The Unwanted Implicature

From today's World Wide Words, by M. Quinion:

"Deutscher argues that the key to differences between languages is a
contained in a maxim of the linguist Roman Jakobson: "Languages
differ essentially in what they *must* convey and not in what they
*may* convey." As an example, he quotes the English statement, "I
spent last night with a neighbour", in which we may keep private
whether the person was male or female. In French there is no such
privilege: one must say "voisin" or "voisine"."

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This is a good quote, and 'may' and 'must' are fascinating lexemes. I wonder how one would formalise that, should the need arise (to do so -- formalise it -- as Grice said of Putnam, "I was pretty formal, until Putnam, of all people, said I was TOO formal").

I suppose in French one CAN say,

"I spent last night with a VOISIN or voisine."

I.e. there are all ways ways of being vague.