[SCL] scl 1.1

[Chris Menzel]

There is some fresh SCL meat for working group vultures at

  http://cl.tamu.edu/docs/scl/scl-latest.html

Unfortunately, there were so many little and not so little things that
were wrong and/or unclear in the 1.02 document that most of what I've
ended up doing over the past week (among other things) is just clean up,
focusing primarily on the translation scheme -- I have yet to actually
put in the stuff on identity that we talked about in Florida, though I
have written up a good bit of it I will continue working on it tonite
and tomorrow.  What I've got on identity is still too rough, though, and
I wanted to get something concrete on the web.

The main thing to note about this version is the improved section on
translating a first-order SCL language to a traditional first-order
(TFO) language.  On the current definition, the translation of an SCL
language that is already a TFO language is (structurally speaking)
vacuous; nothing is changed.  This isn't a deep point, but it is
something you'd want to make sure is the case.  At the other end of the
spectrum, the translation of an unconstrained language (one, in effect,
with no distinction between constants and predicates) is very simple and
straightforward in terms of Holds predicates and App function symbols.
So the SCL language that Tanel wants also falls out as a simple special
case.  (I leave it open whether unconstrained languages should be the
*only* type of SCL language, as Tanel has been arguing.)

Just a word about identity.  I will open with a discussion of the issues
involved in using a standard identity predicate in a general SCL
language; this will be illustrated in particular by a Horrocks sentence.
The idea Tanel more or less convinced us of in Florida is to introduce
an axiomatized weaker notion of identity as an SCL extension that just
applies to individuals that are not properties or relations, rather than
including it as part of the language proper (and hence as a
distinguished relation in the model theory.  This will be discussed in
the next version.

In addition to getting the identity stuff banged out, there is still
some housekeeping to do in the syntactic stuff.  I haven't done anything
about incorporating Robert Kent's definition of the grammar; and I'm
still not convinced it is a significant improvement over what we've got
(though I'd be happy to be convinced otherwise).  But that I haven't
incorporated is not a *decision*; it just reflects lack of time and, at
this point, inclination.

Let me emphasize Yet Again that this is an internal document (though
of course anyone can look at it) and is intended only to get the
concepts right.

-chris