Can we use must + be + ing to express obligation or necessity?
You must be studying.
I think that it can only mean a deduction that I'm so sure of and that it can't mean necessity or obligation. Am I right?
While I agree with you that it is natural to hear the example you have given as expressing a deduction (for obligation or necessity, native speakers would naturally use "You need to be studying" instead), the example does not prove that "must + be + ing" can never express obligation or necessity, or even that it is impossible to interpret "You must be studying" in that manner.
One sentence that comes to mind in which "must + be + ing" is commonly used to express obligation or necessity is "I must be getting ready." If you search Google books for that sentence, you will find examples like these, where you wouldn't dream of saying that "must + be + ing" expresses a logical deduction. Rather, they clearly express obligation or necessity:
- "But I must be getting ready, for the council meets this forenoon."
- "Now I must be getting ready for prayer-meeting."
- "'I must be getting ready to teach, you know, sir.'"
- "'But I must be getting ready,” she now exclaimed. . . 'if I don't go at once, Her Ladyship will think I don't want to meet her."