Re: [lojban] {da} and abstractions

Welcome to LoCCan3! There are two and a half answers to your question and a couple of conventions. None of this is clearly spelled out anywhere, though assumed in various places. The syntactic scope is the bridi in which it occurs, but the logical scope may be different, as in "if a boy comes to the party, all the girls there will dance with him" which would be literally converted to "If a boy come to the party all the girls will dance with someone", So the logical scope is sometimes said to be to the farthest occurrence of the variable involved, with the prenex adjusted accordingly, 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. Cutting 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 the 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 LoCCan3 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 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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