RE: Possible incorrect test case (?)

Hi!

This test case [1] really shows a non-entailment under the 
OWL 2 RDF-Based Semantics (and also in OWL 1 Full). This is 
a subtle problem coming from the RDF Semantics. 

The "lethal" bit is that the left-hand side graph of the test 
does not contain the name "c". Since the LHS graph is satisfiable 
under the RDF-Based Semantics, there exists an 
OWL 2 RDF-Based interpretation I that satisfies the LHS graph 
without having "c" in its (I's) vocabulary. According to the 
5th semantic condition "for ground graphs" in Section 1.4 of the 
RDF Semantics [2], this interpretation will fail to satisfy
the RHS of the entailment query, since the RHS contains a triple 
in which the name "c" occurs.

But even if the mentioned semantic condition for RDF Simple Entailment
would not be applicable, there would still be a different approach to 
show the non-entailment-ness: Let's again start from the above 
interpretation I (without the name "c" in the vocabulary), and 
construct a new interpretation I* from I by only adding the name "c" 
to the vocabulary of I*, where I*(c) denotes an individual in 
the /complement/ of the set of all classes (i.e. "c" is not a class). 
I* will still be an OWL 2 RDF-Based interpretation and will still 
satisfy the LHS graph. But I* will /not/ satisfy the RHS graph, since 
for this to hold the name "c" would be required to denote a class 
(see Section 5.3 in the RDF-Based Semantics [3], the table entry for 
property "owl:allValuesFrom").

So, in any case, there exists an OWL 2 RDF-Based interpretation that 
satisfies the LHS but not the RHS of the test case. Hence, the 
test case is a non-entailment for the RDF-Based Semantics.

The "correspondence theorem" [4] between the OWL 2 Direct Semantics 
and the OWL 2 RDF-Based Semantics counters this problem (at least 
for valid OWL 2 DL test cases) by replacing the original 
entailment-query by a new one that mentions all names that 
occur in the RHS also in the LHS, together with the correct typing 
information (aka declaration). This is part of what is called 
"balancing" in the proof of the theorem [5].

Best,
Michael

[1]
<http://km.aifb.uni-karlsruhe.de/projects/owltests/index.php/TestCase:WebOnt
-Restriction-005>
[2] <http://www.w3.org/TR/rdf-mt/#gddenot>
[3]
<http://www.w3.org/2007/OWL/wiki/RDF-Based_Semantics#Semantic_Conditions_for
_the_Vocabulary_Properties>
[4]
<http://www.w3.org/2007/OWL/wiki/RDF-Based_Semantics#Correspondence_Theorem>
[5] <http://www.w3.org/2007/OWL/wiki/RDF-Based_Semantics#def-balanced>

>-----Original Message-----
>From: public-owl-wg-request@w3.org [mailto:public-owl-wg-request@w3.org]
>On Behalf Of Mike Smith
>Sent: Thursday, June 11, 2009 3:35 PM
>To: Ian Horrocks
>Cc: Antoine Zimmermann; W3C OWL Working Group
>Subject: Re: Possible incorrect test case (?)
>
>On Wed, Jun 10, 2009 at 19:45, Ian
>Horrocks<ian.horrocks@comlab.ox.ac.uk> wrote:
>> It isn't obvious to me why this wouldn't be an entailment under the
>> RDF-Based semantics -- at least not at this time of night. Can you
>explain?
>
>I was basing this on the conclusion we drew when discussing the test
>case
>
>http://km.aifb.uni-
>karlsruhe.de/projects/owltests/index.php/TestCase:WebOnt-Class-005
>
>in January [1] -  that the definition of entailment in the OWL 1 Full
>semantics and the OWL 2 RDF Based Semantics does not permit the
>entailed ontology to use vocabulary not present in the premise
>ontology. This led to the description in the Direct Semantics version
>of the test
>
>http://km.aifb.uni-
>karlsruhe.de/projects/owltests/index.php/TestCase:WebOnt-Class-005-
>direct
>
>At present, after digging some I cannot support this position with
>text from the specifications.  It may be that we assumed it to hold
>because the alternative was that the WebOnt group had incorrectly
>labeled and approved these test cases.  I'm now leaning toward the
>latter view.
>
>Can someone more familiar with the OWL 1 Full and OWL 2 RDF-Based
>semantics (e.g., Peter or Michael) refer to the text and come back
>with a conclusive answer for the RDF-Based semantics versions of these
>cases?
>
>Thanks,
>--
>Mike Smith
>
>Clark & Parsia
>
>[1] http://lists.w3.org/Archives/Public/public-owl-wg/2009Jan/0031.html

--
Dipl.-Inform. Michael Schneider
Research Scientist, Dept. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: michael.schneider@fzi.de
WWW  : http://www.fzi.de/michael.schneider
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