I don't know either Frany, I am not a Buddhist scholar, but I guess I recognise it when I see it.
So I will google...hmm... "Buddhist negation logic" ---and this is what I found:
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Catuṣkoṭi (Sanskrit; Devanagari: चतुष्कोटि, Tibetan: མུ་བཞི, Wylie: mu bzhi) is a logical argument(s) of a 'suite of four discrete functions' or 'an indivisible quaternity' that has multiple applications and has been important in the Dharmic traditions of Indian logic, the
Buddhist logico-epistemological traditions, particularly those of the Madhyamaka school, and in the skeptical
Greek philosophy of Pyrrhonism.
In particular, the catuṣkoṭi is a "four-cornered" system of argumentation that
involves the systematic examination of each of the 4 possibilities of a proposition, P:
P; that is, being.
not P; that is, not being.
P and not P; that is, being and not being.
not (P or not P); that is, neither being nor not being.
P stands for any proposition and Not-P stands for the diametrical opposite or the contradiction of P
(in a relationship of contradistinction); P and Not-P constitute a complementary bifurcation of
mutual exclusivity, collectively constituting an exhaustive set of positions for any given (or determined) propositional array.
Brahmajala Sutta: The Supreme Net (What the Teaching Is Not)
'What is the fourth way? Here, an ascetic or Brahmin is dull and stupid. Because of his dullness and stupidity, when he is questioned he resorts to evasive statements and wriggles like an eel: "If you ask me whether there is another world. But I don't say so. And I don't say otherwise. And I don't say it is not, and I don't not say it is not." "Is there no other world?..." "Is there both another world and no other world?..."Is there neither another world nor no other world?..." "Are there spontaneously-born beings?..." "Are there not...?" "Both...? "Neither...?" "Does the Tathagata exist after death? Does he not exist after death? Does he both exist and not exist after death? Does he neither exist nor not exist after death?..." "If I thought so, I would say so...I don't say so...I don't say it is not." This is the fourth case.'
If we focus on the doctrinal agreement that exists between the Wisdom Sūtras[27] and the tracts of the Mādhyamika we note that both schools characteristically practice a didactic negation. By setting up a series of self-contradictory oppositions, Nāgārjuna disproves all conceivable statements, which can be reduced to these four:
All things (dharmas) exist: affirmation of being, negation of nonbeing
All things (dharmas) do not exist: affirmation of nonbeing, negation of being
All things (dharmas) both exist and do not exist: both affirmation and negation
All things (dharmas) neither exist nor do not exist: neither affirmation nor negation
https://en.wikipedia.org/wiki/Catuṣkoṭi
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Aso-deska Frank-san [trans from Japanese: Oh now I see Franky]