From LOJBAN%CUVMB.BITNET@uga.cc.uga.edu Fri Nov 18 23:16:24 1994
Message-Id: <199411190416.AA06299@nfs1.digex.net>
Date: Fri Nov 18 23:16:24 1994
From: Jorge Llambias <jorge@PHYAST.PITT.EDU>
Subject:      Re: PROPOSAL: Lambda Notation For Dummies (and & Rosta) & Lojban
Status: RO

> > > This proposal involves creating an explicit "lambda quantifier", which
 would
> > > formally belong to selma'o PA but would be attached only to da-series KOhA
> > > or BY cmavo.
> > Any reason why this is preferred to a simple KOhA?
>
> Well, one point is that "a simple KOhA" could only be a singleton.  If
> we want to have properties or mekso with two lambda variables, we'd have
> to subscript them, which is unmathematical: it's \lambda(x), not \lambda.

I tend to ignore the mekso part of the language, I don't think we have to
cover for every symbol of mathematics.

Is there any use for properties with two lambda variables? And in any case,
here we could use subscripts if such a thing really ever comes up.

> > Also, it would be nice if we could just use {ke'a} for it. Its function is
> > very similar, and the problems that might arise in rare cases of embedding
> > arise already anyway as it is, so in theory subscripts have to be used.
>
> I'll consider this one.  "ke'a" is pretty narrowly defined,
> and I don't know that I favor extending it.

But the two meanings are very close, if not the same.

{kau} was also mentioned but I don't think that that is the same thing
at all. It can have a very different meaning inside properties. For example,
using ke'a for the lambda variable:

        ko'a zmadu ko'e le ka ke'a citka pixokau da
        Koha exceeds Kohe in the property of how much they eat.

Clearly, {kau} can't be used to mark the lambda variable, because it
already has a function to mark the indirect question.

Notice that {ni} gives a different meaning:

        ko'a zmadu ko'e le ni ke'a citka da
        Koha exceeds Kohe in the amount of eating something.

(Actually, it is not very clear to me what {ni} means.)

Jorge