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Re: Proposed revision to daml-ont

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Sat, 25 Nov 2000 15:19:03 +0000 (GMT)
To: Dan Connolly <connolly@w3.org>
Cc: www-rdf-logic@w3.org
Message-ID: <14879.53395.4565.629481@localhost.localdomain>
On November 22, Dan Connolly writes:
> Dan Connolly wrote:
> > 
> > Ian Horrocks wrote:
> > [...]
> > > The DAML-OIL proposal can be found at:
> > >
> > >         http://www.cs.man.ac.uk/~horrocks/DAML-OIL
> 
> > This one seems broken:
> > 
> >  #3. The semantics of restrictions has been changed...
> > 
> > I'll explain why in a separate message.
> 
> Hmm... I take it back. I got the impression that the
> sematnics of restrictions was based on the XML syntax,
> which, at the RDF graph level, looks like using
> negation-as-failure.
> 
> But now that I look closely at the semantics, I see
> it's specified in RDF terms, i.e. in triples:
> 
> | <type,?R,Restriction> <onProperty,?R,?P> <toClass,?R,?C> 
> |    x in IC(?R) iff IR(?P)({x}) <= IC(?C) 
> |
> | <type,?R,Restriction> <onProperty,?R,?P> <toValue,?R,?V> 
> |     x in IC(?R) iff <x,IO(?V)> in IR(?P) 
> 
> Let me check my understanding with an example...
> let's say a Square is a RegularPolyhedron
> with numberOfSides=4:
> 
> [...]
>
> 	<intersectionOf,Square,[RegularPolyhedron, FourSidedThing]>
> 	<type,FourSidedThing,Restriction>
> 		<onProperty,FourSidedThing,numberOfSides>
> 		<toValue,FourSidedThing,4>

I'm not sure if you intended the restriction to be named, but it may
be worth emphasising that in general it may not be.

> 
> which will end up with
> 
> 	x in IC(FourSidedThing) iff <x,4> in IR(numberOfSides)
> and
> 	x in IC(Square) iff x in IC(FourSidedThing)
> 		and x in IC(RegularPolyhedron)
> 
> Yes, that works.
> 
> I'm still not certain there are no closed-world assumptions...
> I'll try to study the semantics some more. But the problem
> that I initially thought was there isn't.

There is no closed-world assumption. The semantics are as you describe
them for an object x in a given interpretation. However, an individual
i is an instance of Square iff IO(i) in IC(Square) in every
interpretation that satisfies the axioms in the ontology. Similarly
for subsumption, class C is a subclass of class D iff IC(C) is a
subset of IC(D) in every ontology satisfying interpretation.  We
should probably add a section to the semantics that clarifies the
semantics of basic inferences.

Ian
Received on Saturday, 25 November 2000 11:26:57 UTC

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