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

From: Brian McBride <bwm@hplb.hpl.hp.com>
Date: Tue, 25 Feb 2003 14:38:19 +0000
Message-Id: <>
To: pat hayes <phayes@ai.uwf.edu>, herman.ter.horst@philips.com
Cc: www-rdf-comments@w3.org

At 14:23 24/02/2003 -0600, pat hayes wrote:

>>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 .
>>(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 .
>>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 
>Thanks for your detailed comments, in any case.
>>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):
>>   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
>>similarly for domain instead of range
>>   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 .
>>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 Tuesday, 25 February 2003 09:37:40 UTC

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