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Re: [ontolog-forum] Ontology-based database integration

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Wed, 07 Oct 2009 11:07:41 -0500
Message-id: <1254931661.15961.95.camel@kestrel>
On Wed, 2009-10-07 at 00:05 +0000, Len Yabloko wrote:
> ...
> Of course Semantic Web technologies are expanding now into these old
> territories you have referenced with such detail and accuracy. But one
> has to be very careful not to confuse semantic modeling with data
> modeling and data linking with data integration. And, indeed, not to
> confuse model-theoretic semantics (developed by Tarski for first order
> logic and claimed by RDF) with various other semantics.     (01)

By saying RDF has "claimed" model theoretic semantics, do you mean
anything more than that it has been provided with a model theoretic
semantics?  That's a good thing, right?    (02)

> I believe OWL itself is an attempt to go around the inherent
> limitations of Semantic Web.     (03)

I'm not sure what limitations you have in mind.  OWL is an attempt to
provide a standardized ontology language built upon a logical framework
in which questions of consistency, validity, etc are decidable.  In
general, such questions are not decidable, and that is certainly a
limitation, but it predates the Semantic Web by several decades.    (04)

> I have been following these forum long enough to have heard all kinds
> of claims about what is Semantics and many of these claims were tying
> it directly to FOL, like no other logic or semantics ever existed.    (05)

Really?  I can't remember anyone ever having made any such claim.  I
frankly doubt whether you could find a single example.  What people
*have* said is that, whatever representational medium you choose, it
must have a clear model theoretic semantics (regardless of whether it
happens to be that of classical first-order logic) so that the meanings
of its primitive logical vocabulary and its basic grammatical constructs
are well-defined.  Without that, questions of consistency and questions
of whether one thing follows from another are, quite literally,
nonsense.    (06)

I believe this is what Ed had in mind when he wrote:    (07)

> >Formal logic is a means of expression, in which the basic elements of
> >the language have well-defined meanings and a set of well-defined
> >manipulations retain those meanings, and nothing more.      (08)

I think by "well-defined manipulations" Ed means the inference rules of
a logic -- whose legitimacy is justified by the underlying semantics.
But, importantly, model theoretic semantics is very limited; it is
restricted entirely to the assigning meanings to the basic logical
expressions and telling us how to interpret the grammatical
constructs of a language in terms of their simpler parts.  For
nonlogical vocabulary, a model theoretic semantics tells us only the
*kinds* of things signified by each grammatical category: e.g., names
refer to individual things (whatever those are), predicates refer to
classes, etc.  But *which* things the names of an ontology refer to and
*which* classes its predicates pick out and exactly which classes a
given individual belongs to and exactly what logical connections relate
the classes we're interested in --- all of that is the job of what we
might call "applied" semantics, a.k.a.  ontology. And model theoretic
semantics is entirely silent on those questions.  As Ed put it:    (09)

> >As to whether the snark actually is a boojum, classical formal logic
> >offers only two possible interpretations:  it is either true or it is
> >false, and it cannot be both.  And if you make a set of statements
> >that allow the well-defined manipulations to produce a result of
> >"true", then it does.  That's all there is; there ain't no more.
> >Formal logic is about "how to think"; it is not about what you think
> >about.    (010)

That is pretty much spot on.    (011)

Chris Menzel    (012)

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