English modals of deduction

The English modal verbs "must", "have to", "have got to", "can't" and "couldn't" are used to express deduction and contention. Modal verbs are used to state how sure the speaker is about something.

Must

"Must" can be used when the speaker feels sure that something is real because he sees strong evidence of it.

"You're shivering" => "you must be cold".

"Must have" is used with a past participle when the speaker is not totally sure about something.

"Someone must have taken the key, because it is not here."

Have to

"I didn't order ten books. This has to be a mistake."

Have got to

"These aren't mine, they've got to be yours."

Can't

"Can't" is used to say that the speaker thinks something is not right.

It can't be a burglar. All the doors and windows are locked.

"Can't have" + past participle is used for things that the speaker is sure did not occur in the past.

I can't have left my phone at work. You called me when I was running to my car. That’s it. It must be in the car.
You can't have seen him this morning. He was with me all the time.
She can't have liked the show. She dislikes musicals.

Couldn't

If he wasn't there, he couldn't have committed the murder.

References

Modals – deduction (present) learnenglish.britishcouncil.org
Oxford Practice Grammar (Advanced), George Yule, Oxford University Press ISBN 9780194327541 Page:40
Modals Deduction Past ecenglish.com