Re: Still no paradox (was: Re: The Peter paradox isn't.)

>Here is, I think, a major point of difference between our views of how OWL
>has to work.
>
>From: Pat Hayes <phayes@ai.uwf.edu>
>Subject: Still no paradox (was: Re: The Peter paradox isn't.)
>Date: Thu, 21 Feb 2002 20:23:32 -0600
>
>[...]
>
>>  >3/ Next consider DAML+OIL restrictions.
>>  >
>  > >    If John has a child that is a Person, then John belongs to the
>>  >    Restriction that requires that its members have a child that is a
>  > >    Person.
>>  >
>>  >    <John, child, Joe>, <Joe, rdf:type, Person>
>>  >    |= <John, rdf:type, :_1>, <:_1, rdf:type, owl:Restriction>,
>>  >       <:_1, owl:onProperty, child>, <:_1, owl:hasClass, Person>
>>  >
>>  >    This is only a valid entailment if all satisfying OWL 
>>interpretations of
>>  >    the first two statements contain a restriction of the above form.
>>
>>  True, but this does not capture the intuitive meaning of your
>>  example. What this says in RDF is that If John has a child that is a
>>  Person, then a Restriction *exists* such that John belongs to....
>>  There is however no reason why it has to make that claim in OWL.  Why
>>  would OWL want to assert the *existence* of restrictions? Thats like
>>  having FOL assert the existence of its own formulae.
>
>I claim that this precisely captures the intuitive meaning of my example.
>Given an OWL KB, I need to be able to determine if an object in that KB
>satisfies a restriction that is not necessarily mentioned in the KB.
>I would be prepared to do this somewhat indirectly, as in
>
>     <John, child, Joe>, <Joe, rdf:type, Person>
>     |= <John, rdf:type, :_2>, <:2, owl:sameAs?, :_1>,
>        <:_1, owl:onProperty, child>, <:_1, owl:hasClass, Person>
>
>However, I view any approach that does not come up with some way of doing
>the above as fundamentally broken.

Yes, this is a very intense disagreement between us. I view your way 
of thinking here as itself totally broken. It insists on reducing all 
of logic to inferences in set theory, a perspective I have never even 
seen expressed before in any forum, logical or otherwise. I have 
always thought of DLs as a restricted form of logic, but you seem to 
have a completely different perspective, in which DL's are a branch 
of set theory,and even elementary logical reasoning has been 
eliminated in favor of set-theoretic  constructions.

Can you give us any reason at all why we should take this idea seriously?

Pat

PS. Even if we stay within your peculiar universe of Restrictions, 
why would it not be sufficient to infer that if John has a child that 
is a Person, and if a  Restriction exists that requires that its 
members have a child that is a Person, then John belong to that 
restriction?



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Received on Thursday, 4 April 2002 13:57:15 UTC