Is "Not X is Not Required" an example of a double negative?

Well, obviously there are two negatives in the sentence. But, at least I am of the opinion that it can't be contracted into a positive- "Not X is Not Required" means a very different thing to "X is Not Required", but I would like to know what grammatical mechanisms are in play here!

(I was actually sent here after a disagreement with somebody on this topic led them to sarcastically say "go ahead and bring it to english.stackexchange" - seemed like a good suggestion though!

Solution 1:

It is true that there are two negations here and that it is possible to eliminate both of them (and so get a clearer, more natural formulation), but they do not simply cancel out. To see what this sentence actually means, consider first that

Not X is not required.

is equivalent to

It is not required to not X.

A more natural way of saying to not X (where X is some action) is to abstain from X. We thus get

It is not required to abstain from X.

Now, to be required to abstain from something is to be prohibited from doing it. The sentence can therefore be transformed into

It is not prohibited to X.

What is it to not be prohibited to do something? It is, of course, to be permitted to do it. So we get

It is permitted to X.

which is a simple, clear reformulation of the sentence we have started from.

The formal, symbolic apparatus of deontic logic makes such equivalences more obvious than they are in a natural language, such as English.