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Usually, must with the continuous infinitive conveys an inference.

1 He must be repairing his computer now. (I think he is repairing)

But is it possible to use it with the sense of obligation?

2 When he arrives you must (not) be repairing your computer!

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Must expresses obligation and necessity

Must expresses strong obligation and necessity:

"I must talk to you about the new project."

"Seat belts must be worn even in the back of the car."

Cambridge dictionary

Edited - my typing fingers moved faster than my brain. I apologise. Your second sentence says correctly that when he arrives "you are required to be repairing your computer". With the "not" included it must read "you are required not to be repairing your computer" or, as Peter Shore points out "you are not allowed to be repairing your computer.

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    You are correct about the positive case. But this is not what must not means. The second sentence means "you are not allowed to be repairing your computer," not "you are allowed not to be repairing your computer." – Peter Shor Oct 16 '20 at 18:28
  • Silly of me. Many thanks. Now edited accordingly – Anton Oct 16 '20 at 20:35
  • Your opening sentence is incorrect. Only deontic must demands things; epistemic must predicts things. – tchrist Nov 15 '20 at 23:04
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He must be repairing his computer now

You don't need two sentences. The above can be interpreted in at least two ways. In written English, meaning is derived from context. In spoken English, it is derived from context plus tone of voice. Here are two hypothetical conversations:


1. Expression of belief

A: Is John repairing the computer?

B: I'm not sure.

A: Has he arrived yet?

B: Yes he went your office 5 minutes ago. He must be repairing the computer now.

A: Good. It's been out of action for two days now!


2. Obligation

A: Is the engineer repairing the computer?

B: No he's only just arrived.

A: What?!! He must be repairing the computer NOW!

B: Why?

A: Because the boss has just walked in and he will go mad if he doesn't see the engineer fixing it.

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