proposed quant. scope cmavo: xu'u

[Chris Bogart <cbogart@QUETZAL.COM>]

I haven't been following this completely thoroughly, so it may be irrelevant
or redundant.  I especially agree with And that the whole matter of
quantifier scope in afterthought form ought to be looked at all at once,
rather than patched together piecemeal with new cmavo; but it's an
interesting idea...

---

It looks to me like the three/nine dog problem is that there's no way, even
in the prenex, to indicate that two quantified variables exist at the same
scope.  That is, we can say (watch the "such that"s):

        "E3x, x is a man, SUCH THAT E3y, y is a dog, SUCH THAT x bites y"
        (i.e. there could be up to nine dogs)
        is IMO "ci nanmu cu batci ci gerku"
        or "ci nanmu ci gerku zo'u ny. gy. batci"

But I don't know how to say:

        "E3x,3y, x is a man, y is a dog, SUCH THAT x bites y"
        (i.e. there are three men and three dogs, and each man bites each dog)

in Lojban, since the two existential quantifiers are supposed to exist at
the same level of scope (there's no "such that" between them) and I don't
know a way of doing that either in the prenex or in afterthought.

I hate to suggest this, being a general opponent of cmavo proliferation, but:

If we have to add a cmavo, how about a "non-such-that" cmavo (what's left...
xu'u?).  Most of the time, you'd assume that between two existential
quantifiers there was a "such that", getting the up-to-9-dog interpretation.
 But that could be overridden, in the prenex or the main sentence, by
inserting xu'u before the second sumti:

        ci nanmu cu batci xu'u ci gerku
or:
        ci nanmu xu'u ci gerku zo'u ny. batci gy.

"xu'u" might be loosely glossed in Loglish as "the same", as in "Three men
bit the same three dogs".

I'm not sure what would happen if you tried to use this with nested things
like "da poi ko'a nelci xu'u de".

"xu'unai" might be a pedantic and always-elideable way of saying "such
that"; it could be inserted between existentially quantified sumti in order
to stress the up-to-nine-dog interpretation.

[I wonder if there's some way of broadening the concept to fit such things
as "respectively" as well...  "ci nanmu cu batci ri" could be "three men bit
themselves" and "ci nanmu cu batci xu'u ri" could be "three men each bit
each other".  I'm not sure if this makes sense or not, but there seems to be
some similarity between the two problems...]