From: Michael Schneider <schneid@fzi.de>

Date: Fri, 22 Feb 2008 16:56:20 +0100

Message-ID: <0EF30CAA69519C4CB91D01481AEA06A075104C@judith.fzi.de>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

Cc: <public-owl-wg@w3.org>

Received on Friday, 22 February 2008 15:56:34 GMT

Date: Fri, 22 Feb 2008 16:56:20 +0100

Message-ID: <0EF30CAA69519C4CB91D01481AEA06A075104C@judith.fzi.de>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

Cc: <public-owl-wg@w3.org>

Hi Peter Peter F. Patel-Schneider wrote: >> Alan, > >[...] > >> In terms of "completeness," I think pD* rules are complete >(correct me >> if I am wrong on this please). > >Not quite. The pD* rules need an auxiliary test for contradictions. >They could probably be made refutation complete. Hm, I'm not sure whether I understand this. There are of course at least two notions of "completeness" around here. One is the completeness of the triple rules w.r.t. the model-theoretic semantic conditions. The other one is regarding how much of this rule corpus is actually implemented. I will distinguish between these notions by "ruleset completeness" vs. "implementation completeness". But I do not see how any of these two notions matches the "contradiction test" case you mention. For the "ruleset completeness" case, to my understanding this means the following: "Given two RDF graphs G1 and G2. Whenever G1 pD*-entails G2 by means of the model-theoretic semantic conditions, then there exists a finite sequence of rule applications which lead from G1 to G2." For the "implementation completeness" case, I think this means for a specific reasoner: "Given two RDF graphs G1 and G2: If there is a finite sequence of rule applications which lead from G1 to G2, then the reasoner says 'yes'." I do not see where the contradictions come into play here. I can, of course, ask for a special graph G2* which encodes some contradiction in triple form, and ask if another graph G1* entails G2*, e.g: G2* := { x owl:sameAs y x owl:differentFrom y } Do you mean that for pD* there are two such graphs G1* and G2*, where G1* entails G2* model-theoretically, but there is no respective rule-sequence? Or that for each reasoner there exist such two counter-example graphs on which the reasoner fails to recognize the entailment? Btw: What is meant by the term "refutation complete"? Cheers, Michael -- Dipl.-Inform. Michael Schneider FZI Forschungszentrum Informatik Karlsruhe Abtl. Information Process Engineering (IPE) Tel : +49-721-9654-726 Fax : +49-721-9654-727 Email: Michael.Schneider@fzi.de Web : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555 FZI Forschungszentrum Informatik an der Universität Karlsruhe Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe Tel.: +49-721-9654-0, Fax: +49-721-9654-959 Stiftung des bürgerlichen Rechts Az: 14-0563.1 Regierungspräsidium Karlsruhe Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi Studer Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus

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