Subject: Re: [lojban] Re: paroi ro mentu

From: "Jorge Llambias" <[email-masked]>
Date: Sun, 29 Sep 2002 20:58:19 +0000

la djorden cusku di'e

>First of all, what you're talking about here is totally different:
>na behaves differently because it needs to export to the leftmost
>end of the prenex (inverting any quantifiers) before being interpreted.

I did not use {na}. I used {naku} both times, which exports in the
order where it appears. {na} goes directly to the leftmost without
inverting anything.

>Next, though, is that all of the above interpretations work provided
>that ko'a and ko'e either can do quantifier inversion automatically
>(which I think makes sense) or that in this case they were bound
>to single items so inversion is a no op:
> naku ko'a .e ko'e broda ==
> naku zo'u ko'a .e ko'e broda ==
> naku zo'u ge ko'a broda gi ko'e broda
>It is false that: ko'a and ko'e broda.

Correct so far.

>This is the truth function FFFT,

Nope. It is the negation of TFFF, i.e. FTTT.
It is the case that either ko'a is not broda
or ko'e is not broda (or both). In other words:
naku ko'a broda ija naku ko'e broda

Just as passing a negation through {ro} changes it to {su'o},
passing a negation through {e} changes it to {a}.

The rest is an expansion of {ko'a e ko'e naku broda}:

>which you can get with
> ko'a na.enai ko'e broda
> ko'a .e ko'e na broda
>or
> ko'a na broda .ijenai ko'e broda
> ko'a na broda .ije ko'e na broda
>which means
> naku ko'a broda .ije naku ko'e broda ==
> naku zo'u ko'a broda .ije naku zo'u ko'e broda
>works fine.

See the section starting on pg. 407.

>I'm not even sure what the relation you're suggesting is anyway.
>You have "ko'a .e ko'e" and can say "ro le re broda" meaning the
>same thing... so what? You can always say the same thing in many
>different ways, and the transformation loses information.

It's deeper than that. You can think of a quantification with
{ro} as a long string of conjunctions:

ro broda = le broda e le broda e le broda e le broda e ...

where each {le broda} picks one member of {lo'i broda}.
See also

http://nuzban.wiw.org/wiki/index.php?DeMorgan%27s%20Laws

for more about this.

mu'o mi'e xorxes

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