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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: Mon, 11 Aug 2008 11:24:43 +0100
Message-Id: <64FD46BA-6183-442A-AB26-E948585E5465@comlab.ox.ac.uk>
Cc: <public-owl-wg@w3.org>
To: Michael Schneider <schneid@fzi.de>

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
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> Studer
> Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus
>
Received on Monday, 11 August 2008 10:25:23 GMT

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