Re: [OWLWG-COMMENT] Example why current RDF mapping for QCRs might hurt OWL-1.1-Full [Re: PROPOSAL to close ISSUE-68]

I have no objection to the solution that was used in OWL 1.0 for  
this.  So far, if a feature adds problems to DL, we apparently throw  
it out immediately, but if it causes problems to full, we try to find  
a work around without worrying too much if it cases problems or  
confusion - I just fine this asymmetry to be troubling.  So I propose  
we don't include QCRs, since the solution proposed is one that was  
already considered and rejected in OWL 1.0 - what has changed?
  -JH


On Dec 16, 2007, at 4:43 PM, Michael Schneider wrote:

> [ public comment to discussion in OWL-WG;
> also posted to involved WG members ]
>
> Jim Hendler wrote on Thu, 13 Dec 2007
> in <http://lists.w3.org/Archives/Public/public-owl-wg/2007Dec/ 
> 0176.html>
> within thread "Re: PROPOSAL to close ISSUE-68"
>
>> I  would not be happy with  this solution - it creates yet more,
>> seemingly unecessary terms, and it also was, in DAML days, the single
>> feature name that confused the most people - I thought we were
>> proposing a clean solution that didn't require creating a new
>> syntactic feature, this is quite different - so I oppose closing this
>> issue with Peter's suggested solution.
>>   -JH
>>
>> On Dec 13, 2007, at 11:27 AM, Peter F. Patel-Schneider wrote:
>>
>>>
>>> ISSUE-68 has to do with a nonmonotonicity in the mapping rules for
>>> qualified cardinality restrictions.  As pointed out in several  
>>> places
>>> this can be alleviated by using the DAML+OIL solution of having a
>>> different property for qualified cardinalities.
>>>
>>> I thus propose using
>>>
>>> owl:minCardinalityQ
>>> owl:maxCardinalityQ
>>> owl:cardinalityQ
>>>
>>> just as in DAML+OIL and close the issue with this change.
>>>
>>> Peter F. Patel-Schneider
>>> Bell Labs Research
>>>
>>> PS:  Just about any name could be used, but this one has historical
>>>      antecedents.
>>>
>>
>> "If we knew what we were doing, it wouldn't be called research, would
>> it?." - Albert Einstein
>>
>> Prof James Hendler
> http://www.cs.rpi.edu/~hendler
>> Tetherless World Constellation Chair
>> Computer Science Dept
>> Rensselaer Polytechnic Institute, Troy NY 12180
>
> Hi Jim!
>
> Peter has already pointed out in another thread a serious problem for
> OWL-1.1-Full arising from the current RDF mapping of QCRs:
>
>   QCR problem in OWL 1.1 Full - action ?? from F2F
>   <http://lists.w3.org/Archives/Public/public-owl-wg/2007Dec/ 
> 0095.html>
>
> And I had found a second problem with the same RDF mapping, which  
> might at
> least lead to non-desirable effects:
>
>   <http://lists.w3.org/Archives/Public/public-owl-dev/2007OctDec/ 
> 0224.html>
>
> Both problems are easily solved by Peter's proposed change to the RDF
> mapping.
>
> Based on Peter's finding, I want to give an example in this mail,  
> which
> shows what severe consequences it may have for OWL-1.1-Full, if the WG
> sticks to the current RDF mapping for QCRs.
>
> Let's regard the following OWL-1.1-DL ontology in Functional  
> Syntax, which
> makes use of QCRs:
>
>   (A1) SubClassOf(Human ObjectExactCardinality(2 hasBodyPart Leg))
>   (A2) SubClassOf(Dog ObjectExactCardinality(2 hasBodyPart Ear))
>   (A3) SubClassOf(Dog ObjectExactCardinality(4 hasBodyPart Leg))
>   (A4) ClassAssertion(pluto Dog)
>
> In natural English:
>
>   "A human has exactly two legs as body parts (A1),
>   while a dog has two ears (A2) and four legs (A3).
>   There is also some dog named 'Pluto' (A4)."
>
> It is clear that this ontology will be satisfiable in OWL-1.1-DL. I  
> will
> show that the current RDF mapping of QCRs translates this ontology  
> into an
> RDF graph, which will most likely be *inconsistent* under OWL-1.1-Full
> semantics. Note that the above ontology does not look very  
> contrieved, so I
> expect that the problem shown below will hit many OWL-1.1-Full  
> ontologies.
>
> Here is my reasoning why the above ontology will probably be  
> inconsistent
> under OWL-1.1-Full semantics:
>
> The RDF translation for axiom (A1) is, under the current RDF  
> mapping for
> QCRs, given by (leaving out obvious typing triples):
>
>   (R11) <Human> rdfs:subClassOf _:x .
>
>   (R12) _:x rdf:type owl:Restriction .
>   (R13) _:x owl:onProperty <hasBodyPart> .
>   (R14) _:x owl:cardinality 2 .
>   (R15) _:x owl11:onClass <Leg> .
>
> As Peter has already pointed out, the RDF graph {(R12),(R13),(R14)} is
