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From: Jacob Errington <nictytan@gmail.com>
Date: Thu, 12 Jul 2012 18:47:37 -0400
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Subject: [lojban] {da} and abstractions
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coi ro do

I'm not sure if the CLL ever mentions it, or if there's some general
consensus or convention governing this, but to the prenex of which
bridi do logically quantified variables that have not been declared in
any prenex belong? (I feel like that "belong" elides a lot of
non-existent terminators.)

There are some ramifications to consider.
Consider {.i do se zdile lo nu da xebni mi}.
Is it {.i da zo'u do se zdile lo nu da xebni mi}
"There exists an X such that you are amused that X hates me" or is it
{.i do se zdile lo nu da zo'u da xebni mi}
"You are amused that there exists an X such that X hates me" ?

Should it be that the variable binds to the bridi *in which it
appears*, unless bound to a higher prenex beforehand, then does that
mean that we can recycle variables in sibling abstractions?
e.g. {lo ka da xebni ce'u cu kampu lo'i nanmu noi ke'a se kampu lo ka
da prami ce'u}

This becomes especially interesting in the case of certain logical
connectives (bridi-tail connectives) and when the quantifiers of the
variables differ:
#1 {lo nu no da mi xebni cu cabna lo nu ro da mi se prami}
#2 {mi prami roda gi'e se xebni noda}
(I think #2 is a longstanding issue with regards to logical
connectives and logically quantified variables.)

Additionally, logically quantified variables have a similar issue with tu'a.
Consider the formal definition of tu'a:
{tu'a ko'a} == {lo su'u ko'a co'e}.
Is it the case that this formal definition no longer applies when
using a logically quantified variable in the raised sumti slot?
{tu'a da} =? {lo su'u da co'e}
Is the formal definition continues to apply, and logically quantified
variables are bound to the bridi in which they appear unless defined
in a parent bridi, then it is necessary to use a prenex when saying
"There exists an X such that some abstraction involving X irritates
me" -> {.i da zo'u tu'a da mi fanza}.
Otherwise, {.i tu'a da mi fanza} is equivalent to (mangled English
follows:) "Some abstraction in which there exists an X that is
involved in that abstraction irritates me."

I get the impression that sumti inside LAhE don't follow the usual
rules, otherwise lu'i (and possibly some other LAhE) would be
completely pointless. That is to say that if the description of
individuals preceded by lu'i distributes, then lu'i creates a whole
pile of sets whose cardinalities are presumably the inner quantifiers
of the lo-description and that distribute into the containing bridi:
{lu'i ci lo mu nanmu cu se kampu lo ka melbi}. That would create the
additional implication that {PA lu'i LE broda} == {lu'i PA LE broda}.
I don't think that's useful at all.
The useful interpretation of {lu'i ci lo mu nanmu} is "the set
composed of three of the five men" (not to mention that it's highly
unuseful to quantify either sets, predications, or properties).

mu'o mi'e la tsani

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