- From: <herman.ter.horst@philips.com>
- Date: Thu, 10 Apr 2003 15:32:34 +0200
- To: phayes@ai.uwf.edu, www-rdf-comments@w3.org

It seems that the RDFS entailment lemma as currently stated in the RDF Semantics document (last call or editor's version) is not entirely correct. Consider the RDF graph G: x rdf:type rdfs:Class . rdf:type rdfs:domain y . This RDF graph rdfs-entails the triple x rdfs:subClassOf y . ( Proof: let I be an arbitrary rdfs interpretation of G. Clearly I(x) and I(y) are in IC. Suppose z in ICEXT(I(x)), so <z,I(x)> in IEXT(I(rdf:type)). The second triple shows that <I(rdf:type),I(y)> in IEXT(I(rdfs:domain)). With the semantic condition on rdfs:domain it follows that z in ICEXT(I(y)), so that <I(x),I(y)> in IEXT(I(rdfs:subClassOf)). ) However, this triple is not in the rdfs closure of G, unless x = y. (Proof: this closure contains the subClassOf statements x rdfs:subClassOf x . y rdfs:subClassOf y . but no other subClassOf statements involving x or y.) This example could be used as another closure rule ("rdfs11"), but then the RDFS entailment lemma would still be false. Namely, a slightly more complicated proof shows that the graph H: x rdf:type rdfs:Class . rdf:type rdfs:subPropertyOf p . p rdfs:domain y . rdfs-entails the triple x rdfs:subClassOf y ., but that this triple is not in the (extended definition of) closure. I found these examples in an attempt to become completely convinced of the truth of the rdfs entailment lemma. In this attempt I did become convinced of the "soundness" part of the lemma. For the "completeness" part of the lemma, it would perhaps be simpler, and still very useful, to restrict the lemma to "well-behaved" RDF graphs, which might be defined as RDF graphs which do not make (RDF) statements about built-in (rdf or rdfs) vocabulary in addition to the statements given by the axiomatic triples. Herman ter Horst

Received on Thursday, 10 April 2003 09:34:29 UTC