# inverting ji'i

Mentioned on existential requantification:

See the Book, chapter 18.

su'o da means naku no da and no da means naku su'o da; if you don't have at least one then you have zero, and if you don't have zero then you have at least one. We can say that su'o inverts to no and vice versa. Knowing how to invert quantifiers is handy if you want to baffle your critics by precision-dropping naku into the middle of your bridi.

Other numbers used as existential quantifiers can be inverted too. mu inverts to vei ga me'i mu gi za'u mu ve'o, or "(less than 5 or greater than 5)", meaning "not five". Maybe there's a better way to say this--anybody know one? su'e mu (at most five) inverts as za'u mu (more than five). You get the idea.

But I don't see any way to invert ji'i mu that's convincingly symmetrical. Suppose you claim it's vei ga me'i ji'i mu gi za'u ji'i mu ve'o--would you say that "not around five" means "either more than around five or less than around five"? And vice versa? Maybe, but you'd rather have a number that means not that close to five, and I don't see one.

Other vague numbers have the same problem; for example, so'i and no'o (depending on what it means in context).

mi'e jezrax

OK, let's say that ji'imu defines a probability function shaped like a bell curve centered at 5. Call that function j(n). Now, the inversion of j, call it i(n), is nothing other than i(n) = 1 - j(n). Perhaps you knew this and were asking for something else? --la xod

Are you sure it's so simple? Say j(9)=0.05 and j(10)=0.03, then using your formula, we get i(9)=0.95 and i(10)=0.97, and the probability of 9 or 10 is 1.92, which seems a bit high. The sum for all n of j(n) has to be 1. The sum of i(n) should also be 1, but you formula gives infinity. --xorxes

If we normalize the inversion, i(n) is infinitesimal for all n except "near" 5, where it dips even lower. --la xod

I think xod's solution is sort of OK if we consider j(n) to be a fuzzy truth-value function rather than a probability distribution. The problem is that ji'imu is vaguer than j ; the function contains strictly more information than the Lojban quantifier. In a given context people could come up with many fuzzy truth-functions which they might all agree are reasonable interpretations of ji'imu--or might disagree about. In any case, inventing an elaborate way to invert ji'imu certainly won't happen in usual practice; people who are being precise will not move naku freely about the bridi when there's such a tricky point, and people who are not being precise won't care! mi'e jezrax