# RE: ACTION: task force unasserted triples

```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
>
> --
> ---------------------------------------------------------------------
> 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 09:36:35 UTC