- From: <jos.deroo.jd@belgium.agfa.com>
- Date: Mon, 24 Dec 2001 01:28:33 +0100
- To: pfps@research.bell-labs.com
- Cc: www-webont-wg@w3.org
> > > One place to see the problem is in KIF. The KIF definition
> > > http://logic.stanford.edu/kif/dpans.html
> > > gives an example where a truth predicate can cause problems.
> >
> > I see
> >
> > > In the DAML+OIL area, if you require the presence of all syntax-like
> > > constructs in the semantics you can easily end up with structures like
> > >
> > > :_x complementOf :_x .
> > >
> > > in all interpretations. Now consider whether :_x is an instance of :_x.
> >
> > I think that complementOf is an irreflexive property
> > How could we express that in SWOL?
> >
> > --
> > Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
>
> SWOL has no such construct. Even if it did, you could construct a
> three-element loop which has the same problem. There are also lots of
> other constructs that cause similar problems.
ok, so we better simply say that
an odd chain of complementOf is a :schemaInconsistency
i.e. for all :x, :y, :z
{ :x ont:complementOf :y . :y ont:sameClassAs :x }
log:implies { { :x ont:complementOf :y } a :schemaInconsistency } .
:x ont:sameClassAs :x .
{ :x ont:complementOf :y . :y ont:complementOf :z }
log:implies { :x ont:sameClassAs :z } .
so when we have
:aaa ont:complementOf :bbb .
:bbb ont:complementOf :ccc .
:ccc ont:complementOf :aaa .
we can indeed find
{:aaa ont:complementOf :bbb.
{:bbb ont:complementOf :ccc.
:ccc ont:complementOf :aaa} log:implies
{:bbb ont:sameClassAs :aaa}} log:implies
{{:aaa ont:complementOf :bbb} a :schemaInconsistency}.
{:bbb ont:complementOf :ccc.
{:ccc ont:complementOf :aaa.
:aaa ont:complementOf :bbb} log:implies
{:ccc ont:sameClassAs :bbb}} log:implies
{{:bbb ont:complementOf :ccc} a :schemaInconsistency}.
{:ccc ont:complementOf :aaa.
{:aaa ont:complementOf :bbb.
:bbb ont:complementOf :ccc} log:implies
{:aaa ont:sameClassAs :ccc}} log:implies
{{:ccc ont:complementOf :aaa} a :schemaInconsistency}.
--
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
Received on Sunday, 23 December 2001 19:30:15 UTC