[SCL] Approach to a concrete syntax

[Chris Menzel]

On Thu, May 22, 2003 at 10:31:30AM +0100, Murray Altheim wrote:
> I think you're missing my point: in expressing SCL in RDF you have no
> ability to avoid the complexities. You're mistaken if you think you
> can gloss over the interpretive differences between SCL and RDF. This
> would be like saying that expressing SCL in French you've avoided the
> complexities, when in reality all you've done is add French
> interpretation (and any ensuing ambiguities or misinterpretatins) to
> the existing semantics.
> 
> As I said, the only difference between expressing SCL in XML and
> expressing SCL in RDF is that the latter you're going to be dealing
> with even *more* interpretation, not less.

I think this is a point where a bit of terminological caution is called
for, as there are a couple of very different notions floating around
here.  A very important difference between XML and RDF is that RDF is
itself a language (or perhaps a class of languages, depending on one's
choice of nonlogical constants) that expresses a well-defined model
theoretic semantics.  It has been provided with a distinctively XML'ish
syntax (as well as a graphical syntax), but that is not essential to
what it is -- though it is of course essential to its being *used*.

Among all the things that XML is, it is not that; XML is (among other
things) a framework for defining languages, and does not itself have a
model theoretic semantics.

Corresponding to these two very different entities are two very
different notions of "expressing".  When you have two languages with
their own model theoretic semantics, expressing is a semantic matter.
Roughly speaking, to say that L1 can be expressed in L2 is to say
something like this: there is a "meaning preserving" mapping from the
sentences of L1 to the sentences of L2.  There are a number of ways to
cash out "meaning preserving" here, but the important point here is that
meaning preservation is cashed out model theoretically -- the models of
L2 must be capable of "mirroring" the models of L1 in some fashion and
the L2 image A' of a sentence A of L1 must pick out exactly the L2
"mirrors" of the models that A picks out.  There is, for example, a
well-known meaning preserving mapping of this sort from the language of
number theory to the language of set theory that takes "0" to the symbol
for the empty set, sentences involving "+" to sentences that talk about
the unions of sets, and so on.

This is the sense of "expressing" that is relevant in talk of expressing
SCL in RDF.  And, importantly, in this sense, there is simply no way to
express SCL in RDF -- the logical underpinnings of SCL -- more exactly,
of any SCL language -- notably, its full classical quantification
theory, are simply far richer than the underpinnings of RDF; there are
sentences of any given SCL language that will simply have no
"equivalent" RDF counterpart.  However, it IS possible to express RDF in
SCL (that is, to express an RDF language in an SCL language); which also
yields the *fragment* of SCL that is expressible in RDF, which might be
important to identify for various purposes.

By contrast, the simplest and most direct notion of "expressing"
relevant to the idea of expressing SCL in XML is very different.  The
idea here is complete syntactic, namely, to provide an XML DTD that
yields a class of SCL languages with a distinctively XML-ish grammar.
Unlike the model theoretic notion, this notion is simple and
straightforward; I've already given one (that probably can stand some
expert improvement) in the SCL spec.

Now, once we are clear about this, further questions might well arise
about how a basic XML-based SCL language might be enhanced for one
web-based purpose or another.  It seems to me a lot of the controversy
we've seen in the flurry of msgs over the past couple of days can be
seen as concerning *this* issue, which strikes me as important but quite
orthogonal to the current SCL project.

-chris