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Re: Question: disjointness of classes and datatypes

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Thu, 23 Aug 2001 14:36:36 -0400
Message-ID: <15237.19764.152257.102@localhost.localdomain>
To: David Allsopp <dallsopp@signal.qinetiq.com>
Cc: www-rdf-logic@w3.org
On August 23, David Allsopp writes:
> 
> 
> Peter Crowther wrote:
> > 
> > > From: David Allsopp [mailto:dallsopp@signal.qinetiq.com]
> > > However, this disjointness is not expressed in the language
> > > specification of DAML+OIL
> > > (http://www.daml.org/2001/03/daml+oil.daml) as
> > > far as I can see.
> > >
> > > Is there a reason for this?
> > 
> > The language spec specifies the syntax of DAML, not its semantics.  In a
> > couple of places you need to be able to specify that a class or a datatype
> > could occur, so it's difficult to enforce the disjointness in the syntax.
> 
> Ah. I guess one would have to create a superclass of both Class and
> Datatype. 
> 
> I was just curious as to why, for instance 
> [Thing--complementOf-->Nothing]  is in the language spec, which looks
> like semantic content to me, but not [Class--disjointWith-->Datatype],
> that's all.

The reason for this is that Thing and Nothing are not really part of
the language specification but are simply pre-defined names for two
very common/useful ontology classes, namely the class of all (abstract)
objects and the empty class. The daml+oil semantics tell us what it
means to state that ontology class x is the complement of ontology
class y, i.e., that the interpretation of x is equal to the abstract
domain (AD) minus the interpretation of y. This clearly makes sense
w.r.t. Thing and Nothing. 

On the other hand, the daml+oil semantics do not tell us how to
interpret arbitrary rdfs classes (e.g., classes that form part of the
language specification) nor what it means to state that such classes
are disjoint. In this case, Class is the class of all object classes,
and Datatype is the class of all datatype classes. Such classes are
clearly not interpreted as subsets of either AD or DD, and so are
beyond the scope of the daml+oil semantics.

Regards, Ian


> > If you want to find the formal basis, you'll need to look at one of the
> > semantics docs: axiomatic or model-theoretic.  For example, check out the
> > model-theoretic semantics at
> > http://www.daml.org/2001/03/model-theoretic-semantics.html.  The key appears
> > to be in the preliminary mappings to the two domains AD (abstract) and DD
> > (datatype) plus the definitions of IC and IO.
> 
> OK, thanks.
> 
> David Allsopp
> QinetiQ
> UK
> 
> -- 
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Received on Thursday, 23 August 2001 09:37:57 GMT

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