Re: proposed quant. scope cmavo: xu'u

[jorge@PHYAST.PITT.EDU]

la kris cusku di'e

> 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"

Right, this is what seems to be the preferred meaning.

> 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.

In the prenex it can be done with {e}:

        ci da poi nanmu e ci de poi gerku zo'u: da batci de
        There are three men AND there are three dogs, such that each
        man bites each dog.

With {e} the two quantifiers must be at the same level. For example, in:

        la djan cu batci re gerku e re mlatu
        John bites two dogs and two cats.

the two cats are not selected for each of the dogs. The four animals
are selected at the same level.

In afterthought, it can be done if non-outermost quantifiers are to be
understood as having widest scope. Then in that case:

        ci nanmu cu batci ro lo ci lo gerku
        There are three men such that for each of some sentence-fixed
        three dogs, the man bites it.


> 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.

As an aside, there already is a "such-that" cmavo, namely {zo'u}. It is
grammatical to write:

        ci da poi nanmu zo'u ci de poi gerku zo'u da batci de

But there's nothing equivalent in afterthought, and I don't think this
is enough to change to the 3-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".

Interesting, but do we really need a new cmavo? I wonder if {ro} could not
be used for that. It wouldn't cause ambiguities because the interpretation
for a single {ro} is the same in both the 3-dog and the up-to-9-dog schools.

> 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".

That's "at least one x such that x likes at least something". {xu'u} has
no effect there because there is only one possible interpretation.
(I assume you meant {ke'a} instead of {ko'a})

> "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.

There's already {zo'u} for that, but only in the prenex.

> [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...]

I'm happy with {ci nanmu cu batci ri} (themselves) and {ci nanmu cu batci
ro ri} (themselves and each other). This gives even more plausibility to
{xu'u} = {ro}.

Jorge