- From: Pat Hayes <phayes@ai.uwf.edu>
- Date: Thu, 27 Sep 2001 19:54:46 -0500
- To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
- Cc: www-rdf-logic@w3.org
>From: Pat Hayes <phayes@ai.uwf.edu> >Subject: Re: model theory for RDF/S >Date: Thu, 27 Sep 2001 13:04:15 -0500 > >> >> >17/ Because of the complexity of RDFS, I won't believe the Schema Lemma >> >> > until I see a completely worked out proof. >> >> >> >> Fair enough. I no longer believe it myself. What I am sure of is that >> >> there is *some* closure table for which it is correct, however. Also, >> >> it should be stated so as to explicitly rule out the rdfs:Literal >> >> class. >> > >> >Probably. However there might not be a finite schema-closure for full RDF! >> >> There must be, since the Herbrand universes are always finite. Until >> one can build functional terms recursively, any set of generation or >> closure rules is just going to do combinatorics on the finite set of >> possible triples. >> >> Pat > >Not necessarily so, at least not in the thinking of at least one RDF >person. I have heard comments to the effect that every statement in RDF >has a reification (although, of course, not vice versa). This would, I >think, require an infinite Herbrand universe. Phrases like 'every statement in RDF' are meaningless out of context. In the model theory we are always talking relative to a vocabulary, and if that vocabulary is finite then there are only finitely many triples. Of course for an infinite vocabulary, the closure may be infinite; the comment in section 5 says that the process will terminate for any *finite* graph. For a mathematical audience I would have defined the closure in terms of the set-theoretic least upper bound, rather than in terms of a set of rules terminating, but that seemed inappropriate here. 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, 27 September 2001 20:54:50 UTC