What Was Probably True
Modal Verbs of Probability - Past
Modal verbs of probability express an opinion based on what a speaker knows about a situation at the moment of speaking. The following forms are used to speak about past situations.
Example:
William can't have been ready to log off.
The users must have been dissuaded from signing up by the legalese.
Spreadsheet programs can't have been one of the tools Chesterton used to organize his books.
'Must' plus the perfect form (must have done) expresses the idea that you are almost 100% sure of your opinion about a given situation which took place in the past.
Subject + must + have + past participle + objects
Example:
The users must have been dissuaded from signing up by the legalese.
Tim must have been ready to launch his product online.
'Might' or 'could' plus the perfect form of the verb (could / might have done) expresses an opinion that you think was probably true at a past moment in time.
Subject + might / could + have + past participle + objects
Example:
The spam filter could have been responsible for blocking that email message.
The link could have been put up last week.
'Can't' plus the perfect form of the verb (can't have done) expresses the idea that you are almost 100% sure that something was not true at a past moment in time. Note that the form is 'can't have done' NOT 'couldn't have done'.
Subject + can't + have + past participle + objects
Example:
The library patron can't have been able to log on without help.
Google's spiders can't have been ignoring do not follow links.