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Re: Model Theory

From: Lynn Andrea Stein <lynn.stein@olin.edu>
Date: Thu, 03 Jan 2002 14:30:07 -0500
Message-ID: <3C34B154.55BB9C39@olin.edu>
To: Ian Horrocks <horrocks@cs.man.ac.uk>
CC: www-webont-wg@w3.org
Ian Horrocks wrote:
> 
> To expand on the point I made at the end of the teleconf, I really
> don't believe that this emphasis on model theory helps much w.r.t. the
> point that Lynn was making, i.e., the question as to why I should
> care.

Thanks, Ian, for an articulate statement of the problem.

> As far as I am concerned, model theory is just one way (some would say
> a very elegant way) of precisely specifying the meaning of the
> language (its semantics). I think that the reason for needing such a
> specification is pretty obvious: a language (particularly an ontology
> language that is intended to be interpretable by "automated agents")
> is of limited (zero?) utility if we can't be sure of the meaning of
> what we write down in that language (yes, I know that natural language
> works reasonably well for humans without satisfying this
> requirement). Moreover, people writing/using software for the language
> need a precise specification as to how it should behave and when it is
> broken.

There are some important points buried here.

1) The issues that arise in natural language arise are more general to
human interaction.  We will have them on the web, whether we like it or
not.  (In formal languages, we call this misuse or abuse, but it's real
use.  See my previous message [1])  We will need to deal with it. 
(E.g., there *will* be contradiction on the web, and it'd better not
make OWL collapse.  There will also be "shades of meaning" and other
things that traditional semantics are lousy at capturing.  (Tell me
about the semantics of beauty....))

2) It's not just natural language, either.  Programming languages have
formal specifications, but implementations still vary and people code
with different interpretations of the programming language.  (That's why
you get dialects or "write once, debug everywhere" or....)  To think
that we will be able to precisely specify all meanings on the web is to
fundamentally misunderstand the web as well as semantics.

Really, this is an issue of semantics being applicable to
well-formulated concepts and specifically to their truth.  Semantics are
not really about *meaning*, they're really about *truth*.  And it is
admissible -- even conventional -- to say that something is ill-formed
and therefore without (or outside of) semantics.  This is just a bad fit
for some aspects of human activity.  (I can hear Pat Hayes getting fired
up now....)
 
> There is an argument that goes something like "the web will be full of
> inconsistencies, so logical reasoning will be useless (everything will
> be inconsistent), so why should we care about formal semantics". I
> don't believe that this holds water for a variety of reasons including:
> 
> 1) Usually we will only be dealing with a (very small) part of the
> web. It is reasonable to ask if the information there is logically
> consistent and useful to know if it isn't.

But this isn't how semantics works; it's not piece-wise.  (This is
precisely how traditional logical semantics will break on the web, and
also perhaps how we can hope to  "fix" it.  But piece-wise or local
consistency is not at all sympatico with traditional semantics.  (It's
why I think this is potentially a really exciting endeavor from the
semantic end of the universe.)
 
> 2) There is a big difference between an inconsistent ontology and web
> pages that state contradictory facts w.r.t. an ontology - if I am
> going to use/trust an ontology I would like to know that it is
> logically consistent. As far as the web pages are concerned, if I know
> that they are contradictory then I can make an informed decision about
> how to deal with them.

This presumes that you can delineate "an ontology", which for your
purposes (as an ontology designer/provider) you probably can, but from
the perspective of a naive web consumer may be completely untenable.

I do think that we agree about a lot of things, and I do think that we
can find useful pragmatic ways to move forward.....

Lynn


[1] http://lists.w3.org/Archives/Public/www-webont-wg/2002Jan/0009.html
Received on Thursday, 3 January 2002 14:30:29 GMT

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