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Re: minor typos in Test doc

From: Sean Bechhofer <seanb@cs.man.ac.uk>
Date: Wed, 13 Aug 2003 10:57:53 +0100 (GMT Daylight Time)
To: Jos De_Roo <jos.deroo@agfa.com>
cc: connolly@w3.org, <www-webont-wg@w3.org>, <jjc@hpl.hp.com>
Message-ID: <Pine.WNT.4.44.0308131033010.1724-100000@potato>

On Wed, 13 Aug 2003, Jos De_Roo wrote:

>
> [Sean's explanation of
> http://www.w3.org/2002/03owlt/description-logic/inconsistent107.rdf]
>
> > The role hierarchy is a bit of a red herring here, as is the definition
> > of a.
>
> I never clearly understood what "red herring" meant; now I got it ;-)

A wonderful language!

> > The definition of Unsatisfiable says that anything that's an instance of
> > Unsatisfiable has to have at least 1 r, has to be related to a c via r
> and
> > has to be related to a d via r. It must also be related to no more than
> > one thing via r (the complement of [minCard 2 r] is [maxCard 1 r]). But
> > this leads to a contradiction as c and d are disjoint.
>
> OK - my understanding of owl:someValuesFrom was wrong
> I thought that the intersectionOf
>   restriction(a:r someValuesFrom a:d)
>   restriction(a:r someValuesFrom a:c)
> wasn't that strongly constrained ie that it has
> some members related to a c via r and some other
> members related to a d via r but I guess that's
> what you call a unionOf isn't it?

Well, in general, the intersection of

   restriction(a:r someValuesFrom a:d)
   restriction(a:r someValuesFrom a:c)

means that there must be a d related via r and a c related via r, but they
don't *have* to be the same individual -- there could be two of them.

In this case of this test, however, the extra constraint on the
cardinality of r (due to the negation of the minCardinality) means
that there can *only* be one, hence the contradiction.

The various different ways of combining restrictions using intersection
and union are related as follows:

1. some R.(C and D)
2. (some R.C) and (some R.D)
3. some R.(C or D)
4. (some R.C) or (some R.D)

Given no other contraints, we know that it's always the case that:

1. => 2.
2. => 3.
2. => 4.
3. == 4.

Apologies if this is teaching grandma to suck eggs (another marvellous
phrase :-).

	Sean

-- 
Sean Bechhofer
seanb@cs.man.ac.uk
http://www.cs.man.ac.uk/~seanb
Received on Wednesday, 13 August 2003 06:00:20 GMT

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