To make guesses or deductions about past actions or states use a past modal of deduction. This is formed with a modal verb + have + past participle also called the perfect infinitive.
Where's my phone?
You could have left it in your office.
To make deductions about continuous actions or states use modal verb + have + been + ing form.
Why didn't Sarah come to the party last night?
She must have been feeling ill.
For deductions using the passive use modal verb + have + been + past participle.
Your phone could have been stolen from your jacket.
Usage of different modals:
must have – you are almost certain that something is true based on some evidence.
I must have left the window open. That's how the cat got in.
might/could/ may have – you think it's possibly true based on evidence.
They could have been delayed by rain. It does rain heavily in the mountains this time of year.
Couldn't/ can't have – you are almost certain that this is true or impossible based on evidence.
He can't have left the office yet. It's only 4 o'clock. He must be in a meeting.
Lesson by Tristan, English teacher at EC Malta English school
Choose the correct form for the following: