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Re: [engelang] Xorban multivar bindings; "complements"


On Tue, Aug 28, 2012 at 10:07 PM, Jorge Llambías <jjllambias@hidden.email> wrote:
 
On Tue, Aug 28, 2012 at 7:14 PM, Mike S. <maikxlx@gmail.com> wrote:
>
> In the above, trying to reduce a Xorban _expression_ using experimental
> double binding, I carelessly left two "lu" binders that that I should have
> removed. The _expression_ should be:
>
> la liku ja je "/O/"i "/o/"u je "/E/"i "/e/"u frcikuka
>
> The original was:
>
> la ja li "/O/"i lu "/o/"u frcikuka li "/E/"i lu "/e/"u frcikuka
>
> Which better shows the difference, which could be much bigger if frcikuka
> were replaced with a complex formula.

Interesting.

lake ptfake tvlake

= la sma le ptfake tvlake.
"Something, the one fathered by that, he talks to them."
"Someone talks to the one whom he is the father of."

Fiddling around doesn't seem to get us anywhere:

?= la (le sme ptfake) tvlake.
... doesn't work so well.  There's no implicit restriction for free "e" in "tvlake". And,

?= la (le ptfake sme) [le ptfake] tvlake.
"That such that the one fathered by that is something talks to them [one fathered by that]"
... is a mess.

So, unless I'm missing something, Bake is a equivalent to "Ba sma Be".  Not strictly needed, but a useful tool whenever two variables have restrictions using different arguments in the same formula.

 
is this a way to deal with donkey-sentences:

rake je frmra je xsle je pnsake drxake
Every (a,e) farmer(a) & donkey(e) & owns(a,e): beats(a,e)

We have to remove one "je" to get this donkey sentence. 

rake je frmra je xsle pnsake drxake


I think that we actually can shed a syllable expressing it the usual way.

ra frmra re je xsle pnsake drxake
every(a) farmer (a): every(e) donkey(e) & owns(a,e): beats(a,e)


Prenex normal form can be gotten, I think, doing something like this.

ra frmra re (je xsle pnsake) drxake
ra sma re (je frmra je xsle pnsake) drxake
ra sma re sme (ja na je frmra je xsle pnsake drxake)

= rake smo'e ja na je frmra je xsle pnsake drxake

... where "smo'e" can be used to mark the vacuousness of the restriction.

So Bake is helpful if the restrictions of "a" and "e" are closely related, and maybe slightly helpful in PNF (which combines all restrictions into one unified predication). It is not too helpful in other places, as far as I can see.


One last thing, on donkey sentences:  It's been pointed out that not all donkey sentences support an "r-" reading for the nested quantification. For example:

"Every mother that had a credit card used it to pay for her meal."
?ra mmta re je krdtkrde pnsake snmpljplnake.
"Every mother used every credit card that she had to pay for her meal."

snmpljpln = X uses Y to pay for meal Z

It seems doubtful that if a mother had three credit cards then she paid the same bill three times, or broke up her bill into three parts and paid for each with a different card.

What we need is the "naive" approach (i.e. the approach that says that English indefinite articles are not universal quantifiers after all):

ra (je mmta se krdtkrde pnsake): snmpljplnake.
every(a) (mother(a) & exists(e) credit-card(e) & have(a, e)): meal-pay-use(a, e)

There we see the well known problem, "e" is free in snmpljplnake.   Things clear up, almost magically, using the implicit restriction rule (and note here, I am assuming there's a way to derive the implicit restriction formally and get a credit card owned by the right "a".):

ra (je mmta se krdtkrde pnsake): [le je krdtkrde pnsake] snmpljplnake.
"Every mother that had at least one credit card paid for her meal with it [credit card that that mother had]"

What's nice about this is that "l-" leaves open the possibility that every mother used all her credit cards, but doesn't force it.  She might have used just one, or maybe she used two, or maybe she did use all.  IMHO the original donkey sentence can be analyzed the same way.*
















(*Did you the usage of "she" seem marked to you?).