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RE: DTTF: summary (gasp!)

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Tue, 28 May 2002 19:53:44 +0100 (BST)
Message-ID: <15603.53816.558436.112453@excalibur.oaklands.net>
To: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>
Cc: "Jonathan Borden" <jonathan@openhealth.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, <www-webont-wg@w3.org>

I'm afraid that much of what is being said about Tbox/Abox
distinctions is not correct and is simply confusing this issue.

In a DL it is sometimes convenient (for computational reasons) to
separate the set of axioms in the KB into those of the form "C
subClassOf D" (the Tbox) and those of the form "x Type C" or "x P y"
(the Abox). This does not, however, reflect some strange distinction
that is peculiar to a DL. Moreover, in DAML+OIL (or in any DL with
extensionally defined classes, e.g., SHOQ) the distinction completely
breaks down because "Abox" axioms can easily be transformed into
"Tbox" axioms. E.g., instead of saying "x Type C" I can say "(oneOf x)
subClassOf C" (I can also state x P y using a subclass and a

The real point is that in a DL, classes are interpreted as sets of
objects (in the domain of discourse), individuals are interpreted as
single objects and properties are interpreted as sets of pairs of
objects. Classes and properties are not themselves members of the
domain of discourse.

Even this is not, IMHO, the cause of the problems that we are
wrestling with and for which dark triples are proposed as a possible
solution. These problems are caused by the fact that even the syntax
of the language and the axioms within a knowledge base are in the
domain of discourse. This opens up several cans of worms, and leads to
the unpleasant consequences that Peter has delineated on numerous

Regards, Ian

On May 24, Jeremy Carroll writes:
> The T-Box is the description of the classes and properties used in an
> ontology or schema, the A-Box is the description of the objects in the
> domain of discourse.
> Thus rephrasing the very short summary, embedding these definitions of
> the A-Box and T-Box words comes to:
> All formally specified Description Logics separate the assertional
> descriptions of objects in the domain of discourse from the
> terminological descriptions of the classes and properties used within
> these assertional descriptions. RDFS does not make this separation. Thus
> the WebOnt WG has considered doing Description Logic without this
> separation and concluded that it is too difficult. Darkness is a bit
> that allows distinguishing: some (non-dark) parts of an RDF graph as
> following RDFS semantics, this will correspond to the assertional
> descriptions, from some parts of an RDF graph that correspond to the
> terminological descriptions, these will not follow the RDFS semantics.
> In particular the following implication that is valid under RDFS will
> not hold under OWL.
> eg:prop rdfs:subClassOf owl:Restriction .
> _:x rdf:type eg:prop .
> entails
> _:x rdf:type owl:Restriction .
> Jeremy
> Jeremy:
> > > Description Logic makes a distinction between the A-Box and
> > the T-Box;
> > > we have tried and failed to remove this distinction while not "doing
> > > research". We will use darkness to identify the T-Box; whereas A-Box
> > > semantics will extend RDFS semantics.
> > >
> >
> > Ok, can you give me some specific, relatively non-technical
> > language, that I
> > could incorporate into a message appropriate for RDFCore WG?
> > Or does RDFCore
> > need be concerned with this distinction (i.e. that's something we can
> > discuss amonst ourselves)?
> >
> > Jonathan
> >
> >
> >
Received on Sunday, 2 June 2002 11:27:37 GMT

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