I agree that 'must' does seem to be a very strong obligation, and I can see where you are coming from about the 'official' origins - I'd never really thought that hard about it before!
I did it - maybe only? - while I was learning English as a foreign language and my attention was drawn to it (by books, teachers, etc.).
The "official" was a reference to "authority" (mentioned as well), which exists everywhere (at least in theory
Although it is true that "obligation", "authority", etc. has a special flavour in English.
It may not even occur to us that "innocent" words, expressions sound impolite for an English speaking listener because for him they may indicate "ordering other people around".
I think this is why this question (involving the expression of authority, orders, strong needs, etc.) is particularly important to be studied carefully.
However, what about cases like "You must stay! I will not allow you to leave!" - possibly it is because you are 'creating' your own 'law'?
I think I called it an obligation coming from the speaker. But in this case "laws" are not necessarily the first things to think about, rather some personal "urgency"/(strong) need.
Another "trick": the opposite of "you must stay" is not
"you mustn't stay" but something like "you may go" (couldn't care less...!
Imagine you are at home with a friend who is a very enthusiastic birdwatcher and you've just found out that your husband invited a great expert on the subject (for dinner, say) who would surely be interested in meeting your friend and (above all) it would be very useful for your friend to meet him as well.
Even if this friend wanted to go away (did not plan to stay for the evening, doesn't want to "disturb", a shy person, etc.), you could say to him (probably with a lot of enthusiasm, encouragment in your voice): "You must stay!" (Meaning something like: Don't be shy! It'll be absolutely good for you even if you don't think so at the moment! or Help! I don't want to stay "alone" in such a crowd! It's only you who can save me from dying of boredom! This is the moment to show that you are a friend! Etc.)
The point is not that you oblige him to do a particular thing (even if it looks like that; it can be a "playful" obligation) but to express that you find it very important, good, useful, etc. for him to do that. (Either for himself or for you.)
(It is not equal to "I will not allow you to leave!", a prohibition is expressed by mustn't
. There you don't leave any choice for your listener and therefore it is very "serious"; to be used with a lot of caution!)
Do you think it has the connotations of 'andare + p.p', but in an active sort of way?
Do you mean something like this: You must see this film - Vai visto questo film.
? Sorry, I never met this construction. You must have meant something else.
As for the 'deduction' idea, I was struggling in trying to translate that...
It is true that you are fairly sure of what you are saying when you use must
to express deduction. I suppose this is why it is replaced by "have to" in some cases as was mentioned above... (But not in BE.)
But the fact that there are several ways of translating it into Italian indicates that there are also other factors to be taken into consideration when translating it. What these factors are exactly depends mainly on the Italian.
In any case, translation is made easier when you have a context (know what the author wants to express exactly), you just have to imagine that in such a situation what would be the most natural thing to say...
This is why there is a preference for translating into your own native language because you are supposed to master that language the best.
Monica, just the other way round!