[lojban] Re: xorlo and the expansion of bridi

[Jorge Llambías <jjllambias@gmail.com>]

2009/10/29 Roman Naumann <roman_naumann@fastmail.fm>:
> Thanks for your reply.
>
> Jorge Llambías wrote:
>>
>> (BTW, what does "B dogs exist" mean to you exactly? Is that the number
>> of dogs alive at the time of the utterance, the number of dogs that
>> have ever existed or will exist on this planet, or something else,
>> depending on the context?)
>
> I'm not sure what it means, I just remember the 'old' lo implied existential
> claims.

I just wanted to point out that the 'old' meaning is not really that
different from the new one, at least as far as it can be understood.
The inner quantifier gives the number of referents that the sumti has.
This was always the case. The old exposition seemed to assume that any
given sumti headed with 'lo' has a certain number of referents
independently of the context in which it is used, but that doesn't
make a lot of sense. It is hard to come up with sumti that are so
context independent.


> What I meant to say was: {B da poi gerku zo'u A da vasxu}
> But still, I don't see why you say the variable is being bound twice.

In "A da vasxu", the variable "da" is bound by the quantifier "A". It
is equivalent to "A da zo'u da vasxu".

"B da poi gerku zo'u A da vasxu" is equivalent to B da poi gerku zo'u
A da zo'u  da vasxu", with apparently two bindings for the same
variable.

> According to the example from CLL:16, it should be locally requantified
> instead of being bound again:
>
> ( 14.1)    ci da poi mlatu cu blaci .ije re da cu barda
>    Three Xs which-are cats are white, and two Xs are big.
>
> What does Example 14.1 mean?

In normal predicate logic, it's equivalent to "ci da poi mlatu cu
blabi .ije re de cu barda". The two variables are independent of one
another. In CLL-logic it means something else, but since Lojban is
supposed to be based on predicate logic, I prefer to stick to that.
The CLL-logic of quantifiers is not completely coherent or consistent.

> The appearance of ``ci da'' quantifies ``da''
> as referring to three things, which are restricted by the relative clause to
> be cats.

The way I would say it is that the variable "da" takes values from the
things that are cats, and (exactly) three of those values satisfy the
predicate "blabi" (which also means all but three of those values
don't satify it). If there is any reference going on here at all it is
to all cats, not just to the three that do satisfy the predicate
"blabi". If we were to say "no da poi mlatu cu blabi" then "da" again
takes values from the same set of referents, but now the number of
them that are said to satisfy blabi is zero. Would we say that "da"
doesn't refer to anything in this case?

> When ``re da'' appears later, it refers to two of the those three
> things --- there is no saying which ones.

That's the CLL story, yes. It's appealing in simple cases like this,
but it doesn't work in general. (Or at least nobody has given any
satisfactory account of how these "double quantifications" should work
in general.)


>>> How does {A lo B gerku cu vasxu} expand with xorlo?
>
> I should have been more specific about what kind of expansion I had in mind.
> The thing I'm looking for is a canonical form of {A lo B <sumti> cu broda}
> with a proper prenex.

"A lo B <sumti> cu broda" or "A lo B <selbri> cu broda"?

Both are grammatical, at least if <sumti> doesn't have another
quantifier. I assume you want an expansion of "A lo B broda cu brode".
The proper expansion would be:

 A da poi ke'a me lo B broda zo'u da brode

>That canonical form should not contain {lo}.

OK, but this is independent of the quantifiers.

I expand "lo broda" to "zo'e noi ke'a broda".

And an "inner quantifier", which is not a logical quantifier, can be
expanded thus: "lo B broda" = "lo broda noi ke'a klani li B".

Putting all three expansions together (which are all inependent of one
another) we get:

A lo B broda cu brode
= A da poi ke'a me zo'e noi ke'a broda gi'e klani li B zo'u da brode

We have shifted the outer quantifier A (a logical quantifieer) to a
proper prenex, we have transformed the "inner quantifier" B to an
ordinary number "li B" used as an ordinary argument, and we have got
rid of "lo".

B cannot be transformed into a proper prenexed quantifier because it
was never a true quantifier to begin with, it's just a cardinality.


>> A <sumti> cu broda
>> = A da poi me <sumti> cu broda
>> A of the referents of <sumti> are broda.
>
> Isn't A an _inner_ quantifier here?

No, an "inner quantifier" (which is not a logical quantifier) always
goes after the gadri.

An inner quantifier gives the number of referents of a sumti. It is
only concerned with a sumti, not with a whole bridi.

An outer quantifier binds a variable and quantifies a whole bridi, it
says for how many values of the variable the bridi in which that
variable appears is true.

mu'o mi'e xorxes


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