Re: RDF Semantics review: RDFS closure lemma / entailments from empty graph

>RDF Semantics document,
>last call version, 23 january 2003
>This comment was mailed earlier to the WebOnt WG [1].

For the record, the editor accepts these as editorial comments.

>
>Consideration of rdfs-entailments from the empty RDF graph
>shows that there is an error in the RDFS entailment lemma.
>In line with the definition in 3.3, one triple
>should be entailed for each of the 13 entries following
>"IC contains":
>   rdfs:Resource rdf:type rdfs:Class .
>etc.
>(including a triple
>   rdfs:XMLLiteral rdf:type rdfs:Class .
>although rdfs:XMLLiteral does not appear in the table in 3.3)
>and one triple should be entailed for each of the
>entries following "IP contains":
>   rdf:type rdf:type rdfs:Property .
>etc.
>Each of these 13 + 16 + aleph-0 triples
>(16 is counted without duplicates; the "aleph-0 triples" are
>from rdf:_1 etc.) follows by using the axiomatic triples in
>combination with the closure rules from 4.2, apart from one
>of these triples:
>The triple
>   rdf:value rdf:type rdfs:Property .  (*)
>is rdfs-entailed by but is not in the rdfs-closure of the empty
>rdf graph, since rdf:value never appears in either the
>axiomatic triples or the closure rules.

True. This should be one of the axiomatic triples. This omission was 
an editorial oversight. I will correct this.

>
>(This gives a test case for this problem:
>according to the normative definition, the empty graph
>rdfs-entails the triple (*), but this is not confirmed
>by the rdfs entailment lemma.)
>
>In particular, moreover, each of the 11 triples mentioned
>under part 1. of the definition of rdfs closure
>can safely be omitted from that definition.
>(Note that one of these 11 triples,
>   rdf:nil rdf:type rdf:list .
>is already in the definition of rdf closure.)

Some of the redundancy you refer to has been corrected in the 
editor's draft.  I will check the patterns you mention below and 
decide whether or not to remove any of the redundant conditions. Note 
however that some redundancy in the closure rules is harmless and is 
to be preferred to the intention being unclear, particularly as this 
part of the document is informative.

Thanks for your detailed comments, in any case.

Pat

>
>The following 4 derivation patterns suffice for each
>of these 13 + 15 + aleph-0 proofs
>(This might be added to the proof sketch of the
>rdfs entailment lemma):
>I
>   x rdfs:range y .
>   rdfs:range rdfs:domain rdf:Property .
>   rdfs:range rdfs range rdf:Class .
>together imply
>   x rdf:type rdf:Property
>   y rdf:type rdf:Class
>II
>similarly for domain instead of range
>III
>   rdfs:subClassOf rdfs:domain rdfs:Class .
>   rdfs:subClassOf rdfs:domain rdfs:Class .

You mean rdfs:range in one of these, I assume.

>   x rdfs:subClassOf y .
>together emply
>   x rdf:type rdfs:Class .
>   y rdf:type rdfs:Class .
>IV
>similary for subPropertyOf instead of subClassOf
>
>(For the proofs involving rdf:_1 etc. also the triples from
>part 2. of the definition of rdfs closure are used.)
>
>Herman ter Horst
>Philips Research
>
>[1] http://lists.w3.org/Archives/Public/www-webont-wg/2003Feb/0313.html


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Received on Monday, 24 February 2003 15:23:40 UTC