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Re: ISSUE: DAML+OIL semantics is too weak

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Fri, 17 May 2002 12:17:21 -0400
To: jos.deroo.jd@belgium.agfa.com
Cc: hendler@cs.umd.edu, www-webont-wg@w3.org
Message-Id: <20020517121721K.pfps@research.bell-labs.com>
From: "Jos De_Roo" <jos.deroo.jd@belgium.agfa.com>
Subject: Re: ISSUE: DAML+OIL semantics is too weak
Date: Fri, 17 May 2002 10:35:38 +0200

> 
> [...]
> 
> > Well, suppose WebOnt fixed the layering issue, perhaps by using an approach
> > with explicit comprehension principles that did not have paradoxes.
> > (Remember, however, that there are several people who believe that this is
> > probably not possible, and there is no proponent for this approach.)  It
> > still would be possible to have a too-weak solution.  For example, Jos has
> > been producing log:implies stuff that are, in a sense, like the
> > comprehension principles.  As far as I can remember, every set of
> > implications that he has produced has been shown to be too weak, in the
> > sense that there are desirable consequences that do not follow from the
> > rules.
> 
> 1) there is one thing I would like to reiterate
> suppose we have a paradoxical pair such as e.g.
> 
> I1 = { ?x a :R } log:implies { ?x a [ owl:complementOf ?x ] } .
> I2 = { ?x a [ owl:complementOf ?x ] } log:implies { ?x a :R } .

This says that a resource belongs to :R iff it does not belong to itself.

So, does :R belong to :R, and what can be gained from this?
Well, if :R belongs to :R then :R does not belong to :R, which cannot be,
so no model of the above has :R belonging to :R.
However, if :R does not belong to itself then :R belongs to :R, which
cannot be, so no model of the above has :R not belonging to :R.
Therefore the two implications above have no models.

> then deriving a contradiction from that is indeed a
> VALID inference but it is not a SOUND inference and

The above reasoning is SOUND.  
SOUND reasoning means that the derived formulae semantically follow from
the assumptions, i.e., that if you can derive X from A1, ..., An, 
then A1, ..., An entails X.  But I1, I2 has no models, so I1, I2 entails X
for any X, so deriving any X from I1, I2 is indeed SOUND reasoning.

> I think we should aim for sound reasoners giving
> sound arguments (an argument is sound if and only if
> it is valid and all its premises are true).


> 2) yes, more desirable consequences should follow
> from more implications, but also there should
> be more rules for deriving inconsistencies
> such as e.g.
> 
> { :rule16r1 .
>   ?s ?p ?o .
>   ?s a [ a owl:Restriction;
>          owl:onProperty ?p;
>          owl:minCardinality ?min;
>          owl:maxCardinality ?max;
>          owl:toClass ?C ] .
>   { ?s ?p ?o . ?o a ?C } math:entailCount ?n .
>   ?n math:lessThan ?min
> }
> log:implies
> { ?s :inconsistentWith owl:Restriction } .
> 
> where math:entailCount is just something to count
> how many times we can entail its subject graph
> from what was given

The above DAML+OIL restriction says that the set of resources that have
atleast ?min fillers for ?p that belong to ?C is the same as the set of
resources that have atmost ?max fillers for ?p that belong to ?C.  From
this weird restriction lots of unusual consequences result.  I think that
it would be much better if you revised your example to eliminate the
weirdness.  I can't determine what is supposed to be happening here otherwise.

Also, I have no idea what

> how many times we can entail its subject graph

means.  

Entailment just is, it is not a process that can be performed a number of
times. 

> --
> Jos

peter
Received on Friday, 17 May 2002 12:17:40 GMT

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