TECH: nunsucta sidbo

[i.alexander.bra0125@oasis.icl.co.uk]

Some ideas for identifying focus points, "objects of interest",
in abstractions.

Option 1:  The direct approach

I've tried expressing some of these "indirect question"-type
phrases without using {kau}.  I came up with the idea of
using {lu'e} to turn "X" into "a symbol for X", as an
approximation to "the identity of X".  This seems to work
reasonably well for some things

        mi djuno lu'e le klama be le zarci
        I know the-symbol-for the-one-I-describe-as-a goer to the store
        I know who goes to the store

(instead of
        mi djuno ledu'u dakau klama le zarci
)

but a lot of other types don't yield so easily.  For instance,
"how many" questions are awkward.

        mi djuno ledu'u tu'okau da klama le zarci
        I know how many went to the store

There isn't even an ideal gismu which relates a set to the
number of elements it has.  The best I could find was

        mi djuno le te kancu be le'i klama bele zarci

Even if we can ignore the suggestion of an agent in {kancu},
this is starting to get clumsy, and quantities are one of the
things we need good expressions for.

Other uses of {kau} are even more problematical, such as
{xy. jikau .ybu}.

There may be a way of getting this to work, which would free
up {kau} for other things such as the "property of X"
construction, but it's not clear at the moment.


Option 2:  Tweak the status quo

Option 2a:  More UI tags

Scrape up another cmavo or two, and/or invent a pseudo-scale
for {kau} (kau-kaucu'i-kaunai, or whatever), to extend the
possibilities.  The situation I'm fairly sure needs a solution
is the quantified property - the property of X which is the
number of Y in P(X, Y).  So if {kaunai} (ugh!) was used to
flag the number which we are interested in, and
{kau} as in the abstraction paper for the DA whose property
we are describing, we could get something like

        mi zmadu do le ni dakau citka tu'okaunai plise
        I exceed you in the number of apples we eat.
or
        mi zmadu do le ni dakaunai prami dekau
        I exceed you in the number of those who love us.

While we're at it, we might want to allocate a LUhE for
"the number of elements in the set".


Option 2b:  {kau} vs. non-{kau}

Of course there's always my previous idea of using an
un-{kau}-ed variable for the lambda-binding and {kau}
for the quantity of interest.  I don't see shortage of DA
being a real problem - a lot of the time you won't even
bother putting one into a property abstraction;
and occasionally you'll need lots of them,
but we've got subscripts to handle that.


Option 3:  Extend the prenex/quantifier construction

The main mechanism in Lojban for introducing bound variables
is the prenex, and the way the variable is quantified in the
prenex tells what kind of binding is intended.
A (frequently implicit) {su'o} introduces an existentially
bound variable, an explicit {ro} introduces a universal
binding, an ordinary number introduces an exact numerical
binding, and most other situations (e.g. a simple pro-sumti
or a description with no explicit quantifier) suggest a
mere topicalisation.

How about we introduce some quantifiers or pseudo-quantifiers
for other kinds of binding, such as lambda-binding or
number-of binding.  This would be more-or-less conventional,
and could potentially be extensible to allow things which
we've forgotten to be added later.

Time for an example.  Just using existing syntax, we can say

        vei ge'o ly. da zo'u da blanu
        lambda x: x is-blue

        vei ni bu da zo'u da plise
        number-of x: x is-an-apple

Ultimately this ends up not too different from option 2,
since of course you can move the pseudo-quantified
variables out of the prenex and into the bridi, and then
throw away the prenex, just as we do with the more
conventional quantifications.

Of course these are unbearably clumsy for everyday use,
so we'd probably try and allocate them a couple of the
few remaining cmavo (as PA), but in an emergency you could
invent a new quantifier on the spot using the
long-winded method.

If we use {xa'a} for lambda and {xa'i} for number-of, we get

        xa'a da blanu
        lambda x: blue(x)

        xa'i da plise
        number-of apples

        xa'i da prami xa'a de
        lambda y:  number-of x:  loves(x, y)

What's happened to {du'u}, {ka} and {ni} in all this?
I'm not sure - they seem to be mutually redundant,
but we might retain them all for convenience.

pinka fi ko .e'o

mu'o mi'e .i,n.