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When we want to indicate that we think a past situation (seen from a present viewpoint) is certain, we use will(or won't) have + past particle:

ex1) As you will have noticed, he has cut off his beard. (the past(you noticed) seen from a present viewpoint)

ex2) They will have reached home by now. (the past(they reached home) seen from a present viewpoint)

cf1) Next Thursday, I will have owned my present car for exactly 20 years. (future perfect)

cf2) When the trees are all cut down, something of great value will have been lost. (future perfect)

(from Advanced Grammar in Use 1st edition by Martin Hewings)

According to the above explanation from AGU 1st ed., I think "I can't think why he will have been willing to accuse me yesterday" is grammatically correct.

(In the above sentence, I think, the speaker("I") feels like the hypothetical past situation(he was willing to accuse me yesterday) seen from a present viewpoint is certain.)

Is "I can't think why he will have been willing to accuse me yesterday" grammatically correct?

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I don't think it's grammatically incorrect, but there is no reason to use will have been in that context.

Your first two examples refer to something the speaker regards as probably true (that the listener has noticed the man's appearance and that the people have reached home).

If the past situation was hypothetical (you don't know whether the man accused you or not), you would say

I can't think why he would have been willing to accuse me.

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  • Then, if the speaker is regarding the past situation that the man was willing to accuse him as probably true, can he say "I can't think why he will have been willing to accuse me"?
    – gonju yi
    Commented Aug 3, 2023 at 9:45
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    It just seems odd to combine the two clauses. We use will have in this sense to state that something is probably true, but "I can't think why" refers either to a definite fact - "I can't think why he did it" - or a hypothetical situation - "I can't think why he would have done it". Commented Aug 3, 2023 at 9:54
  • O.K. I got it. Many thanks for your helpful answer.
    – gonju yi
    Commented Aug 3, 2023 at 10:13

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