Re: response to comment pfps-05

From: pat hayes <phayes@ai.uwf.edu>
Subject: response to comment pfps-05
Date: Mon, 3 Feb 2003 17:14:15 -0600

> The closure rules for RDFS are incomplete.  For example,
>      ex:foo ex:prop "a" .
> RDFS-entails
>      ex:foo ex:prop _:x .
>      _:x rdf:type rdfs:Resource .
> However, this does not come out of the RDFS closure rules.
> This means that the RDFS entailment lemma is false.
> 
> ------
> Indeed, good catch!
> 
> This is actually a deeper observation, which is that we need to treat 
> the basic entailment operation of generalization (replacing a name 
> with a bnode) as a genuine inference rule, and include it in the 
> notion of closure. I therefore propose to add the following to 
> section 2 (simple entailment), just after the statement of the 
> instance lemma:
> 
> ------
> We can summarize the second of these as an inference rule on triples, 
> in a style which we will use extensively later in the document. Here, 
> ppp stands for any uriref, aaa for any uriref or bNode, and bbb for 
> any uriref, bNode or literal.
> 
> Rule name se1:
> 
> If E contains
> aaa ppp bbb .
> 
> then add
> aaa ppp _:n .
> 
> where _:n is a new bNode.
> 
> 
> Rule name se2:
> 
> if E contains
> aaa ppp bbb .
> 
> then add
> _:n ppp bbb .
> 
> where _:n is a new bNode.
> 
> 'New' means 'not occurring in the graph'. The instance lemma 
> guarantees that these rules are valid, so they can be safely used to 
> add triples to any RDF graph. There is no inference rule 
> corresponding to the subgraph lemma: it would amount to the 
> observation that one can ignore a triple.
> 
> ---
> 
> then, in the definition of the RDF (RDFS) closures, we require that 
> the closure rules include SE1, SE2 and the RDF (and RDFS) rules.
> 
> This is actually a more unified treatment and solves this objection 
> (I believe), by the following inference path:
> 
> ex:foo ex:prop "a" .
> ex:foo ex:prop _:x . by rule SE1
> _:x rdf:type rdfs:Resource . by rule RDFS4b
> 
> Pat

This is a major change to the closure rules.  Without a revised version of
the entire semantics document, I am unable to determine whether it will
solve the problem.

peter

Received on Tuesday, 4 February 2003 18:01:00 UTC