One thing that used to bother me a bit about English is the fact that ‘must not’ is not the negation of ‘must’ in the logical sense. ‘Must’ represents necessity and the converse of necessity is just the absence thereof, and not the necessity of the opposite. For instance, the logical negation of ‘I must sleep’ is simply ‘I need not sleep’ or ‘I can not-sleep’. However, ‘I must not sleep’ is another prohibition. In contrast, ‘may’ and ‘may not’ behave in a much more logical fashion. Here ‘may not’ is a strong directive while ‘may’ is a soft allowance.
The German counterpart of ‘must’ is müssen. Fortunately, it is more ‘logical’ - ‘Ich muss nicht arbeiten’ means ‘I don’t have to work’ and not ‘I should not work’ (the latter would be ‘Ich darf nicht arbeiten’, where darf is a form of dürfen, the German ‘may’).
Not all imperative modal verbs are ‘logical’ though - the word for ‘should’, sollen is a counter-example. ‘Sollen’ and ‘Sollen nicht’ mean roughly the same as ‘should’ and ‘shouldn’t’. Well no language is perfect.
