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Date: Sun, 9 Oct 2011 13:03:07 -0400
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
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* Sunday, 2011-10-09 at 12:11 -0400 - John E. Clifford <kali9putra@yahoo.co=
m>:

> On Oct 9, 2011, at 0:27, Martin Bays <mbays@sdf.org> wrote:
>=20
> > * Saturday, 2011-10-08 at 19:56 -0400 - John E. Clifford <kali9putra@ya=
hoo.com>:
> >=20
> >> It seems the only logically sensible out is to allow unfilled
> >> spaces only for variables (the general case) and require something
> >> more specific for the rest,preferably the appropriate pronouns in
> >> those case and {zo'e} on the last, though I suppose that in most
> >> cases {zo'e} could do for all three.
> >=20
> > But unless I'm misunderstanding what you mean by variables, the other
> > three cases (which are arguably really just one case) are just special
> > cases of the variable case - namely, where the glorked domain of the
> > existential quantification is a singleton (whose single element might be
> > a plurality, of course).
> >=20
> Here is the problem, then.  In standard semantics, the universe or
> domain of discourse is a given and all variables range over the items
> in that domain.  There is no case of a special domain to be used for
> just one variable, separate from the domain that applies to all the
> others (there are complications here but none that bear on this
> point).  I suppose some mechanism could be worked out to do something
> like this, but it seems a lot of work for no apparent gain.
>=20
> > So I'm understanding you as having {zo'e} force the domain to be
> > a singleton, but otherwise to work like an unfilled place
>=20
> No. Domains don't change like that.  {zo'e} is simply a constant.  Is
> this strange ad hoc domain what you mean by "close-scope"?  Rather
> than its effect in the structure of the sentence?

I didn't mean to do anything funny with the domain of discourse. By
'domain', I meant the domain of this particular quantification - so in
{da poi broda}, the set of (atomic) brodas is the domain of that
quantification.

So having {zo'e} give existential quantification over a glorked
singleton domain is equivalent to having it give a constant.

To be more precise about how I'm suggesting zo'e works / should work:

If we have a predication P(zo'e noi broda, zo'e noi brode), it resolves
as:
    EX (X1,X2). (C(X1,X2) /\ P(X1,X2))
where C is a context-glorked relation which depends on any quantifiers
(including ones over worlds) which the current predication is in the
scope of, and which is such that C(X1,X2) implies broda(X1)/\brode(X2).

(X, X1, X2 all plural mundane variables, i.e. not allowed to take kinds,
but not restricted to atoms)

(Here I've made C a relation rather than a set, which is a subtle
difference but I think an improvement)

Furthermore, I'm suggesting that at least some uses of {lo} follow this
pattern - i.e. that P(lo broda, lo brode) means the above, at least
sometimes.

Something else which might not be obvious: I think this resolution
of zo'e-terms happens *after* most other processing, in particular after
resolution of anaphora. So e.g. {broda zo'e ri} is just equivalent to
{broda zo'e zo'e}.

More generally, I think we can split semantic analysis of lojban into
two broad stages - a pre-pragmatic stage, in which there is no
vagueness, ambiguity or glorking, but which leaves behind tanru,
zo'e-terms, non-anaphoric prosumti like {ti}, and perhaps some other
such things; and a pragmatic stage which applies glorking to handle
those leftovers. We're talking here about how the pragmatic stage
handles zo'e-terms.

The prepragmatic stage should return a sentence in a logic something
like Montague's IL, but with basic terms and relations having some
structure, like zo'e-terms and abstractions and tanru. I think this is
quite doable, and that doing it is the best way to specify the logical
parts of lojban.

But that's branching from the point.

> > It seems reasonable to want a word for that. Maybe it should be {zo'e},
> > I'm not sure. If it were, we'd need to find another word with the
> > meaning of an unfilled place, say {zo'e'e} - if only because {lo broda}
> > would then be {zo'e'e noi broda} rather than {zo'e noi broda} (to
> > whatever extent that equivalence ever works).
> >=20
> >> So, back to the question case: the appropriate negative responses to
> >> the question { xu do klama le zarci} are {na}(or should that
> >> be{naku}?), {na go'i}, {mi na klama zy} ( or some more official
> >> pronoun), and the basic {mi na klama le zarci}, with {mi na klama
> >> zo'e} as a marginal possibility.
> >=20
> > And {mi na klama} as a definite possibility, yes?
>=20
> I would say, no, because that would have me going nowhere, not merely
> not to the store.

Right. But I don't think having the quantification always be over the
whole domain of discourse, rather than a glorked portion thereof, is
very usable. For example, one arguably is always klamaing somewhere -
even if just to the place one already is at.

Martin

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