History: naku

See also le broda ku na brode Gotcha.

naku is a bridi negation like na, meaning "It is false that..."
but it interacts differently with quantifiers. In this use, ku cannot be elided, since that would make na and naku indistinguishable.

In particular, when creating a prenex for a sentence, na is immediately put at the beginning of the prenex (and turns into naku, since na can't syntactically appear in a prenex); naku goes into the prenex in bridi order, intermixed with any quantifiers — to move it to the front, DeMorgan's Laws must be applied.

Thus "All men don't have hair" can be represented in Lojban as

• ro nanmu na se kerfa

which prenexes as

• naku ro da poi nanmu zo'u kerfa daIt is false that for each X that is a man, (something) is X's hair

which is true: some men are bald. On the other hand,

• ro nanmu naku se kerfa

prenexes as

• ro da poi nanmu naku zo'u kerfa daFor each X that is a man, it is false that (something) is X's hair

which is false: not all men are bald.