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RE: [OWLWG-COMMENT] Re: Cardinality Restrictions and Punning

From: Michael Schneider <schneid@fzi.de>
Date: Wed, 2 Jan 2008 16:30:55 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A05A6092@judith.fzi.de>
To: "Pat Hayes" <phayes@ihmc.us>
Cc: "Owl Dev" <public-owl-dev@w3.org>

Happy new year, Pat!

Pat Hayes wrote on December 22, 2007:

>I hereby officially shut down my semantic engine for 12 days.

Ok, then let's turn it on again! :)

You answered to me:

>>I don't think that it is a useful idea to allow 
>OWL-DL-consistent ontologies
>>to become inconsistent in OWL-Full.
>I disagree. These are two distinct languages which differ profoundly 
>in their basic methodology and semantics, one more expressive than 
>the other and which has the less expressive language embedded into it 
>as a proper subset. In fact, under these conditions it is almost 
>inevitable that this will occur. Why would one not expect this? 
>Obvious contradictions in quantified logic, such as
>(forall (x)(= x a))
>(not (= b a))
>are consistent in propositional logic.

Hm, I would rather say that the first of these two formulas is simply a
non-wellformed expression in propositional logic. And thus, the whole
expression is non-wellformed. And as a non-wellformed expression, it cannot
be given a (semantical) interpretation. In particular, it cannot be given a
/satisfying/ interpretation. So it cannot be consistent in propositional
logic (but also not inconsistent, of course).

So for the question about DL-consistent/Full-inconsistent OWL ontologies: I
am only interested in examples, where the ontology is syntactically ok in
OWL-DL, so that it may have a model, of course.

>>And if this should not be preventable in
>>general, one should at least take care that the cases for 
>which this happens
>>reduce to artificially looking "research examples".
>Again I disagree. You may be being spooked by the word 
>"inconsistent"; but as I am sure you know, this is simply another way 
>to say that the more powerful language is able to prove entailments 
>which are invisible to the less expressive language. 

I understand that inconsistent ontologies entail /everything/ (every RDF
graph in the case of OWL-Full), since they entail some contradiction (ex
falso quodlibet). So from a formal point of view, I receive more information
from an inconsistent Full-ontology than from a consistent DL-ontology.

>So, sometimes 
>there will be cases where a result is entailed in OWL-Full which is 
>not entailed in OWL-DL. I don't find this at all a bad thing, or 
>something to be avoided: on the contrary, this is often the chief 
>motivation for wanting to use a more expressive language.

I perfectly agree that it is generally desirable to get more entailments
from OWL-Full than from OWL-DL. But the scenario we are discussing here is
not just about "more" entailments. Inconsistency gives me *all* entailments,
which I do *not* regard to be desirable. An inconsistent ontology is
effectively useless. Whatever entailment I am querying for, the answer will
always be "yes". 

So, from a practical point of view, I do *not* really learn more from an
inconsistent OWL-Full ontology than from the same ontology being OWL-DL
consistent. In effect, I do not learn anything from an inconsistent
ontology. See below for a discussion of your example.

>And I am 
>talking about real examples, not "research examples". Such as being 
>able to infer, from the fact that a taxonomy represented as a class 
>of classes contains only three members and that a thing is not in any 
>of them, that it is not classified by the taxonomy.

I don't see how to express this example in OWL-DL. So, at least, it does not
seem to be intended to be an example for the DL-consistent/Full-inconsistent
problem. But let's discuss it from the Full-inconsistent perspective solely.

If this ontology is inconsistent, it definitly *will* entail this "thing is
not classified by taxonomy" statement. But the ontology will then also
entail the converse statement, i.e. that the thing *is* classified by the
taxonomy. And this is certainly not something what one wants to receive as a

If the above ontology is inconsistent, I would say that it is a fallacy to
believe that one receives the desired entailment from the premises you
mentioned above (taxonomy with three classes, none of them containing the
regarded thing). Instead, one receives this entailment simply from the state
of inconsistency (or more precisely, from the entailed contradiction) of
that ontology. One would receive the same entailment from *any* other
inconsistent ontology, too, regardless what other "facts" there are in such
an ontology. So one really does not get any valuable information from an
inconsistent ontology.

This is the reason, why I would regard it to be a real problem, when OWL-1.1
would get a Full version, in which it could happen *too easily* that an RDF
graph is DL-consistent, but Full-inconsistent. For OWL-1.0, I pondered a
while now about an example. But the only method, I am currently aware of, to
produce such an example, is the "finite-universe" trick, as originally
brought to my attention by Peter [1]. 

The existence of this method for OWL-1.0 shows me that it would, of course,
not be reasonable to demand that the DL-consistent/Full-inconsistent problem
must not occur in OWL-1.1. On the other hand, if playing with the
cardinality of the OWL universe is the only way to evoke this problem in
OWL-1.0 [FIXME!], then I am not very scared from a practical point of view.
Because the only usecase for this I know is to get a notion of "closed
world" with OWL [2]. And I regard this to be more of a niche application.
Anyway, it is kind of abuse of OWL, since the open world assumption is
fundamental to OWL. 

So, to conclude, I do not regard the "finite-universe" trick to be a show
stopper. But if you would show me examples of simple and natural looking
OWL-1.0 ontologies, which are DL-consistent but Full-inconsistent, then I
would probably have to reconsider my opinion. 

For OWL-1.1, I do not yet know whether the new features like QCRs, sub
property chains, or additional property characteristics will bring such
examples nearer to us. Well, I would certainly want to live with this
situation then, because these new features are much too important to be
dropped w.r.t. this OWL-Full related problem. But at least for data/object
property punning, I can already see from Jeremy's example [3] that the
DL-consistent/Full-inconsistent problem can easily arrive even for very
simple and natural looking ontologies. And in this case, my opinion is that
the tradeoff should rather be in favour of OWL-1.1-Full instead of property
punning. (But, of course, I already know that you will agree with me in this
very single point :)).



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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Received on Wednesday, 2 January 2008 15:31:09 UTC

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