Most websites say that must, might, may, could, can't can be used to make a guess of something or to deduce something.
British Council says:
We use must when we feel sure that something is true because there’s very strong evidence.
He must live near here because he comes to work on foot. We don’t know where he lives but we’re sure it’s not far away.
- might, may, could
We use might, may or could to say that we think something is possible but we’re not sure.
Did you hear that? I think there might be a burglar downstairs. She’s not sure there’s a burglar but she thinks it’s possible.
We’ll try to get there early but we may arrive late if there’s a lot of traffic.
Don’t put it up there. It could fall off and hit someone.
We use can’t when we feel sure something is not true (an opposite of must).
It can’t be a burglar. All the doors and windows are locked. He doesn’t know it’s not a burglar but he feels sure it’s not.
I agree that the negative form of "must" is "can't", but what about the negative forms of "might, may, could?
So, we have: He might / may / could be lost (We think it is possible but we are not sure).
Now how about their negative forms?
This site (slide 19) says we can say:
It may / might / could rain later
and we can say:
It may not / might not rain later
but we cannot say:
could notrain later
Can we say "He couldn't be lost now"?
Also, the past of "must / might / could / may / can't + infinitive" is "must have / might have / could have / may have / can't have + PP".
So, we say
"He must / might / could / may / can't be lost now"
"He must have / might have / could have / may have / can't have been lost yesterday"
We say "It may not / might not rain later", then
Can we say: "It may not have / might not have rained yesterday"?
Can we say "It could not have rained yesterday" to express a deduction?