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Re: semantics document revised

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 23 Sep 2002 20:39:34 -0500
Message-Id: <p05111b48b9b56c083489@[65.217.30.172]>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: www-webont-wg@w3.org

>From: pat hayes <phayes@ai.uwf.edu>
>Subject: Re: semantics document revised
>Date: Mon, 23 Sep 2002 17:34:24 -0500
>
>>  >From: pat hayes <phayes@ai.uwf.edu>
>>  >Subject: Re: semantics document revised
>>  >Date: Mon, 23 Sep 2002 10:45:45 -0500
>>  >
>>  >>  >From: pat hayes <phayes@ai.uwf.edu>
>>  >>  >Subject: Re: semantics document revised
>>  >>  >Date: Fri, 20 Sep 2002 21:09:00 -0500
>>  >>  >
>>  >>  >[...]
>>  >>  >
>>  >>  >>  PPS. As you will see, Ive reinstated the restriction closures even
>>  >>  >>  for the unrestricted syntax. I was worried about paradoxes until I
>>  >>  >>  had a few beers and realized that there isn't anything to worry
>>  >>  >>  about, since the closures only apply to the actual semantic domains,
>>  >>  >>  and of course the relevant sets exist: none of these constructions
>>  >>  >>  violate anything in ZF-AC. So Dan C. can have all the entailments he
>>  >>  >>  wants in unrestricted OWL/RDF, but God help him finding out if its
>>  >>  >>  consistent or not.
>>  >>  >
>>  >>  >Precisely.  I have no idea whether there are *any* Large OWL
>>  >>  >interpretations.
>>  >>
>>  >>  Oh, sure there are. That is, simple non-looping assertions certainly
>>  >>  have satisfying interpretations.
>>  >
>>  >But what about restrictions on rdf:type and rdfs:subClassOf, like the one I
>>  >pointed out earlier?  These are a sort of looping assertion.  I don't know
>>  >whether all of them are kosher.
>>
>>  Neither do I.  OK, so some of them have no interpretations. Its easy
>>  to write contradictions and hard to detect them, in general. But that
>>  doesn't make the semantics incoherent.
>>
>>  Pat
>
>But in Large OWL, every interpretation satisfies
>
>	_:x owl:onProperty rdfs:subClassOf .
>	_:x owl:maxCardinality 57 .

Sure, but _:x  might be empty.  For example, start with one 
class/property ICEXT(a) = {a, b} , IEXT(a) = {<a,a>} and ICEXT(b) = { 
} in the interpretation.  The members of the class a are also its 
only subclasses, so IEXT(I(rdf:subClassOf)) = {<b,a>,<a,a>} is 1:1 
with ICEXT(a).  rdfs:subPropertyOf is {<a,a>}. No matter how much you 
restrict on these classes with this property or anything in RDFS or 
OWL, you are never going to get more than one of these classes. The 
_:x in your example is a; if you had used minCard or plain card it 
would be b.  And so on.

>so all these OWL restrictions better have interpretations, and, moreover,
>they all better have a common interpretation, or else there are *no* OWL
>interpretations.

I don't follow you. Of course, in general, they won't have a single 
common interpretation.  RDF doesn't have a single common 
interpretation, after all, so the interpretation of the RDFS 
vocabulary is going to change across interpretations.  Maybe in some 
of them there will be classes with more than 57 subclasses, in others 
there won't. Some RDFS graphs can be satisfied in very small 
interpretations.

Pat

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Received on Monday, 23 September 2002 21:39:27 GMT

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