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RE: ACTION: task force unasserted triples

From: Smith, Michael K <michael.smith@eds.com>
Date: Thu, 25 Apr 2002 08:36:11 -0500
Message-ID: <B8E84F4D9F65D411803500508BE322140D5DB6B0@USPLM207>
To: Pat Hayes <phayes@ai.uwf.edu>, 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

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

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
> 
> -- 
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> 
Received on Thursday, 25 April 2002 09:36:35 GMT

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