Perhaps "logical deduction" rather than "logically deduced certainty"? I'm not sure it always expresses certainty. I actually think it can be found in sentences expressing uncertainty (without any irony).
I don't get it. With all the balloons and the funny hats and stuff, it must have been a lot of fun, right? How come then my son won't speak to me? He's acting like I've done something wrong.
Here, the speaker is deducing something, but they are not certain their deduction is correct. They see there's a problem they don't understand, and they accept that their may be a flaw in their deduction.
I see your point, but am not totally convinced. I think the speaker is very nearly certain (not absolutely certain - that's
will). Given that near-certainty, they cannot understand why their son is unhappy. There is not necessarily a flaw in their deduction. The party may have been fun for everybody except their son. If that's the case, they want to know why.
One point about logically deduced certainty (or even absolute certainty) is that it is
certainty, not
fact, expressed by the speaker:
A:
You co-authored a book with Arthur Nicholls once, didn't you?
B1:
Yes, that was in 1969. (I remember that clearly. It was the year my daughter was born. My wife did some proof-reading in the maternity ward! Apart from that, I have shamelessly cited the book whenever I can, so 1969 is fixed in my mind.)
B2:
Yes. That will have been in 1969. ( It was the last year we shared a flat together, and I am certain that that was 1969)
B3:
Yes That must have been in 1969. (That was while we still sharing a flat. I left the following year to get married. I got married in 1970, so I am now certain, after logical deduction, that we wrote the book in 1969).
I readily concede that there is not a clear-cut difference between
will have and
must have in my examples, and that
must have is possible for B2 and
will have is not impossible for B3. My point is that
must have is, in my opinion, closer to the idea of certainty than it is to the idea of probability and that, for each individual speaker,
will have is more absolutely certain than
must have.