This article is additional to the main page dedicated to Modal Verbs.
Modals of deduction are the verbs that we use to express how sure we are about something. You need to be very attentive when choosing a verb because each modal has its own level of certainty.
Certainty
When we are sure about something and have reasons for our belief or suggestion we use modal verbs 'must' and 'should'.
He has been working all day long. He must be very tired.
The dog doesn't want to eat at all. It must be ill.
You can call your Granny. She should know the recipe.
Possibility
When we are not sure about something but make a guess that something is possible to happen we use modals 'may', might' and 'could'. Some learners think that 'can' is also suitable in this case. But this is a mistake. We use 'can' for possibilities in general.
Carol may/might/could be at work.
They may/might/could visit us soon.
It can get hot in summers in this region.
Impossibility
When we need to say that something is impossible to happen we use the modal 'can't' for present and future and 'can't have' or 'couldn't have' for the past.
I don't believe you. Your words can't be true.
I don't believe you. He can't have done such a terrible thing.
If they left the house at eight o'clock, they couldn't have been late.