- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Fri, 31 Oct 2003 11:51:22 -0500 (EST)
- To: pfps@research.bell-labs.com
- Cc: herman.ter.horst@philips.com, w3c-rdfcore-wg@w3.org
I have not received any response to this comment on the change to Herbrand interpretations. (This change may have been rescinded but I would like some indication thereof.) peter From: Peter F. Patel-Schneider <pfps@research.bell-labs.com> Subject: Re: LC2 semantics proof appendix Date: Fri, 10 Oct 2003 06:17:31 -0400 (EDT) > From: pat hayes <phayes@ihmc.us> > Subject: LC2 semantics proof appendix > Date: Thu, 9 Oct 2003 22:41:25 -0500 > > > Guys, in case you plan to review the appendix in the LC version of > > the semantics document, I ought to tell you that I was mortified to > > found a huge bug in the proofs of the RDF and RDFS entailment lemmas > > just hours before the publication deadline, and had to do some very > > hasty repair work, so the proofs in the published version are > > extremely ugly and seriously incomplete. Frankly, the RDFS lemma > > proof is not worth the bother of trying to review - it is a > > placeholder - so please feel free to ignore them other than to say > > they are trash. I am writing up a better version which I will send > > you as soon as it is ready, early next week. That will, I hope, > > include a version of the RDFS consistency lemma which Peter has > > suggested. > > > > Pat > > > > PS. You may notice that I have restored a condition on IP in Herbrand > > interpretations which you suggested earlier that I remove. I had > > forgotten that this condition, although inelegant, is necessary in > > order to handle the case of the RDF lemma when the graph contains a > > triple > > > > aaa type Property . > > > > but aaa is not used as a property. In this case, with the 'standard' > > definition of IP in a Herbrand interpretation being just the set of > > property URIrefs, the construction used in the RDF lemma fails, since > > the RDF interpretation requires that IP be exactly the class > > extension of rdf:Property. Adding these URIs to IP makes no extra > > triples true, so does not affect the minimality of the Herbrand > > interpretation, and is harmless for the other (elementary) Herbrand > > results, so I have restored this condition. Just to let you know that > > I didn't do so carelessly or on a whim. > > Consider the RDF graph > > ex:foo rdf:type rdf:Property . > > The Herbrand interpretation, H, for this is then > > IRH = { ex:foo, rdf:Property } u LVH > IPH = { ex:foo, rdf:type } > IEXTH(rdf:type) = { <ex:foo,rdf:Property> } > IEXTH{x) = {} otherwise > ISH = id > ILH = id > LVH = strings u pairs > > What I would consider to be the minimal interpretation, M, is > > IRM = { ex:foo, rdf:Property } u LVM > IPM = { rdf:type } > IEXTM(rdf:type) = { <ex:foo,rdf:Property> } > IEXTM{x) = {} otherwise > ISM = id > ILM = id > LVM = strings u pairs > > I do not believe that H << M. > > Ignoring strings and pairs (where the mapping is identity) the projection > mapping is going to have to look like > > k(rdf:Property) = rdf:Property because ex:foo is the only object > k(rdf:type) = rdf:type because rdf:type is the only predicate > k(ex:foo) = ex:foo because ex:foo is the only subject > > but then ex:foo is in IPH and k(ex:foo) is not in IPM. > > By the way, the IL mapping of typed literals in Herbrand interpretations is > broken. It is defined to be the identity mapping but LV only contains > string, pairs of strings and language tags, and well-formed XML literals in > G. What then is IL("foo"^ex:bar)? > > > The basic reason for this being necessary is that RDF allows > > properties to exist which have an empty extension, by the way. > > > > > peter
Received on Friday, 31 October 2003 11:52:11 UTC