Modal verbs of deduction

We use modal verbs of deduction to make guesses or draw conclusions based on the information available.

You must be tired after such a long drive.

deduction (noun): guess; reaching a conclusion by reasoning and logic, based on evidence

If we see a man in police uniform, a reasonable deduction is that he is a policeman. If we see a large grey cloud in the sky, a possible guess is that it is going to rain—maybe.

To make a deduction, we need facts and evidence (the uniform, the cloud).

The usual modal verbs that express deduction are:

Deduction has degrees of certainty, say from 99% to 30%. Modal verbs of deduction express certainty like this:

modal verb of deduction approx. certainty +/-
must 99% positive
might/may
could
50%
30%
 
can't 99% negative

Structure

The basic structure for deduction about the present is:

subject modal verb main verb
(base form )
 
He must be a policeman

The basic structure for deduction about the past is:

subject modal verb have main verb
(past participle)
 
They must have been hungry

Modal of deduction: must

We use MUST when we have strong evidence and we are certain that something is true.

Modal of deduction: might/may, could

We use MIGHT/MAY when we have some evidence and we think something is possible but we’re not certain. Note that the possibility can also be negative — might not, may not.

And we use COULD when we're a bit less certain.

Modal of deduction: can't

We use CAN'T (CANNOT) when we have strong evidence and we are certain that something is NOT true.

Note that these modal verbs can have other uses too. In some cases, they may be used to express a suggestion or a recommendation. For example, "You could try calling him to see if he's available."