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finiteness of closures

From: Jeremy Carroll <jjc@hpl.hp.com>
Date: Wed, 18 Jun 2003 20:10:28 +0300
To: w3c-rdfcore-wg@w3.org
Message-Id: <200306182010.28816.jjc@hpl.hp.com>


One of the bugs that came up in the comments list, but after the LC period 
seems to be about the idea that the closure rules could be applied until 
termination.

Pat's current approach is to have given up on completeness: the simple 
entailment rules do not even come close.

He had complete? simple entailment rules in:

http://lists.w3.org/Archives/Public/www-rdf-comments/2003AprJun/0202


However, given a small RDF graph like:

<eg:a> <eg:b> <eg:c> .
<eg:c> <eg:b> <eg:a> .

we get a lot of richness

we can have an arbitrary number of edges

<eg:a> <eg:b> _:XNNN .

we can have pairs of edges

<eg:a> <eg:b> _:XNNN .
_:XNNN <eg:b> <eg:a> .

again in arbitrary number

we can have finite paths of blank nodes of arbitrary length, with all triples 
labelled with <eg:b>.

i.e. the simple closure is infinite in some strong sense

Given the role the entailment rules play, I see no problem with this. 
We just need to accept it.

Jeremy
 
Received on Wednesday, 18 June 2003 14:10:35 EDT

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