Re: SUO: Re: IFF Model Theory Ontology 1.0, Request For Comment
Bill,
Jim F. is out of town, so I'll give a preliminary response to your comment.
----- Original Message -----
From: "Bill Andersen" <andersen@ontologyworks.com>
To: "Robert E. Kent" <rekent@ontologos.org>; "Jon Awbrey"
<jawbrey@oakland.edu>; "West, Matthew R SITI-ITPSIE"
<Matthew.R.West@is.shell.com>
Cc: "SUO" <standard-upper-ontology@ieee.org>
Sent: Tuesday, May 14, 2002 11:08 AM
Subject: Re: SUO: Re: IFF Model Theory Ontology 1.0, Request For Comment
[snip]
> Forgive me for being impertinent, but you don't need a bunch of category
> theoretic machinery to do what you've just described. For what you have
> described are standard relations in intension. They are like relations,
> but their identity isn't extensional. They have an extension, but aren't
> identical to that extension.
Yes, OK. But the purpose of the IFF-MT is more general than this; it is to
provide a well-structured semantics for object-level ontologies represented
in various FOL languages, and a semantics that is smoothly compatible with a
principled approach towards the "lattice of theories" framework that has
been advocated by folks in the SUO-WG. We need a semantics for these
object-level representations, and this can be either set-theoretic or
category-theoretic. The IFF-MT offers a category-theoretic approach that is
based upon the simple notions of classification and hypergraph.
And besides, category theory is not more complicated than set theory. It is
just better structured. ;^) Seriously, it is my experience than the attempt
to define morphisms for various notions is an acid test as to whether that
notion has good (and simple!) structure.
> So, given the right syntax and semantic support from a logic (which the
> Common Logic standard proposal happens to provide - http://cl.tamu.edu)
> there is no problem whatsoever saying:
>
> Red(ColorOfRobertsRedFerrari)
>
> Color(Red)
>
> or even
>
> Property(Property)
Yes, that is a nice syntax. But you still need a good semantics. I presume
the CL doc
<http://cl.tamu.edu/discuss/cl-syntax-semantics.pdf>
provides a set-theoretic semantics (I have not been able to read it as of
yet, since I get a corrupted file when I try.) But we want to define an IFF
Common Logic portal that will provide an (alternate, if you will)
category-theoretic semantics. And again one that meshes well with the
"lattice of theories" approach.
Thanks for the comment.
Robert E. Kent
rekent@ontologos.org