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Re: ISSUE 131 (OWL R Unification): Different semantics on syntactic fragment

From: Ian Horrocks <ian.horrocks@comlab.ox.ac.uk>
Date: Tue, 12 Aug 2008 13:08:28 +0100
Message-Id: <7ECF8F5C-E159-4457-AD19-ADB4791F394E@comlab.ox.ac.uk>
Cc: Michael Schneider <schneid@fzi.de>, public-owl-wg@w3.org
To: Ivan Herman <ivan@w3.org>

Ivan,

I'm not sure what it means for an implementation to be "perfectly  
o.k." or "proper". According to what we discussed, implementations  
based on the OWL RL rules is that they are sound for OWL Full  
semantics and also complete for query answering (the key entailment  
in the kinds of application that motivate OWL R) for ontologies  
inside a given syntactic fragment. This was always clearly stated  
(see Section 4.4 of the existing spec).

What Michael showed in his example is that the rules won't find all  
valid entailments, even on the relevant subset. Of course this is the  
case -- rule based implementations deliberately choose to give up on  
such entailments in favour of scalability. "Solving" this "problem"  
by introducing a 3rd semantics for OWL which simply declare the  
entailments found via the given rule set to be the all only valid  
ones is completely crazy -- Michael's example nicely illustrates just  
how crazy this would be -- and totally misses the point of the OWL RL  
profile, which is to deliberately give up (some) completeness in  
favour of scalability.

Michael's example actually shows just how broken the existing design  
is, and that closing the issue without action just isn't an option.  
In contrast, the unification proposal would allow us to have a single  
OWL RL profile, with exactly the same rule set, with the same  
semantics as OWL Full, and enjoying all the benefits that motivate  
the profile in the first place. The only thing that I have heard  
against this are some strange arguments about OWL RL reasoners not  
being "competitive" with OWL DL/Full reasoners/semantics. As I  
mentioned above, this misses the whole point of OWL RL which is to  
"complete" on scalability and *not* on completeness.

Regards,
Ian






On 12 Aug 2008, at 09:35, Ivan Herman wrote:

