The NOT (¬ /.) function is of course a standard operator of that commonly known contemporary cipher, first order predicate calculus. Nevertheless it is also very Russian. That is not just because Russians like things not to be; but also because they have acquired a sinisterism of discourse about sensitive subjects which involves their saying the opposite of what they really mean.
One reason for this may be to veil thinly threats of violence (e.g. "We have no idea what will happen to you at your hospital appointment", the recipient of the message having no anticipated future hospital appointment at all). But more generally it is just a feature of Russian obtuseness, in which they like to refer to sensitive matters by reference to events, situations or circumstances that have not happened at all. (e.g. "Congratulations of the Chairman of the Investigative Committee of Russia on the New Year") or are impossible (e.g. "White's Third Knight to take King's Pawn").
The reason for all this shadow language undoubtedly derives in substantial part from the legacy of Stalin's Russia, in which any conceivably normal social, private or political observation might be reported upon by one's neighbours to the NKVD (the FSB of the time) whereupon one might be taken away in the middle of the night to be tortured or shot. Therefore people became used to expressing their private and personal expressions by talking nonsense.
Stalinism was a cruel, harrowing, scarring and enduring episode in Russian history. Nevertheless those of us who engage with the art (not science) of cryptology must likewise engage with this curious Russian mysticism. Because referral to things that are not happening, or other curious references to impossible things, is a staple of a substantial proportion of the communities within which professional or casual readers of this article must engage.
The "not" rule involves saying the opposite of what one really means in Russian English, for example "We don't know anything about that", which means roughly "we know all about this subject and we have been placing you under surveillance". This is essentially a silly cipher unless it is a hidden method of making criminal threats. It is silly because if everyone universally uses the "not" rule then it ceases to be a cipher - you just apply yo the "not" operator to everything someone says and if it is not a consistent rule then it reveals everything as completely meaningless as there are no reliable ways of establishing when the "not" rule is being applied and when it is not (pun not intended).
Unless of course you embody the "not" rule applicability principles in a synchronous private dictionary that your enemies soon learn and so can an AI algorithm.
What is interesting about the "not" rule, which makes it so peculiarly Russian, is that it straightens out the directional ambiguity of suggestion, because use of the "not" rule tends to imply that you mean something very bad - at least when Russians use it. But arguably there is no directional ambiguity in most Russian ciphers, because Russians predominantly use ciphers to make threats and to suggest very bad things.
The "not" rule turns out to be quite pointless. If you simply go around saying that things are the opposite of what they are, then you turn conventional meaning into a joke and the decryption key is simple: just reverse the "not" operator. If you mean something else by "not" then it is solely sinisterism and it becomes impossible to understand what you really mean. The "not" rule is not a cipher. It is either something pointless because it is predictably applied, or it is something pointless because it is unpredictably applied. It is just a bizarre feature of the Russian intelligence services' use of language, by reason of that country's sad and tragic history.