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 interested in that social enterprise.
The company managers might have been obsessed by their short-term goal.
Tim must have been doing his self assessment for management.
'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:
Tim must have been confused by the legal definition.
Tim must have been doing his self assessment for management.
'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 company managers might have been obsessed by their short-term goal.
Samuel could have been confident that the legislation would pass.
'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:
Whitley can't have been lobbying for transparency.
Monahan can't have been convinced that he would succeed through litigation.