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:
The company managers might have been obsessed by their short-term goal.
William can't have been interested in that social enterprise.
Monahan can't have been convinced that he would succeed through litigation.
'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:
My parents must have been monitoring service delivery.
Tim must have been aiming at legal compliance.
'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:
Samuel could have been confident that the legislation would pass.
The company managers might have been obsessed by their short-term goal.
'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.
Pirsig can't have been interested in any social goal.