From: Michael Schneider <schneid@fzi.de>

Date: Fri, 19 Oct 2007 10:12:06 +0200

Message-ID: <0EF30CAA69519C4CB91D01481AEA06A04A85A2@judith.fzi.de>

To: "Owl Dev" <public-owl-dev@w3.org>

Date: Fri, 19 Oct 2007 10:12:06 +0200

Message-ID: <0EF30CAA69519C4CB91D01481AEA06A04A85A2@judith.fzi.de>

To: "Owl Dev" <public-owl-dev@w3.org>

A correction! I wrote on Tuesday, October 16, 2007 in my mail "Are the acyclicity "nonstructural restrictions" too strict?" http://lists.w3.org/Archives/Public/public-owl-dev/2007OctDec/0082.html >Now, let's regard an ontology which contains the following two axioms: > > (A1) SubObjectPropertyOf(p1 p2) > (A2) SubObjectPropertyOf(p2 p1) > >Note that these two axioms may either be explicitly stated in >the ontology, >or may be entailed by other axioms, e.g. by an >'EquivalentObjectProperties(p1 p2)' axiom. For our discussion >here this does >not make a difference, because the nonstructural restrictions >deal with any >axioms occuring in the "axiom closure Ax" of an ontology. This is wrong! The term "axiom closure" is used several times in the "Nonstructural Restrictions" chapter <http://www.webont.org/owl/1.1/owl_specification.html#7> but it is not explained in this chapter. So I *wrongly* assumed that this term means the set of all axioms which can be *semantically* entailed from the explicitly stated axioms in an ontology. But I now see that the term is actually defined in chapter 3 of the same document: <http://www.webont.org/owl/1.1/owl_specification.html#3> "The axiom closure of an ontology O is the smallest set containing all the axioms of O and of all ontologies that O imports." So the "axiom closure" is the set of axioms which I get when I collect the axioms of the "base" ontology and all directly and indirectly imported ontologies. This is completely different from what I thought, and, specifically, it has nothing to do with the model theoretic semantics of OWL. I came to this point when I was wondering if the "Syntax" document is the right place for the "Non-Structural Restrictions" chapter or not. The reason for my wondering was, in the first place, my misunderstanding of the term "axiom closure": If this *were* a semantical term, then the "Syntax" document would perhaps not be the right document for this chapter. Another reason for my wondering was that the "Non-Structural Restrictions" chapter appears to be very different from the rest of the "Syntax" document, both in style and what it deals with. So this alone deserves a critical consideration, IMHO. But now that I know what the term "axiom closure" really means, my impression is that the "Syntax" document is really the right place for this chapter. All aspects, which are dealt with in this chapter, are clearly "non-semantical": * The definition of "property expressions" is more or less a repetition of what is said in chapter 4.2 of the "Syntax" document. * The question if a property expression is "composite" or not only depends on the position where such a property expression occurs in certain /explicitly/ stated axioms. This question can always be answered by checking the form of the syntactical expression, by which such an axiom is given. * The "object property hierarchy relation" "-->" can always be obtained by "mechanically" looking if certain axioms /explicitly/ exist. Again, only syntactical expressions have to be analysed. * The reflexive-transitive closure of the "object property hierarchy relation" "-->" can be algorithmically calculated after "-->" has been obtained. No more information is needed. * The question if a property expression is "simple" or not can be mechanically decided by simply traversing the above reflexive-transitive closure "-->*", and check if certain expressions of the form "PE' -->* PE" exist. * The first "non-structural restriction" can be checked for "non-simple" property expressions by checking all /explicitly/ existing axioms, which are of the given kind (cardinality restrictions and the like): The check is a lookup, if the inspected property expression is contained in any of these axioms or not. * The second "non-structural restriction" (acyclicity condition) again is only about checking the form of certain /explicitly/ existing axioms. So this all convinces me that the "Nontructural Restrictions" chapter is well placed in the "Syntax" document. It's all about checking the forms of certain /explicitly/ existing axioms, and if certain expressions occur in them or not. This all has nothing to do with semantics, but it has a lot to do with syntax. The only thing one could think about is if the title "Nonstructural Restrictions on Axioms" is the best title possible. But I don't have a better idea for now. :) Cheers, Michael PS: I have already raised an issue, where I suggest to clarify in the "Nonstructrural Restrictions" chapter what the term "axiom closure" means, see http://code.google.com/p/owl1-1/issues/detail?id=57 -- 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 LeßnerkrausReceived on Friday, 19 October 2007 08:12:22 GMT

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