[SCL] Re: Stating the model theory free from lexical categories

[Chris Menzel]

On Fri, Jun 06, 2003 at 05:11:38PM -0500, pat hayes wrote:
> ...
> >> As you know, I havnt liked your 'standard' way of defining languages
> >> from day one, but Ive shut up about it because its just us guys
> >> talking and you are the one writing the documents. But I think that we
> >> have got to a point where we have to get this thrashed out, because
> >> this notion of a logical language is now causing problems. SCL isn't a
> >> language in this sense: its an ontology notation with a model theory.
> >> The 'languages' are just side-effects of ontologies.
> >
> >I really don't know how to write things up much differently.  Where does
> >the notion of a formula come from?
> 
> I'll try to sketch it this weekend.

Careful not to waste effort.  It seems to me the standard model
theorist's dream of reason is still the right way to present the
theoretical underpinnings, so long as care is taken not to mislead the
reader into thinking that it is also a model for implementation.  This
is a job for documentation, not theory.  In reality we discover the
lexicon/language of an ontology after the fact.  But it is still the
case that the language of that ontology has to be thought of in
principle as based upon the implicit lexicon.

> >> >Granted, we don't stipulate overlap relations between lexical
> >> >categories in SCL, because SCL permits any kind of overlap in its
> >> >instances; but a *given* lexicon will have to stipulate those
> >> >relations explicitly -- theoretically at least.
> >>
> >> I disagree, see above. In fact I don't think we even need the idea of
> >> a lexicon (other than some kind of global lexicon to enable a parser
> > > to distinguish names from eg whitespace.)
> >
> >Well, *that* might be true, but the point is that you DO need a lexicon
> >of basic syntactic elements to bring any semblance of order to the
> >language and its semantics.
> 
> We are in a slightly odd position here, though, in that we have 
> 'lexical' categories which are allowed to overlap. That is, we have a 
> *category* which can't really be identified with a predefined set of 
> strings. Maybe we need an intensional notion of a lexicon (??I can 
> hardly believe that I just typed that, but that's what it seems to 
> say...)

I don't think so, but I'm going to save that quote for posterity to
demonstrate how far you've come! ;-)  I see don't why it isn't enough
just to allow overlap between the PredCon and IndCon categories -- the
overlap defining the category in question.  If, in parsing an ontology,
you find both p(x) and q(p), then p must be in the overlap.

> >> It would be OK to have a notion of the lexicon of an interpretation,
> >> actually; but it has to be understood to be a semantic notion, not a
> >> syntactic one.  The lexical category of an interpreted symbol is
> >> defined by the interpretation mapping,
> >> ...
> 
> On reflection, this is really just the old CL idea of merging the 
> lexical categories of individual and relation symbol categories, 
> thought of as a pre-defined lexical categorization; but it allows us 
> to 'classify' them into categories depending on how they are used in 
> an expression.  You know, we didn't ought to find this troublesome 
> since we do exactly the same, in effect, for terms and atoms. You can 
> only tell them apart by looking at their surrounding context.

Well, I think you are tending more in the direction of saying that there
really isn't anything to tell apart -- they is but One Category (and
Hayes is its Prophet!), but *in situ* different members might assume
different syntactic roles.

> In a nutshell: the syntax depends on having syntactic categories of 
> relationName and individualName. 

What I've been calling PredCon and IndCon.

> BUt these are syntactic categories rather than lexical categories.
> Making them be lexical categories is a decision for a particular
> concrete syntax to make: some may, but this is not required by the
> abstract syntax. Make sense?

I think so, if my account above is right -- you are saying (very
roughly) that the categories only emerge out of a given ontology.  But
again, I'm for just working in the dream of reason for theory.  My
recollection anyway is that one of the things we wanted to do in SCL was
preserve the familiar lexical categories, albeit jacked around a bit
vis-a-vis overlap.  If we head back too far in the direction of CL, we
risk having to fight those traditionalist battles over again.  SCL, with
genuine lexical categories (even if discovered in reality after the
fact) strikes as a most excellent Middle Way that preserves most all of
what we wanted of CL while side-stepping largely superficial disputes
over form.

-chris