RE: Differences in current OWL-R DL and OWL-R Full

Hi Ian!

Ian Horrocks wrote on Monday, July 21, 2008:

>Hi Michael,
>
>As I was explaining in my earlier emails, the suggested syntax
>specification for OWL-R does not restrict the applicability of the
>rules, 

Yes, I understand this. 

>it only provides a sufficiency condition for the semantic
>guarantees currently described in Section 4.4 of the current Profiles
>document; i.e., if an RDF graph satisfies the syntactic condition,
>then the semantic guarantees hold. For graphs outside this set, the
>rules will still derive many useful consequences.

I have to admit that I am pretty lost. So it will be best to come up with a series of questions and comments.
 
In your initial mail to Ivan [1] you write w.r.t. "conformance":

  """
  we could define conforming OWL-R reasoners as those that, 
  when presented with an RDF graph that can be parsed into the 
  relevant structural spec, will satisfy the semantic conditions 
  set out in Section 4.4 
  (http://www.w3.org/2007/OWL/wiki/Profiles#Relationship_between_OWL-R_DL_and_OWL-R_Full).
  """

But I do not understand how conformance can be defined based on the cited criterion. This criterion only talks about a certain semantic relationship between OWL-R-DL (or: the OWL-R specification) and the set of OWL-R rules. How are arbitrary implementations covered by this criterion? In particular such implementations, which are /not/ based on the OWL-R rule set? So, how can I apply the criterion in order to decide, whether a given implementation is conformant or not? It's perhaps an easy technical point which I overlook here, but I simply do not see it.

I have some other issues with the criterion itself. On the one hand, there is the utility of the criterion: It seems to be pretty restricted by only taking assertion data into account. I am not sure whether this criterion is too weak for our purpose, in the sense that it might allow me to change the definition of either OWL-R-DL or OWL-R-Full to a significant degree, without making the stated relationship invalid. On the other hand, I am having trouble to check that the relationship stated by the criterion actually holds. The complicated definition of OWL-R-DL (the asymmetry of subClassOf axioms, etc.) makes it hard for me to see this easily. But these are just first thoughts, and I will need to do further checks on these questions, so let's defer a discussion about them for the moment.

Another point which I wanted to make is on what you said in [1] was an "advantage" of the unification:

  """
  * OWL-R implementations can provide additional functionality while  
    still being fully OWL-R compliant because the extra functionality  
    won't affect those graphs for which a guarantee of completeness is  
    being made.
  """

This is something, which I do not really see RDF people regarding as an advantage, but rather as a mess. :) This sounds like, as if I can add arbitrary rules to the rule set given in the spec, and the result will still be a conformant OWL-R system. Or, in the most extreme case, as if I can produce a system, which simply produces all possible triples from all subject, predicate, and object nodes of triples in the base RDF graph. Even if the base RDF graph happens to be a syntactically valid OWL-R ontology in RDF graph form, the result would be "virtually everything". Calling such a "reasoner" to be OWL-R conformant is simply not a useful characterization from an RDF semantics point of view.

But, perhaps, the notion of "OWL-R conformance" isn't really meant with such a vague and wide meaning. Perhaps, it is much more restricted by the criterion given in sec. 4.4. But this seems to lead back to my first question stated above, so I will wait for your answer, first, to get a better understanding.  

Cheers,
Michael

[1] <http://lists.w3.org/Archives/Public/public-owl-wg/2008Jul/0347.html>

>It is easy to see that deriving *all* the consequences of the
>equivalentClass axiom you describe would *in general* require non-
>deterministic reasoning of a kind that implementations based on the
>OWL-R rules will not provide. This kind of reasoning would obviously
>cause an undesired increase in worst case complexity.
>
>
>Regarding your second point, the reason for the relatively low
>complexity of reasoning with ontologies that satisfy the syntactic
>conditions is, intuitively, that they have a single canonical model
>whose domain of interpretation consists exactly of those individuals
>occurring in the ontology. The property axioms can thus be treated
>simply as a set of rules that add implicit property assertions
>(triples) -- which is exactly how they are implemented in the rule
>set (See Table 4).
>
>Regards,
>Ian
>
>
>
>On 19 Jul 2008, at 16:12, Michael Schneider wrote:
>
>> Hi Boris!
>>
>> On the last telco, we had this short discussion about to what
>> degree the
>> current definitions of OWL-R DL and OWL-R Full are aligned. As
>> intended, I
>> did a few checks afterwards, and here are my results and questions.
>>
>>
>> (A) Restrictions on class related axioms
>> ----------------------------------------
>>
>> In OWL R DL, sub class axioms are asymmetrically specified: Not
>> every class
>> expression, which is allowed on the LHS of a sub class axiom is
>> also allowed
>> on the RHS, and vice versa. An example is that a unionOf class
>> expression
>> may only appear on the LHS.
>>
>> Other examples for class expressions, which are not allowed to
>> appear on
>> both sides of a sub class axiom are AllValuesFrom, SomeValuesFrom and
>> (<=1)MaxCardinality.
>>
>> Other kinds of axioms which are also restricted in their use of
>> certain
>> class expressions are class equivalence and disjointness axioms,
>> range and
>> domain axioms, and class assertions.
>>
>> All these syntactic restrictions do not hold for OWL-R Full. For
>> example,
>> the following RDF graph is *not* a valid OWL-R DL ontology in RDF
>> graph
>> form, but it *is* a valid OWL R Full ontology:
>>
>>   ex:C owl:equivalentClass _:x .
>>   _:x owl:unionOf ( ex:D1 ex:D2 ) .
>>   ex:w rdf:type ex:D1
>>   ex:w rdf:type ex:D2
>>
>> And this isn't even a particularly strange ontology from a DL point
>> of view,
>> i.e. it doesn't contain, for example, syntax reflection parts. In
>> fact, it
>> is a valid OWL 2 DL ontology in RDF graph form.
>>
>> Applying the OWL-R (Full) triple rules will result in:
>>
>>   ex:w rdf:type ex:C
>>
>> Again, this is not a weird result, but one which one would expect
>> from OWL 2
>> DL, too. And the entailed triple is of course syntactically valid
>> in OWL-R
>> DL.
>>
>> If the unification process is performed without a change of either
>> the OWL-R
>> (DL) syntactic restrictions, or the OWL-R (Full) rules, then the
>> set of
>> OWL-R rules will produce such additional "DL-meaningful looking"
>> results
>> from "DL-meaningful looking" RDF graphs, which will go beyond the
>> OWL-R
>> specification.
>>
>>
>> (B) Unrestricted property related axioms
>> ----------------------------------------
>>
>> In the telco, I specifically asked for sub property chains as an
>> example for
>> a language feature, which is in OWL-R Full, but not in OWL-R DL.
>> However, I
>> now see that sub property chains are really included in OWL-R DL.
>> On the one
>> hand, property expressions are unrestricted:
>>
>>   4.2.2 Property expressions
>>
>>   "Property expressions in OWL-R DL are identical to the
>>   property expressions in OWL 2 [OWL 2 Specification].
>>
>> And further, property axioms are also unrestricted:
>>
>>   4.2.5 Axioms
>>
>>   OWL-R DL redefines all of [OWL 2 Specification] that refer to
>> ClassExpression.
>>   [...]
>>   All other axioms in OWL-R DL are defined as in OWL 2.
>>
>> But I wonder how this can be the case. Is it really certain that the
>> unrestricted use of all the property axioms will maintain
>> tractability?
>> Again, my test case would be sub property chains here.
>>
>> 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
>>


--
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