> Hi Ian,
>
> In a thread you started a while ago (after a long discussion on  
> another thread):
>
> http://www.w3.org/mid/AEDBB4D5-D0D4-4B0D-8A2B- 
> B308C51E8518@comlab.ox.ac.uk
>
> we seemed to converge toward a solution based on first finalizing  
> the conformance issues. However, _my_ assumption back then was that  
> if an implementation implements the OWL R Rule set (and _only_  
> that), then this would be a perfectly o.k. OWL R implementation for  
> all those RDF graphs that fall under the OWL R syntactic  
> restrictions. The issue we had, and for which the thread offered a  
> good way forward, was what would happen to graphs that fall outside  
> the syntactic restriction of OWL R.
>
> However... I was clearly wrong. Michael's example shows that the  
> Rule set would not provide a proper implementation of OWL R. A  
> conformant OWL R implementation must do more than just implementing  
> the rules or, put it another way, an implementation using the rules  
> only could not claim to be OWL R conformant. This is a different  
> and pretty serious issue which, I must admit, would make me vote  
> against unification at this point.
>
> In another mail Michael says that we should close this issue  
> without action. Maybe so. At the minimum we should acknowledge that  
> there is no consensus on this issue at the moment...
>
> Sigh...
>
> Ivan
>
> Ian Horrocks wrote:
>> Michael,
>> It has never been claimed that OWL R DL and OWL R Full are  
>> completely equivalent on the syntactic fragment. What is claimed  
>> (see Section 4.4 of the existing Profiles doc) is that for  
>> ontologies within the syntactically defined fragment the OWL RL  
>> rules will be complete w.r.t. certain kinds of entailment -- in  
>> particular w.r.t. those entailments that correspond to query  
>> answering.
>> Your example is a good illustration of why it would be *a very bad  
>> idea* to define a 3rd semantics for OWL based on the OWL RL rules.  
>> According to this semantics, it would NOT be the case that  
>> owl:intersectionOf (C D) is a subClassOf D. Any reasoner finding  
>> this entailment would be unsound and non-conformant w.r.t. this  
>> semantics. This would, IMHO, be highly counter-intuitive.  
>> Moreover, I expect that many rule based implementations *will*  
>> find this entailment, or at least answer "yes" to a query asking  
>> if it holds, because they will use the standard rule-based  
>> technique for answering such a subsumption query, i.e., assert a  
>> fresh individual to be an instance of owl:intersectionOf (C D) and  
>> check if it is entailed that this individual is an instance of D.  
>> This entailment *will* follow from the rules.
>> Regarding the guarantees that are made, guaranteeing soundness and  
>> completeness w.r.t. OWL RL Full semantics for ontologies in the  
>> syntactic fragment and certain kinds of entailment seems to be the  
>> best that we can do -- as you yourself have clearly illustrated. I  
>> don't pretend to fully understand your statements about reasoners  
>> based on subsets of the OWL RL rules, but they seem to be based on  
>> a misunderstanding about what is being stated w.r.t. soundness and  
>> completeness, and on some strange assumptions about how  
>> conformance will be defined.
>> Regards,
>> Ian
>> On 10 Aug 2008, at 15:45, Michael Schneider wrote:
>>> Dear WG!
>>>
>>> I was able to find an example, which demonstrates that the  
>>> semantics of OWL R DL and OWL R Full differ on the syntactic  
>>> fragment of a unified OWL R language (see below). The example  
>>> shows that entailments exist w.r.t. the semantics of OWL R DL  
>>> (actually, the OWL 2 DL semantics), for which there is no  
>>> equivalent sequence of rule applications in OWL R Full. This  
>>> means that the semantics of OWL R ontologies, which match the  
>>> syntactic fragment of OWL R, cannot be defined in parallel by  
>>> both the DL semantics *and* the ruleset.
>>>
>>> An alternative approach would be to define the semantics of OWL R  
>>> on the syntactic fragment by the OWL 2 DL semantics only.  
>>> However, I would expect that this would lead to significant  
>>> acceptance problems for implementers, who want to base the  
>>> implementation of their OWL R reasoner on the OWL R ruleset (and  
>>> for customers/users of such reasoners, either).
>>>
>>> An implementer, who plans to create a reasoner based on the  
>>> ruleset, certainly wants to be ensured that his reasoner  
>>> implements *all* of OWL R, not only a subset, i.e. is complete  
>>> w.r.t. the OWL R semantics. It would at least be very confusing  
>>> and hard to accept that it is not sufficient to just implement  
>>> the "OWL R rules", in order to create a complete OWL R reasoner.  
>>> But with my counter example, it now turns out that completeness  
>>> will not be achievable for such a rulebased reasoner.
>>>
>>> Even worse, having such a concrete counter example makes it easy  
>>> to create a proper *superset* of the current ruleset, which will  
>>> still be sound w.r.t. the OWL R semantics. This means that the  
>>> implementer cannot even claim that his reasoner is at least the  
>>> "best possible" triple-rule based implementation of OWL R.
>>>
>>> The only thing which the implementer can claim is that his  
>>> reasoner is a "valid" OWL R reasoner, i.e. is sound w.r.t. the  
>>> OWL R semantics. But this will also be the case for any reasoner,  
>>> which is based on an arbitrary *subset* of the OWL R rules, and  
>>> even for trivial reasoners, which do not produce any inferences  
>>> at all. So, OWL R soundness alone isn't a very interesting  
>>> property of an OWL R reasoner in practice.
>>>
>>>> From this p.o.v., I would expect that, after a unification,  
>>>> implementers will not regard the OWL R ruleset to be relevant as  
>>>> a base for the implementation of OWL R reasoners. IMO, the OWL R  
>>>> rules will then be no more than just an arbitrary example for  
>>>> how one MAY create a valid OWL R reasoner. Without completeness  
>>>> guarantees, this ruleset won't be better than any other ruleset  
>>>> which provides formal OWL R soundness. Compared with the  
>>>> ruleset's current status in OWL R Full, where it specifies the  
>>>> semantics of the language, this would be a significant demotion.
>>>
>>>    * * *
>>>
>>> The example below is not simply a bug in the current ruleset,  
>>> which could easily be fixed. Instead, it shows two general problems:
>>>
>>>  (1) The ruleset would need to be able to create fresh bNodes on  
>>> the right hand side of derivations. To my understanding, it was a  
>>> design goal to avoid this. At least, none of the current rules  
>>> creates such new bNodes on the consequent side.
>>>
>>>  (2) Since the semantics of the current OWL R DL language is the  
>>> DL semantics, it allows for very flexible reasoning with complex  
>>> class expressions, as long as an ontology conforms to OWL R DL's  
>>> syntactic restrictions. The current triple ruleset isn't able to  
>>> compete with this amount of flexibility. And don't believe that  
>>> this can be overcome.
>>>
>>> Here is the example. We start from the RDF graph
>>>
>>>   G_L := {
>>>     ex:C rdf:type owl:Class .
>>>     ex:D rdf:type owl:Class .
>>>     ex:C rdfs:subClassOf ex:D .
>>>   }
>>>
>>> This is a valid OWL R DL ontology in RDF graph form, since only  
>>> named
>>> classes are used on the LHS and RHS of the subclass axiom (see  
>>> sec. 4.2.3
>>> of [1]).
>>>
>>> The second RDF graph is
>>>
>>>   G_R := {
>>>     ex:C rdf:type owl:Class .
>>>     ex:D rdf:type owl:Class .
>>>     _:X owl:intersectionOf ( ex:C ex:D ) .
>>>     _:X rdfs:subClassOf ex:D .
>>>   }
>>>
>>> Again, this is a valid OWL R DL ontology, because this graph RDF- 
>>> maps to the
>>> following expression in Functional Syntax (omitting declarations):
>>>
>>>   SubClassOf( IntersectionOf(ex:C ex:D) ex:D )
>>>
>>> According to sec. 4.2.3 of [1], intersections of named classes  
>>> may occur on
>>> the LHS of subclass axioms.
>>>
>>> The semantic meaning of these two graphs is given in OWL R DL by  
>>> applying
>>> the OWL 2 DL semantics. According to the OWL 2 DL semantics, the  
>>> entailment
>>>
>>>   G_L |= G_R
>>>
>>> is true, because from
>>>
>>>   C subset D
>>>
>>> follows
>>>
>>>   (C and D) subset D
>>>
>>> However, there is no sequence of applications of OWL R Full  
>>> rules, which
>>> starts in G_L, and which produces G_R (or a super graph of G_R)  
>>> as a result.
>>> Actually, there is no single triple rule in OWL R Full that would  
>>> allow to
>>> produce the bNode '_:X', which occurs in G_R but not in G_L.
>>>
>>> Regards,
>>> Michael
>>>
>>> [1] <http://www.w3.org/2007/OWL/wiki/Profiles#Class_Expressions_3>
>>>
>>> -- 
>>> 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
>>>
>
> -- 
>
> Ivan Herman, W3C Semantic Web Activity Lead
> Home: http://www.w3.org/People/Ivan/
> PGP Key: http://www.ivan-herman.net/pgpkey.html
> FOAF: http://www.ivan-herman.net/foaf.rdf
>
Received on Tuesday, 12 August 2008 12:09:09 GMT

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