[lojban] Re: xorlo and the expansion of bridi

[John E Clifford <kali9putra@yahoo.com>]

----- Original Message ----
From: Roman Naumann <roman_naumann@fastmail.fm>
To: lojban-list@lojban.org
Sent: Thu, October 29, 2009 3:47:59 PM
Subject: [lojban] Re: xorlo and the expansion of bridi

Jorge Llambías wrote:
> 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.

In {ci da poi mlatu cu blaci .ije re da cu barda} [according to your (more mathematical) use of logic, not the CLL use], is {da} only to be considered an independent variable, because there is a leading PA before it?

(If not:) If reusing a variable in a connected bridi generally introduces a new, independend variable, expressions like {lo gerku cu vasxu gi'e bajra}, which expand to {da poi gerku zo'u da vasxu ije da bajra} would mean {da poi gerku zo'u da vasxu ije de poi gerku zo'u de bajra}, which means, we could be talking about different dogs. That would collide with my understanding of {gi'e}.

Well, no.  Although Lojban mucks up here a bit by making it look like the prenex only goes with the first chunk, it does, in fact, cover the whole.  The error comes in forgetting the step in the expansion {da poi gerku zo'u da vasxu gi'e bajra}, which does not lead to the next step logically, though appears to CLL wise. The scope is set at the beginning and does not change as the sentences within it develop.  

>> 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?

That's an interesting question. I would say it refers to all referents in the set, but the bridi is negated. At least the statement still has an implication on all referents in the set, your explanation includes that, the CLL one does not. (..or was that a rethorical question of yours..?)

xorxes' point also points out why translating out of 'lo' language into quantifiers is not preservative: you lose information at every step if you are not very careful and just a bit sneaky (this was true of "old" lo as well as xorlo, but more for xorlo where they differ -- which is not here, by the way).

>> 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.)

I understand.

> "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".

You are right about that.

> 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".

Indeed and thanks. That's the form I was looking for. I think it could be useful for letting the computer reason about lojban.

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

I understood that now. The inner quantifier is just incidential information about the cardinality of the set-of-things we are talking about.

> 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.

Well explained. By the way, is there any document about lojban logic on the web which sticks closer to what you explaned/to logic than the CLL?

mu'o mi'e namor

I think that my starts in that direction got taken down a long time ago as being both incoplete and in some cases inaccurate for one side or the other.  There are some minor notes at pckipo.blogspot.com under LoCCan.  But someone else may have taken up the slack.


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