
In the above sentence, the time referred to - the time of her finishing her project (Tr) - is anterior to some time (To) which is simultaneous with 'now' (Td). That is,
Tr < To = Td
The present perfect locates the time referred to (the time of her finishing the project) as anterior to the time of now in two steps, and the reason for this is that the present perfect is a combination of two tenses: it is a compound tense, unlike the simple preterite. The semantic implications of this need not be discussed here. For more information, see CGEL, p. 125 - 172.
In the case of matrix clauses (of which raising constructions are an example), things are a little more complicated. Consider the below sentence.
She intends to have finished the project by Tuesday.
In this sentence, the Tr is the time referred to in the participle clause (done the deed). The auxiliary in have locates the Tr as anterior to some To; this To is then temporally related to what is known as the matrix time (Tm), which is the time referred to in the matrix clause (that is, the clause in which the non-finite clause is embedded). In this case, the matrix clause is the time of her intention. The temporal relation between To and Tm depends on the type of catenative verb. Here,
Tr < To, To > Tm
which is to say that her doing the deed is anterior to some time which is posterior to the time of her having the intention.
Here's another example:
She is believed to have been in hiding.
Here, Tr < To, To = Tm That is, the time of her having been in hiding is anterior to some time which is simultaneous with the time of the belief. In other words, the time of her having been in hiding is anterior to the time of the belief (though the present perfect does this in two steps). For more information, see CGEL, 159 - 162
My question here relates to the temporal interpretation of raising constructions that take a complement headed by the auxiliary 'have'. In particular, I want to know what the Tm of these constructions is. For instance,
She seems to have been ill.
He appeared to have been absent.
In the first sentence, the time of her having been ill (Tr) is anterior to some time (To) which is simultaneous with the Tm. But what is the time of the matrix clause here? Is is the time of 'seeming'? To me, that can't make sense, especially since the very verb 'seem' is semantically empty, apart from its modal interpretation.
Likewise, what is the Tm in the second sentence. The time of 'appearing'? How can this be considered a time? With some of the earlier examples, it was possible (and still is) to identify and understand what the Tm was. For instance, I can understand that the matrix verb in 'intend' has an associated time: the time of the intention's existing. With raising constructions, however, this is not the case. So what is the Tm here?
Some enlightenment would be appreciated. I apologise for the poor wording of my question.