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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:

  1. must

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.

  1. 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.

  1. can’t

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:

It could not rain 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?

  • Sure, you can say "it could not have rained yesterday." But its meaning will be similar to "It must not have rained yesterday," in other words, that it certainly rained. "It might/may not have rained yesterday" mean the same whether negated or not – RaceYouAnytime Jul 22 '17 at 5:28
  • Hmm. . . I got back from a trip (say, a one-day trip) and I say "The ground is dry--it couldn't have rained yesterday"--meaning it's impossible that it rained yesterday, or there would be some evidence. So, a deduction. – Xanne Jul 22 '17 at 6:05
  • "He can't have been lost yesterday, because we know from his GPS signal that he passed the direction marker . . . " Odd, but possible. – Xanne Jul 22 '17 at 6:10

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