Message-Id: <m0seDF6-0000ZHC@xiron.pc.helsinki.fi>
Date:         Thu, 3 Aug 1995 19:54:38 -0700
Reply-To:     "John E. Clifford" <pcliffje@CRL.COM>
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         "John E. Clifford" <pcliffje@CRL.COM>
Subject:      lu'a
To:         lojban list <lojban@cuvmb.cc.columbia.edu>
Content-Length: 6742
Lines: 143

lojbab:
The lu'a series has two origins.  One was as a solution for the multiple
connectives problem:  how do you for example specify a 4 term XOR - pc
found that by the time you got to 4 terms that Lojban's grammar did not
generate all possible truth-table combinations without repetition and
rearranging.  But the tough ones could all be expressed using the form
"1 from the set {a,b,c}} and 2 from the set {d,e,f}".  Hence lu'a.
pc:
Boy, that stuff about multiple connectives sounds familiar, though the
details escape me
now.  In particular, I am not sure how lu'a fits in: it creats a set from
even a sentential
structure and then allows quantification over it?
lojbab:
Then the others were added as a way to disambiguate conversion among sets,
masses and indivudals.  I can't remember the archetype of this, but it
may have
been the multiple interpretations of mi'o, do etc as individuals or masses.
pc:
That looks like a likely source, although the difference between masses
and averages --
and probably the distributive sense -- seem to be generating more
problems right now.
So the question is what these really do do, keeping both the original
solutions and yet
making the structures as useful as possible.  So far, I have just been
following the brief
entries from the dictionary (often not the clearest help,alas) and trying
to make some
sense of xorxes' comments.  These are becoming more numerous and more
detailed,
though still examples rather than principles.  For example,
>       lu'i mu lo plise: a set of exactly five apples.
This and similar items seem to be no problem: xorxes' interpretation
coincides with the
one I hypothesized.  mu lo plise gives  us five apples distributively and
lu'i groups them
into a set, a five-membered subset of lo'i plise (here we really are
forced to use set talk).
The set is presumably definite (or is it specific) even though the
members have not been
identified. Presumably lu'o mu lo plise would mean the five apples were
massifed for
both of us. But I suspect that lu'a mu lo plise may be treated
differently.  Indeed, I am not
sure how to treat it, because I do not know what the implicit quantifier
on lu'a is, ro or
su'o.  If it is ro, then I would take the lu'a as being redundant, since
mu lo plise already
takes all the five apples distributively.  If lu'a is su'o lu'a then this
would distribute only
some of the original five.  I am unclear how, in that case, lu'a mu lo
plise is related to lo
mu lo plise (or even le mu lo plise, which seems a particularly useful
notion, if I
understand it: the old "a" - "the" game in English, though that has
better explanations
within logic).  But I see that this is clearly not what xorxes has in mind:
>> lu'a ci le selcku might make sense, bringing us down to a new set
>> (assuming that I was calling more than three things selcku originally).
>No, to talk about one of the three books one would say {lo ci le selcku}.
>{lu'a ci le selcku}, if it makes any sense, should be a component common
>to each of the three books in question.
I cannot see how lo ci le selcku means "one of the three books"; it seems
literally to mean
"some of the three things which are among the books," i.e., " at least
one of some three of
the books," selecting distributively from a selection already made (but
not specified)
from the specified books.  If there were four originally specified books,
there are fourteen
arrays of books that might be covered by lo ci le selcku, but only four
by "one of the three
books" (assuming we could figure out what the three books are).  But that
gets us no
nearer to understanding  xorxes' lu'a ci le selcku: whence comes this
"component
common to each of the three books"?  There is nothing about that either
in ci le selcku,
which is just some three books, or in the notion of the members of a set
or component of
a mass (neither of which ci le selcku refers to anyhow).
>>  Massification is a logical operation, not a
>> Waring blender.
>Of course it is. but you don't need to refer to the mass always in terms
>of its components. Consider this:
>       lei pare plise cu gunma  i mi citka re lu'a le gunma
>       The twelve apples are a mass. I eat two components of the mass.
>The second sentence should not say that I eat two masses. To say that
>I can simply say {mi citka re le gunma}. The whole point of the lu'a
>series is that they work on top of the previous gadri. If they are
>going to bypass them then there's no point in having them.
As to the point, I suspect that the original use was to make sets, masses
and distributions
from things that did not quite fit those patterns, that did not start
with gadri (mi'o was
mentioned).  And there is the convenient subsetting routine just explored.
        I don't quite understand the latest example here: lei pare plise
cu gunma is
analytic, "the mass of  (the) twelve apples is a mass."  But the second
part is very unclear,
even given xorxes reading.  le gunma refers to all the masses the speaker
has in mind,
presumably the one mass of 12 apples.  lu'a le gunma is then said to be a
component
common to all of these, i.e., a component, in this case, of the one mass
referred to.
Ahah! we are to wander through the la'e/sa'e (old style -- what have they
become? the
symbol for a referent and the referent of a symbol) complex here.  That
might be very
useful, in fact, if it does not interfere with more fundamental uses.
But what then
becomes of a case where we DO refer to a mass throughits components: what
is lu'a le'i
pare plise or, worse, lu'a le pare plise?  There does not seem to be any
components here,
since this phrase does not refer beyond itself.  But, in fact, we want to
get back to the
same apples.  I'm not convinced that this is a consistent interpretation,
as the one I
guessed at is (even if useless -- which I don't think it is).
>       lu'i re lu'o mu lo plise: a set whose two elements are masses
>                                of five apples each.
Presents another set of problems, since presumably re lu'o mu lo plise is
not legitimate,
masses getting at most fractional quantifers (and  those only on
idiomatic sufferance).
Thus, there is no form to add lu'i to.  I suspect that somewhere here we
have stepped over
from making new descriptions to introducing new predicates.  There are,
of course, many
lu'o mu lo plise, since there are many ways to meet the conditions of mu
lo plise, but I
think to start talking about this multiplicity, we have to introduce
gunma.  But then I am
still unsure just how this is to work.  It does seem to offer some useful
devices if they can
be made to work consistently, but I need some explanation -- or an
enormous number of
examples -- before I can begin to be convinced.

pc>|83