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RE: ACTION: task force unasserted triples

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Thu, 25 Apr 2002 11:27:24 -0500
Message-Id: <p0510154bb8eddbcc604a@[65.217.30.94]>
To: "Smith, Michael K" <michael.smith@eds.com>
Cc: www-webont-wg@w3.org
>Pat,
>
>I wrote a note about this last week.
>http://lists.w3.org/Archives/Public/www-webont-wg/2002Apr/0200.html
>

Sorry I missed that. Excellent message!

>I don't this lemma works, given the definition of light provided.

You are right. Rats, I need to not send out things called "lemmas" 
before I have actually got a proof written out. Thanks for noticing 
this complication, I will re-think the matter and get back later.

I was in fact thinking about rdf-entailment. I think it works there, 
but the transitivity of subClassOf needs to thought through more 
carefully. Maybe it would be better to think of the darkening as 
strictly as an RDF matter.

Pat

>Lemma: If S rdfs-entails G, then light(S) rdfs-entails light(G).
>
>Consider:
>
>S =
>  a3 rdfs:type owl:dark
>  a1 rdfs:subclass a2
>  a2 rdfs:subclass a3
>  a3 rdfs:subclass a4
>  a4 rdfs:subclass a5
>
>G =
>  a1 rdf:subclass a5
>
>S entails G
>
>light(S) =
>  a1 rdfs:subclass a2
>  a4 rdfs:subclass a5
>
>light(G) =
>  a1 rdf:subclass a5
>
>light(S) does not entail light(G)
>
>Perhaps there is more to the light function than I captured.  Though the
>mods I considered tend to return an empty graph in case the owl:dark
>component participates in any relations.
>
>- Mike
>
>Michael K. Smith
>EDS Austin Innovation Centre
>98 San Jacinto, #500
>Austin, TX 78701
>512 404-6683
>
>>  -----Original Message-----
>>  From: Pat Hayes [mailto:phayes@ai.uwf.edu]
>>  Sent: Wednesday, April 24, 2002 9:22 PM
>>  To: www-webont-wg@w3.org
>>  Subject: RE: ACTION: task force unasserted triples
>>
>>
>>  A few more observations about the owl:Dark proposal
>>  (http://lists.w3.org/Archives/Public/www-webont-wg/2002Apr/0290.html).
>>
>>  Given an RDF graph G, consider the subgraph containing all the
>>  triples in G that do not contain any uriref that occurs as the
>>  subject of a triple of the form
>>
>>  aaa rdf:type owl:Dark .
>>
>>  which is rdfs-entailed by G, ie which is in the rdfs-closure of G.
>>  Call this the 'light' subgraph of G, light(G).  Any RDF graph has a
>>  unique light subgraph which can be figured out by an RDFS reasoner.
>>
>>  (This allows implicit 'darkening', eg by defining an rdfs:subClassOf
>>  owl:Dark and asserting something to be in the subclass, or by using
>>  rdfs:range. An alternative proposal would be to require the triple to
>>  occur in the graph explicitly. While syntactically simpler, that
>>  would complicate the relationship between RDFS and OWL since drawing
>>  a valid conclusion in RDFS could alter the 'darkness' of the
>>  vocabulary. )
>>
>>  The desired semantic relationship between the languages can then be
>>  stated as the condition: Any satisfying OWL-interpretation of G is a
>>  satisfying rdfs-interpretation of light(G).
>>
>>  Lemma: If S rdfs-entails G, then light(S) rdfs-entails light(G).
>>
>>  This means that drawing valid RDFS conclusions from some OWL (even on
>>  the 'dark' vocabulary) isn't going to produce any unwanted
>>  conclusions. It might produce some conclusions that are dark, but it
>>  isn't going to produce any light ones that it shouldn't produce, ie
>>  that OWL would find embarrassing.
>>
>>  More later, hopefully with some test cases.
>>
>>  Pat
>>
>>  --
>>  ---------------------------------------------------------------------
>>  IHMC					(850)434 8903   home
>>  40 South Alcaniz St.			(850)202 4416   office
>>  Pensacola,  FL 32501			(850)202 4440   fax
>>  phayes@ai.uwf.edu
>>  http://www.coginst.uwf.edu/~phayes
>>


-- 
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IHMC					(850)434 8903   home
40 South Alcaniz St.			(850)202 4416   office
Pensacola,  FL 32501			(850)202 4440   fax
phayes@ai.uwf.edu 
http://www.coginst.uwf.edu/~phayes
Received on Thursday, 25 April 2002 12:27:19 GMT

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