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Re: SEM: integration with RDF MT

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Fri, 9 Aug 2002 15:48:17 +0100
Message-ID: <15699.54833.804655.22234@merlin.oaklands.net>
To: "Jonathan Borden" <jonathan@openhealth.org>
Cc: <www-webont-wg@w3.org>

On August 8, Jonathan Borden writes:
> This back and forth between axiomatic and model theoretic semantics is
> confusing me a bit. I take it that the RDF model theory is being developed
> as a model theoretic semantics. Pat Hayes and Guha have proposed Lbase as a
> framework to integrate various model theories for semantic web languages. Is
> this the right question?

It may be interesting from a theoretical perspective, but it wont
change any of the issues we have been debating or solve any of the

> Does the choice of axiomatic vs. model theoretic semantics affect this? Is
> it possible to extend a model theoretic semantics via axiomatization? It is
> possible to develop the OWL semantics as an extension of Lbase? How are the
> RDF and OWL semantics intended to be related?

The question we need to ask ourselves is what we want semantics for
and what we want to do with them. My idea is that they should be a
declarative specification of the meaning of the language that is both
simple enough for people to understand and agree that it really does
capture the intended meaning, and precise enough to act as yardstick
against which algorithms and implementations can be measured.

If we choose a language that has a natural mapping to standard FOL then we
can satisfy these requirements by using either (or both) a standard MT or a
direct mapping into standard FOL, i.e., a mapping where classes
(resp. properties) map to unary (resp. binary) predicates, intersection
maps to and, union maps to or, negation maps to not, etc.

If we choose a language without a natural mapping to standard FOL, e.g., a
language that attempts a complete integration with RDF and includes classes
of classes, then our job becomes much tougher.  We can devise a MT for the
language, one that extends the RDF MT, but it will be much more complex,
e.g., including comprehension principles.  We may be able to devise a
complete axiomatisation of the language in FOL, but the axiomatisation will
be complex.  We may even be able to map the language into a different
logic, such as Lbase, but then we would be dependant on the properties of
this other logic.

Apart from the fact that it may not even be possible to generate a coherent
specification (i.e., one free from paradoxes), the difficulty with the
first two of these is that they become sufficiently complex that it is no
longer easy to be sure that they correctly capture the intended meaning. We
then have the problem Chris described, where we have to be concerned not
only with possible errors in our implementations of the specification but
also with possible errors in our model of the specification.

Regards, Ian

> Jonathan
Received on Friday, 9 August 2002 10:50:36 UTC

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