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Re: UPDATE: initial message concerning syntax

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
Message-Id: <OF9DB4BEA9.37FB73F7-ON41256B2B.00823170@bayer-ag.com>

> > > 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 GMT

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