Message-Id: <m0pXqpS-0000PYC@xiron.pc.helsinki.fi>
Date:         Sat, 19 Feb 1994 07:29:24 -0500
Reply-To:     Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Sender:       Lojban list <LOJBAN%CUVMB.bitnet@FINHUTC.hut.fi>
From:         Logical Language Group <lojbab@ACCESS.DIGEX.NET>
Subject:      TECH: quantifiers - I'm probably not reading enough to see the
              problem
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 1931
Lines: 50

>Subject: Re: TECH: Quantifiers (was: cukta)
Cowan writes:
>This may mean that a variable appearing in a "poi" clause attached to a
>variable within a prenex is a >forward< reference to the same variable
>appearing later in the prenex.  As you say, this is potentially
>recursive:
>
>        ro da poi broda de vau ro de poi brode de zo'u da brodi de
>
>meaning something like:
>
>        All X's which foogle a Y (every Y?) snorgle all Y's which
>                zarkify an X (every X?)
>
>I nominate this sentence for Most Confused Sentence Of The Year.

Not following the thread which led to this, the above looks like an
ill-formed (grammatical, but logically unsound) prenex.

I think that a restriction that occurs in a prenex shouldn't refer to
future prenex variables, and maybe not even to past ones.

(Note that I just checked with the parser and it does seem to allow
multiple prenexes on a single sentence e.g. da zo'u de zo'u da broda de.
I think that if this is the case then any prenex with multiple variables
should be separable into multiple nested prenexes with one term per
prenex.  This is an of-the-cuff instictual hunch rather than one
seriously thought about (or discussed with Nora, who didn't flunk logic
class like me).

What is wrong with

roda rode zo'u goke ge da broda de gi de brode de gi da brodi de

For all x's and y's, to say that both x foogling y and y snorgling
itself is equivelent to saying that x zarkifies y

Now I can indeed see many variations of this with different quantifications
on different elements, but then you need to introduce more variables and
quantify them accordingly:

roda rodexipa rodexire zo'u goke ge da broda dexipa gi dexipa brode
dexire gi da brodi dexi?xo

For all x's and y1's and y2's, to say that both x foogling y1 and y1
snorgling y2 is equivelent to saying that x zarkifies y?  (context of
the original makes the subscript unclear)

Yours illogically
lojbab