> itself the RDF translation of an *other* OWL construct, which is an
> UN-qualified cardinality restriction on property 'hasBodyPart'. For  
> this sub
> graph, there already exists an OWL-1.0-Full semantic condition,  
> given in
> sec. 5.3 of [1], table "Conditions on OWL restrictions", which in  
> essence is
> defined to be:
>
>    (S-CARD)
>       IF
>         r owl:onProperty p .
>         r owl:cardinality n .
>       THEN
>         CEXT(r) = { x : card({y: x p y}) = n }
>
> This semantic condition tells that if there exists an (un-qualified!)
> "=n"-cardinality restriction r on some property p in an RDF graph,  
> then the
> /class extension/ of r ("CEXT(r)") equals to the set of all  
> instances x
> which have exactly n ocurrences of property p assigned to them.
>
> So given that (S-CARD) is reused in OWL-1.1-Full (what I regard to  
> be very
> likely), we will receive from the RDF graph {(R1*)} the following
> entailment:
>
>   (E1) CEXT(_:x) = { x : card({y: x hasBodyPart y}) = 2 }
>
> Now, OWL-1.1-Full will have to contain an additional semantic  
> condition for
> handling QCRs, and I strongly believe that such a semantic  
> condition will
> have the following form:
>
>    (S-QCR)
>       IF
>         r owl:onProperty p .
>         r owl:cardinality n .
>         r owl11:onClass c .
>       THEN
>         CEXT(r) = { x : card({y: x p y AND y rdf:type c}) = n }
>
> In this case, we will receive the following /additional/ entailment  
> from the
> RDF graph {(R1*)}:
>
>   (E2) CEXT(_:x) = { x : card({y: x hasBodyPart y AND y rdf:type  
> Leg}) = 2 }
>
> Taken together, entailments (E1) and (E2) tell that
>
>   (E3) { x : card({y: x hasBodyPart y}) = 2 }
>        = CEXT(_:x) =
>        { x : card({y: x hasBodyPart y AND y rdf:type Leg}) = 2 }
>
> This alone looks odd, and it is in essence, AFAICT, what Peter was  
> about in
> his original mail. However, (E3) alone is still satisfiable under  
> specific
> conditions.
>
> But let's now look at axiom (A2): With an analog argumentation as  
> for (A1)
> we receive the following set equality:
>
>   (E4) { x : card({y: x hasBodyPart y}) = 2 }
>        = CEXT(_:y) =
>        { x : card({y: x hasBodyPart y AND y rdf:type Ear}) = 2 }
>
> where '_:y' denotes the cardinality restriction used in (A2), after  
> being
> translated into an RDF graph. Note that '_:y' is a different bNode  
> from
> '_:x', so it /may/ denote a different restriction class.
>
> But looking closer to (E3) and (E4) reveals, that the respective  
> left hand
> sides of these equations are the /same/ in both cases. So we learn:
>
>   (E5) CEXT(_:x) = CEXT(_:y)
>
> Now, looking again into sec. 5.2 of [1], table "Characteristics of OWL
> vocabulary related to equivalence", first entry, we see that the  
> following
> semantic condition holds (please mind the "iff" in the right table  
> header!):
>
>   (S-EQUIV)
>     IF
>       CEXT(x) = CEXT(y), for classes ("IOC") x and y
>     THEN
>       x owl:equivalentClass y
>      ("<x,y> IN EXT_I(S_I(E))" with E := "owl:equivalentClass")
>
> Thus, from (E5) and (S-EQUIV) we obtain:
>
>   (E6) _:x owl:equivalentClass _:y .
>
> And this means that the two QCRs from axioms (A1) and (A2) are  
> actually
> equivalent classes. Or in English:
>
>   "Everything which has exactly two ears
>   also has exactly two legs, and vice versa."
>
> So axiom (A2) is semantically OWL-1.1-Full equivalent to (in  
> Functional
> Syntax for easy read, but assume it were given in RDF instead):
>
>   (A2') SubClassOf(Dog ObjectExactCardinality(2 hasBodyPart Leg))
>
> The QCR in (A2') is obviously disjoint from the QCR in (A3), so  
> class Dog,
> being a subclass of both QCRs, turns out to be empty:
>
>   (E7) <Dog> rdfs:subClassOf owl:Nothing .
>
> And by stating through (A4) that Pluto is a Dog, we see that our  
> ontology is
> inconsistent in OWL-1.1-Full:
>
>   (E8) <Pluto> rdf:type owl:Nothing .
>
>
> Cheers,
> Michael
>
> [1] OWL S&AS - §5: RDF-Compatible Model-Theoretic Semantics
>     http://www.w3.org/TR/owl-semantics/rdfs.html
>
> --
> 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
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"If we knew what we were doing, it wouldn't be called research, would  
it?." - Albert Einstein

Prof James Hendler				http://www.cs.rpi.edu/~hendler
Tetherless World Constellation Chair
Computer Science Dept
Rensselaer Polytechnic Institute, Troy NY 12180