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Date: Sun, 13 Nov 2011 11:23:50 -0500
From: Martin Bays <mbays@sdf.org>
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Subject: Re: [lojban] Lojban and Truth-Conditional Semantics
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* Saturday, 2011-11-12 at 23:39 -0500 - maikxlx <maikxlx@gmail.com>:

> The only way, I suspect, that jbo(ske)pre are ever going to sort out
> some of these sticky issues involving gadri and related stuff is by
> adopting a much stronger and more rigorous formalism than has been
> adopted up to now.

I completely agree.

> Ultimately it would require a very good mathematician/logician to work
> out the whole system and then break it down for others (in English or
> Spanish or whatever metalanguage).  There are many ways to go, but
> I think what might best serve a logical language is a formalism
> focused on model-theoretical, truth-conditional semantics.  In other
> words, from any given Lojan sentence S, e.g. "su'o lo ctuca cu tavla
> ro le tadni", one ought to be able to work out, in a straightforward
> manner, every truth condition that would make S true with respect to
> an interpretation of basic terms (e.g. descriptions & predicates) and
> a given model (universe of discourse).

Yes. For much of lojban, this is straightforward in principle.

There have been a few attempts to do it in practice - I know of Nick
Nicholas' Prolog semantic analyser
http://www.lojban.org/files/software/analyser
, Rob Speer and Catherine Havasi's Jimpe
http://web.mit.edu/rspeer/www/research/jimpe.tar.gz
. I haven't managed to get either to run, due to bitrot, but they're
interesting anyway. I also have a WIP of my own along similar lines,
taking a more completionist tack, which I may release one day (I got
stuck on handling gadri).

However, there are plenty of hurdles in the way of completion of such
a project.

One is just that there isn't actually full agreement on the broad shape
of the semantics. For example - there is some, but as far as I know no
official, agreement that lojban has plural semantics. This would mean
that the domain is structured as a complete atomic boolean algebra
- i.e. we have individuals, but we also have bunches of individuals
(singleton bunches being identified with individuals). Then e.g. {ro
broda} probably quantifies only over individuals which broda, rather
than over arbitrary bunches which broda.

Another related one is how to handle descriptions. It's clear that these
go beyond first-order logic, and also that they involve context in some
way. But we do e.g. want the logic to encode the fact that {lo broda}
must broda, since this is part of the truth conditions of the sentence,
and this gets a little complicated when we note that broda may mention
bound variables. This also ties in with the question of the structure of
the domain - allowing {lo} to get a bunch deals with some issues;
I currently suspect we may end up wanting to add further structure to
the domain to incorporate "kinds". DRT may be relevant, but maybe not
very.

Anaphora are painful to deal with, though only donkey ones pose
theoretical problems.

GOhA is a minor nightmare.

But basically, I totally agree that developing a model-theoretic formal
semantics is (a) essentially doable, and (b) the best way to specify
this currently woefully underspecified language.

Martin


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