From: Turner, David <davidt@hp.com>

Date: Fri, 9 Mar 2007 15:51:09 -0000

Message-ID: <86FE9B2B91ADD04095335314BE6906E8D6D4B2@sdcexc04.emea.cpqcorp.net>

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

Date: Fri, 9 Mar 2007 15:51:09 -0000

Message-ID: <86FE9B2B91ADD04095335314BE6906E8D6D4B2@sdcexc04.emea.cpqcorp.net>

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

Hi all, Executive summary: The text of [1] is a little unintelligible, and does not quite match what the SROIQ paper [2] says. At the very least, it is not clear whether some of the bulleted lists are conjunctions or disjunctions without very careful reading. The definition of 'regular' order doesn't seem to be standard (at least, I've not come across it) so perhaps it should be defined in the OWL spec rather than deferring to the reference [2]. I spent a good few minutes puzzling about the seemingly circular definition of simplicity before I moved on to the regularity definition (which breaks the cycle). Perhaps regularity should be defined before simplicity for the sake of other readers? I think the translation of the definition of regularity from [2] into the language of OWL should read as: [[ ... each axiom in Ax of the form SubObjectPropertyOf(SUB PE) in Ax fulfils at least one of following conditions: * SUB is of the form SubObjectPropertyChain(PE PE) * SUB is of the form InverseObjectProperty(PE) and * SUB = SPE where SPE < PE * SUB = SubObjectPropertyChain(SPE1 ... SPEn) where n >= 2 and SPEi < PE for 1 <= i <= n * SUB = SubObjectPropertyChain(PE SPE1 ... SPEn) where n >= 1 and SPEi < PE for 1 <= i <= n * SUB = SubObjectPropertyChain(SPE1 ... SPEn PE) where n >= 1 and SPEi < PE for 1 <= i <= n ]] (NB I'm assuming that conditions 3, 4, and 5 of [2] permit n = 1; if they also permit n = 0 then add [[ * SUB = PE ]] to the list -- it's not clear whether they do or not but this would seem like a reasonable (trivial) extension) Now to the definition of simple. The SROIQ paper only talks about role *names* on the RHS of an inclusion, not inverted roles, and seems to delete double-inversions, so this doesn't quite match up with OWL's syntax. I'm going to be conservative about this until I get a chance to sit down with pencil and paper and check a more liberal approach. If OPU is an objectPropertyURI then it is not clear to me whether SubObjectPropertyOf(InverseObjectProperty(OPU) OPU) permits OPU to be simple - I suspect it does, although I don't think this is implied by the conditions in [2]. Also the trivial axiom SubObjectPropertyOf(OPU OPU) should not break the simplicity of OPU, either. If my reading is right: [[ An objectPropertyExpression InverseObjectProperty(OPE) is simple if (OPE) is. An objectPropertyURI OPU is simple if both of the following conditions hold: * For all axioms in Ax of the form SubObjectPropertyOf(SUB InverseObjectProperty^n(OPU)) (n >= 0), SUB is a single objectPropertyExpression (not a SubObjectPropertyChain) which is either simple or of the form InverseObjectProperty^m(OPU) for some m >= 0. If Ax has no axiom of the form SubObjectPropertyOf(SUB InverseObjectProperty^n(OPU)) (n >= 0), then OPU is simple. * Ax contains no axiom of the form TransitiveObjectProperty(InverseObjectProperty^n(OPU)) ]] Finally, the constraint on the use of non-simple OPEs is clear enough, except a little nomenclature has changed since it was written. [[ * ObjectMinCardinality, ObjectMaxCardinality, ObjectExactCardinality, and ObjectExistsSelf descriptions, * FunctionalObjectProperty and InverseFunctionalObjectProperty axioms, and * IrreflexiveObjectProperty, AsymmetricObjectProperty and DisjointObjectProperties axioms. ]] The two bullet-points of axioms is a little confusing; the first are cardinality constraints in disguise and the second are from role assertions rather than the role hierarchy, but this distinction is unimportant for the spec so it might be better to concatenate them. Finally, there's something a little troubling about not having a wellfoundedness constraint on the role hierarchy, which means that checking for simplicity could not be decidable. Phew. Cheers, Dave [1] http://www.w3.org/Submission/2006/SUBM-owl11-owl_specification-20061219/ #7 [2] http://www.cs.man.ac.uk/%7Esattler/publications/sroiq-tr.pdf -- Dave Turner Cube T400, HP Labs Bristol, Filton Road, Bristol BS34 8QZ davidt@hp.com +44 117 3129104 (Work) +44 7962 811627 (Mobile)Received on Friday, 9 March 2007 15:51:19 GMT

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