Modals of deduction

Present modals of deduction 

Must

We use must when we feel sure that something is true because we have some information about the situation. We have strong evidence.

must + infinitive without 'to'

Example
You have been working in the garden all day. You must be tired.

We use (might, may, could) when we are not sure about somenthing.

might/may/could+infinitive without 'to'

Example
We might need to work through the night if we want to get this ready on time.



Can't

We use 'can't' to show that we think something is not true.

can't + infinitive without 'to'

Example
They can't be very happy about working during the night.

Past modals of deduction

We can use modal verbs to talk about how sure or unsure we are about something in the past just as we use modals in the present with a slight change in the form.

Example
He must be really happy about his promotion. (present deduction)
He must have been very happy when he was told about his promotion. (past deduction)

Must have + past participle

We use ‘must have + past participle’ when we are quite sure about something.

Example
You must have been very pleased when you received the results of your exams.

Might have/may have/could have + past participle

We use ‘might have/may have/could have + past participle’ when we are not sure about something but we think it was possible.

Example
He was supposed to be here an hour ago but he could have been stuck in a traffic jam.

Can’t have + past participle

We use ‘can’t have + past participle’ for things that we are sure did not happen in the past.

Example
You can’t have seen him this morning. He was with me all the time.

Exercises:

https://elt.oup.com/student/result/engint/a_grammar/unit07/7c_1?cc=global&selLanguage=en

http://www.esl-lounge.com/student/grammar/4g3-modals-deduction-exercise.php 

http://www.autoenglish.org/modalverbs/pastmodalsdeduction.htm