Welcome to= LoCCan3! There are two and a half answers to your question and a cou= ple of conventions. None of this is clearly spelled out anywhere, tho= ugh assumed in various places. The syntactic scope is the bridi in wh= ich it occurs, but the logical scope may be different, as in "if a boy come= s to the party, all the girls there will dance with him" which would be lit= erally converted to "If a boy come to the party all the girls will dance wi= th someone", So the logical scope is sometimes said to be to the fart= hest occurrence of the variable involved, with the prenex adjusted accordin= gly, But this runs into the problem of reusing the a variable, which = is not supposed to be done in short spaces, but happens any how. Cutt= ing across that is the questionable (but often practiced) requantification of a variable, as in "I some boys come to the party, all = of the girls will dance with at least one of them". The situation is = easiest with covert quantifiers (unfilled places), which die at birth. = ; The hardest cases are those inside intentional contexts (nu and ka and th= e like) which ought to die with the context (for semantic reasons, at least= ) but often do not.Getting this straightened out is one major fuel for LoCC= an3 speculation of the sort that could reflect back on Lojban.

From: Jacob Errington <nictytan@gmail.com>
To: lojban@googlegroups.com
Sent: Thursday, July 12, 2012 5:47= PM
Subject: [lojban] = {da} and abstractions

coi ro do

I'm not sure if the CLL ever mentions it, or if there's so= me general
consensus or convention governing this, but to the prenex of = which
bridi do logically quantified variables that have not been declare= d in
any prenex belong? (I feel like that "belong" elides a lot of
no= n-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 z= dile 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 b= ound to a higher prenex beforehand, then does that
mean that we can recy= cle variables in sibling abstractions?
e.g. {lo ka da xebni ce'u cu kamp= u lo'i nanmu noi ke'a se kampu lo ka
da prami ce'u}

This becomes especially interesting in the case of certain logical
connectiv= es (bridi-tail connectives) and when the quantifiers of the
variables di= ffer:
#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 wi= th regards to logical
connectives and logically quantified variables.)
Additionally, logically quantified variables have a similar issue wit= h tu'a.
Consider the formal definition of tu'a:
{tu'a ko'a} =3D=3D {l= o 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 s= lot?
{tu'a da} =3D? {lo su'u da co'e}
Is the formal definition contin= ues to apply, and logically quantified
variables are bound to the bridi = in which they appear unless defined
in a parent bridi, then it is necess= ary 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 fanz= a}.
Otherwise, {.i tu'a da mi fanza} is equivalent to (mangled Englishfollows:) "Some abstraction in which there exists an X that is
involve= d 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 t= he description of
individuals preceded by lu'i distributes, then lu'i cr= eates a whole
pile of sets whose cardinalities are presumably the inner = quantifiers
of the lo-description and that distribute into the containin= g bridi:
{lu'i ci lo mu nanmu cu se kampu lo ka melbi}. That would creat= e the
additional implication that {PA lu'i LE broda} =3D=3D {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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