- From: Michael Schneider <schneid@fzi.de>
- Date: Fri, 21 Dec 2007 10:50:14 +0100
- To: "Jeremy Carroll" <jjc@hpl.hp.com>
- Cc: "Owl Dev" <public-owl-dev@w3.org>
[public comment to OWL-1.1 WG discussion] Hi Jeremy! Jeremy Carroll wrote on Thu, 20 Dec 2007 in <http://lists.w3.org/Archives/Public/public-owl-wg/2007Dec/0239.html>: > Hmmm, this is tricky, harder than I thought. > > Some examples. I'm struggling as to the discussion. > > > Example 1: > Consistent: > [punning on eg:p] > > eg:a rdf:type owl:Thing . > eg:a eg:p eg:a . > eg:p rdf:type owl:ObjectProperty . > eg:p rdf:type owl:DataProperty . > _:r rdf:type owl:DataRestriction . > _:r owl:maxCardinality "0"^^xsd:int . > _:r owl:onProperty eg:p . > eg:a rdf:type _:r . While you do not explain what your mail is about, I believe that you are searching for an example which shows problems or dangers resulting from the interplay between data/object property punning, cardinality restrictions, and OWL-DL vs. OWL-Full semantics. Is it this what you are looking for? If yes, then the following example RDF graph {(R1*)} might be of interest to you, because it is a consistent ontology in OWL-1.1-DL, but it is *inconsistent* in OWL-1.0-Full. Of course, the RDF compatible semantics for OWL-1.1 will have to be constructed in a way that the graph {(R1*)} becomes consistent. Otherwise I would not be willing to say that OWL-1.1-Full is in any way "compatible" with OWL-1.1-DL. Whether and how this can be achieved will be an interesting question. Here is the example graph, which is just a slightly modified version of your "Example 1" above: (R11) eg:a rdf:type owl:Thing . (R12) eg:b rdf:type owl:Thing . (R13) eg:a eg:p eg:b . (R14) eg:p rdf:type owl:ObjectProperty . (R15) eg:p rdf:type owl:DataProperty . (R16) _:r rdf:type owl:DataRestriction . (R17) _:r owl:maxCardinality "0"^^xsd:int . (R18) _:r owl:onProperty eg:p . (R19) eg:a rdf:type _:r . The differences are that we now have an additional individual 'eg:b' defined in (R12), and (R13) is not a loop triple anymore. This graph can be translated into the following Functional Syntax ontology: (F11) Declaration(Individual(eg:a)) (F12) Declaration(Individual(eg:b)) (F13) ObjectPropertyAssertion(eg:p eg:a eg:b) (F14) Declaration(ObjectProperty(eg:p)) (F15) Declaration(DataProperty(eg:p)) (F16) ClassAssertion(eg:a DataMaxCardinality(0 eg:p)) >From this one can see that the ontology is *consistent* w.r.t. OWL-1.1-DL semantics including property punning. This is the case, because (F13) refers to to eg:b as an /Individual/, so eg:p is an /Object/Property in (F13). But the cardinality restriction in (F16) refers to eg:p as a /Data/Property, which may be different from the ObjectProperty eg:p. Here is the reasoning why graph {(R1*)} is an *inconsistent* ontology in OWL-1.0-Full. To see this, let's go through the graph step by step. 1.) Sub graph G_14 := {(R11)..(R14)} is obviously *consistent* in OWL-1.0-Full. 2.) (R15) tells us that property eg:p is a owl:DataProperty. There is no conflict with (R14), because in OWL-1.0-Full we have owl:DataProperty rdfs:subClassOf owl:ObjectProperty Further, we learn from (R15) and (R13) that the URIref 'eg:b' denotes a data value, which means eg:b rdf:type rdfs:Literal Again, there is no conflict with (R12), because in OWL-Full we have rdfs:Literal rdfs:subClassOf rdfs:Resource and rdfs:Resource owl:equivalentClass owl:Thing Thus, the sub graph G_15 := {(R11)..(R15)} is *consistent*. 3.) The sub graph {(R16),(R17),(R18)} specifies a "<=0"-DataCardinality restriction on property eg:p. This is ok, because eg:p is a DataProperty according to (R15). Thus, sub graph G_18 := {(R11)..(R18)} is *consistent*. 4.) From triple (R19) and the "<=0"-cardinality restriction on property eg:p we learn that the following triple does *not* exist in this ontology: eg:a eg:p eg:b # does *not* exist But this directly contradicts (R13). Thus, the complete graph {(R1*)} is *inconsistent* in OWL-1.0-Full. Cheers, Michael > > Example 2: > Inconsistent. > > eg:a rdf:type owl:Thing . > eg:a eg:p eg:a . > eg:p rdf:type owl:ObjectProperty . > eg:p rdf:type owl:DataProperty . > _:r rdf:type owl:ObjectRestriction . > _:r owl:maxCardinality "0"^^xsd:int . > _:r owl:onProperty eg:p . > eg:a rdf:type _:r . > > > Example 3 - not in OWL 1.1 DL, because mapping rules don't apply. > Who knows whether this is consistent or not, and how we would go about > an OWL Full semantics. I think it should be inconsistent in OWL Full. > > eg:a rdf:type owl:Thing . > eg:a eg:p eg:a . > eg:p rdf:type owl:ObjectProperty . > eg:p rdf:type owl:DataProperty . > _:r rdf:type owl:Restriction . > _:r owl:maxCardinality "0"^^xsd:int . > _:r owl:onProperty eg:p . > eg:a rdf:type _:r . > > > Example 4 > Inconsistent > > eg:a rdf:type owl:Thing . > eg:a eg:p eg:a . > eg:p rdf:type owl:ObjectProperty . > _:r rdf:type owl:Restriction . > _:r owl:maxCardinality "0"^^xsd:int . > _:r owl:onProperty eg:p . > eg:a rdf:type _:r . > > Example 5 > Consistent > > eg:a rdf:type owl:Thing . > eg:p rdf:type owl:DataProperty . > _:r rdf:type owl:Restriction . > _:r owl:maxCardinality "0"^^xsd:int . > _:r owl:onProperty eg:p . > eg:a rdf:type _:r . > > > > Summary: > > 1 vs 2 the object restriction is inconsistent, data restriction is > consistent. One triple differs between the two. > > 1,2 vs 3 if we don't specify object restriction or data restriction, > using owl:Restriction with punning declarations, then we are outside the > scope of OWL 1.1 DL, but OWL 1.1 Full semantics needs to say something > > 3 vs 4 > 4 is inconsistent in OWL 1.1 DL, becuase the restriction is read as an > ObjectRestriction. 3 adds more triples, and so must also be inconsistent > in OWL 1.1 Full. > > 3 vs 5 > 5 is 3 without two triples, but is consistent. > -- 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
Received on Friday, 21 December 2007 09:50:28 UTC