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Re: DAML: About Thing, Nothing and the "universe of discourse"

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Mon, 18 Dec 2000 13:34:16 +0000 (GMT)
Message-ID: <14910.4696.690765.87340@excalibur.cs.man.ac.uk>
To: pat hayes <phayes@ai.uwf.edu>
Cc: "Morten M. Christensen" <mmc@mortench.net>, www-rdf-logic@w3.org
On December 6, pat hayes writes:
> >The DAML-OIL suggestions defines Thing as the union of Nothing and the
> >complement of Nothing and stated - but does not explains why - that this
> >provide some benefits regarding semantics?
> >
> >My current perspective is from outside DAML and DL so I hope that the
> >following make sense and is not too misaligned with the proposal::
> >
> >I would like to see the ability to (on a individual basis) express which
> >nodes/classes/instances/etc are in the (current) universe (domain) of
> >discourse and which are not.
> >
> >For this one approach is to be able to specify what is "outside", for
> >which it appears that it would be a good idea to define Nothing simply
> >as the complement of Thing with the usual IC(Thing) = DD.... Than
> >individuals of Nothing would be outside the universe of discourse.
> 
> In general it is always possible to take a lattice-like heirarchy 
> with a top and bottom element and 'wrap' it inside a larger similar 
> structure by adding a higher top and a lower bottom.  The issue here 
> is whether we want to be able to give a name to what are seen as the 
> global extremes, so that any subsequent additions must 'fit inside' 
> these, or whether any such structure is seen as extendable to a 
> larger one. Either strategy is workable, but I think the latter is 
> the most useful.
> 
> I would urge that Morten's suggestion be adopted, if I follow him 
> correctly. The idea then would be that every DAML ontology is 
> understood to be 'about' a universe of discourse, and that Nothing 
> and Thing are understood as relative to that universe. This allows 
> one ontology to align its universe with another by asserting that its 
> Thing and Nothing are equivalent to the other ontology's , but it 
> also allows an ontology to claim a larger universe of discourse by 
> asserting that B#Thing is equivalent to some class name in its 
> heirarchy (and B#Nothing to its complement) thus restricting all the 
> relations imported from the ontology B to the appropriate class in 
> its heirarchy. If this is workable, the complementarity of Thing and 
> Nothing can be preserved in each ontology, even though the exact 
> meanings are implicitly indexed by the ontology they occur in.

In DAML+OIL, Thing and Nothing are just "syntactic sugar": they are
shorthand for (unionOf C (complementOf C)) and (intersectionOf C
(complementOf C)) respectively, where C is an arbitrary class. This is
made explicit in the specification, where Nothing is used as the class
C in the specification of Thing. Note that the complementOf (unionOf C
(complementOf C)) is (intersectionOf (complementOf C) C).

In order to embed your ontology in another in the way that Pat
suggests, you could select the required "Top" and "Bottom" classes
from the target ontology, and make all classes, ranges and domains
subClasses of the "Top" class and superClasses of the "Bottom"
class. Obviously, it would be useful to have an integration tool to do
this for you - any volunteers?

Regards, Ian
Received on Monday, 18 December 2000 09:12:29 GMT

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