The following example is taken from source
A：We saw a police helicopter overhead yesterday morning.
B：Really? They would have been looking for those bank robbers.
The website says that it is an example of usage of would to express an assumption, presumption or expectation in the past.
As this post indicates, the example here does not mean a hypothetical scenario or a past future tense, but a speculation about a past event.
I'm wondering whether the post was correct in explaining such usage. Please share some wisdom!
Only a few grammar books say "would have + past participle" can be used in this way. The following are a couple of the sources I could find, but I don't know whether they are reliable to believe.
Would + perfect. This use of would signals what we expect somebody to do:
John would have scheduled the meeting.
In this case, it tells us that the speaker expected John to schedule the meeting. We do not know if John actually scheduled the meeting.
-- McGraw-Hill's Essential ESL Grammar, for Intermediate & Advanced ESL Students (2008)
and
One of the children offered to help. That would have been Julie. (assumption about the past.)
-- Mastermind Use of English
Answer
The first thing I would say about modal verbs is that their usage extends over many different contexts and so any general rules are bound to fail when taken out of context.
Outline
- Use of 'will' and 'would' to express belief
- Other uses
- The answer
(Credit for this section should go to @snailboat)
To illustrate the difference in use of 'will' and 'would' for expressing certainty, snailboat suggested the following sentences at the ELL chat room:
1A. I'm sure they have been looking for those bank robbers.
1B. I'm sure they will have been looking for those bank robbers.
2A. I'm sure they had been looking for those bank robbers.
2B. I'm sure they would have been looking for those bank robbers.
In sentences 1A (they have been) and 2A (they had been) the speaker knows they have/had been looking for those bank robbers. The main difference is that the use of present perfect in 1A (they have been) indicates that the search has lasted at least until now.
In sentences 1B (they will have been) and 2B (they would have been) the speaker expresses a belief:
in sentence 1B (they will have been), the speaker expresses the belief that they have been looking for those bank robbers.
in sentence 2B (they would have been) the speaker expresses the belief that they had been looking for those bank robbers.
Again, a word of caution, the interpretation above is not unique and can change if the context changes. This section shows other possible uses of will have been and would have been.
To express a hypothesis
I'm sure they would have been looking for those bank robbers if they had any manpower to spare.
To express an event in the future
They will have been looking for those bank robbers for hours before the CCTV footage is shown on tomorrow morning's News.
Let's now consider the example in your question:
A： We saw a police helicopter yesterday morning.
B： I'm sure they would have been looking for those bank robbers.
To be able to use "will have been" is necessary to change the context as described in the first section of this answer:
A： We have seen a police helicopter.
B： I'm sure they will have been looking for those bank robbers.
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