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Re: Model Theory

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Thu, 3 Jan 2002 23:28:08 +0000
Message-ID: <15412.59656.275598.291412@cs.man.ac.uk>
To: las@olin.edu
Cc: www-webont-wg@w3.org
On January 3, Lynn Andrea Stein writes:
> 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.

I don't think a language can collapse, can it? As for reasoning
engines, I don't think anyone would suggest that collapsing is an
appropriate response to inconsistency. All I am suggesting is that it
should be possible to detect inconsistency. If you know that the
information you have is inconsistent you can then make a more informed
decision as to what to do with it.

> There will also be "shades of meaning" and other
> things that traditional semantics are lousy at capturing.  (Tell me
> about the semantics of beauty....))

Sure, but the charter says that we are only developing a relatively
simple ontology language. Of course there will be lots of stuff that
we can't capture using such a language.

> 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.

I don't think that. I think that we are just developing a relatively
simple ontology language that will, hopefully, do some/most of what
some/most people want. 

> 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....)

But ontologies don't consist of concepts, they consist of axioms
asserting, e.g., concept subsumption. This is where the meaning is.
All you can say about a concept is that its extension is/is not empty
in some/all/no models. I suppose that you might want to equate one of
those conditions with *truth* w.r.t. that concept?

Of course one also has to deal with ill-formed syntax (at least in any
practical system). Not quite sure I get what the point is though.

> > 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.)

I disagree. Surely I am free to pick any subset of the entire web that
I like and reason with that. The semantics will work perfectly well
within my selected subset. I hope you aren't suggesting that we
should/must view the whole web as a single knowledge base with which
we can/must reason - that doesn't seem very practical!

> > 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 disagree. I think that much of the early take up will be in the
development of large domain ontologies that people can use in
annotations. The Gene Ontology is a good example, and they are
committed to migrating to DAML+OIL/OWL [1]. Before I use such an
ontology, I would like to know that it is at least logically
consistent (i.e., has at least one model), and I would view with
suspicion any genetic data/annotations that turned out to be
inconsistent w.r.t. that ontology.

> 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.....

I agree. My idea of pragmatism is not to be too ambitious about the
language that we are developing (and I think that this is consistent
with the charter) - I hope that this isn't too far away from your idea


> Lynn
> [1] http://lists.w3.org/Archives/Public/www-webont-wg/2002Jan/0009.html

[1] http://www.geneontology.org/
Received on Thursday, 3 January 2002 18:28:28 GMT

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