Hello Fortiter, welcome to English Forums! Good screen name. Your example A is a 'polite but forceful' use of 'may'.
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I think that what Fortiter was asking about is: can we use the phrase “you may not swim in this pool” as a permission “not to swim” (if one doesn’t feel like it), i.e., a permission to refrain from swimming, and if we can, then how to distinguish such a permission from a prohibition?