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3. Modals of Deduction – must, may, might, could, can't
Merriam Webster says that deduction is a conclusion or opinion that is based on logic or reason.
However, there are different ways to say how sure we are, and we can be more or less certain that what
we are talking about is true. So, we need to use different modals of deduction to show this:
We use must when there is very strong evidence that something is true
We use might, may or could to say we think something is possible, but we don’t know for sure.
There is some disagreement between native speakers on the “order of certainty” that these modals
should be in, but most would agree that:
May suggests: more possibly yes
Might suggests: more possibly no
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May is used more formally than might or could
Could is the most commonly used of the three, and you should use might when you are
less sure
We use can’t when there is very strong evidence that something isn’t true
Here are some modals of deduction examples:
Present deduction:
This must be her house. I can see her car in the garage.
Robert could be at the library now. He has an exam tomorrow.
George may be stuck on the motorway in traffic.
She might go to the cinema with you tonight if you ask her. 
Present deduction negative:
You have been sleeping all day so you can't be tired now!
4. Modals of Obligation & Prohibition – must, should, can’t
Merriam Webster says that obligation is something that you must do because of a law, rule, promise,
etc. On the other hand, prohibition is the act of not allowing something to be used or done.
There are two types of obligation – strong obligation using must and recommendation or moral obligation
where we use should. And with prohibition, we use can’t for when it is strong, and shouldn’t for times
when it is “recommended not to”.
It is also worth saying that there are semi-modal verb forms that we can use here. We can use have to in a
similar way to must, and the semi-modal ought to can be used in the way that we use should. However,
there are some important differences: