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Re: OWL Lite semantics

From: pat hayes <phayes@ai.uwf.edu>
Date: Tue, 10 Dec 2002 09:34:24 -0600
Message-Id: <p05111b3cba1bb5094505@[10.0.100.86]>
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: www-webont-wg@w3.org

>On December 9, pat hayes writes:
>>
>>  >On December 9, Jeremy Carroll writes:
>>  >>
>>  >>
>>  >>
>>  >>  > Jeremy's proposal is that OWL Lite be both a syntactic and *semantic*
>>  >>  > "subset" (I use the expression loosely in this case) of OWL DL.
>>  >>
>>  >>
>>  >>  Nothing loose there ...
>>  >>  my proposal views a language as a pair:
>>  >>
>>  >>  < A set of documents,
>>  >>     an entailment relationship over the set >
>>  >>
>>  >>
>>  >>  Then
>>  >>
>>  >>  OWL DL is a sublanguage of OWL full
>>  >>     in that the set of OWL DL documents is a subset of the set 
>>of OWL Full
>>  >>  documents
>>  >>     the OWL DL entailment relationship is a subset of the OWL Full
>>  >>  entailment relationship (specifically the restriction of OWL Full
>>  >>  entailment to the set of OWL DL documents).
>>  >
>>  >Yes, so an OWL DL reasoner, when asked about entailment between two
>>  >documents will either give the *SAME ANSWER* as an OWL full reasoner,
>>  >or will refuse to answer on the grounds that the document is outside
>>  >the subset it can handle.
>>  >
>>  >>
>>  >>  My OWL Lite is a sublanguage of OWL Full
>>  >>     the set of OWL Lite documents is a subset of the set of OWL
>>  >>Full documents
>>  >>     the OWL Lite entailment relationship is also a subset of the OWL DL
>>  >>  entailment relationship.
>>  >
>>  >You have omitted the crucial fact that, in the case of your OWL Lite
>>  >proposal, the entailment relationship is NOT the OWL full entailment
>>  >relationship restricted to the set of OWL Lite documents, but is
>>  >(probably) a subset of this set (intuitively tempting to believe that
>>  >this is the case, but it remains to be proved). Thus, OWL Lite
>>  >reasoners and OWL DL/full reasoners would give *DIFFERENT ANSWERS* to
>>  >questions about entailment w.r.t. OWL Lite documents.
>>  >
>>  >This is *NOT* simply incompleteness w.r.t. OWL DL/full semantics,
>>  >because a Lite reasoner would be entitled to answer NO to a question
>>  >about entailment when the correct DL/full answer is YES.
>>
>>  There is a delicate point here, actually, guys. If we are thinking in
>>  DL terms, where all reasoners can be expected to be dealing with
>>  decideable questions and so for a complete reasoner a 'not proven'
>>  answer amounts to a 'proven not' answer, then Ian is right. If on the
>>  other hand we are thinking always in terms of subsets of FOL, and
>>  assuming as a basic principle that we are only talking about
>>  provability, then Jeremy is right. That is, positive provability -
>>  corresponding to FOL entailment - in J-OWL-Lite is (almost certainly)
>>  a subset of entailment in current OWL-Lite (let us suppose, anyway).
>>  On this view, however, a J-OWL-Lite reasoner should *never* give the
>>  answer NO to any query, since it can never be sure that a real OWL
>>  reasoner might not have been able to answer it. That is, on this
>>  view, J-OWL-Light is indeed a subset of a logic, but in this sense
>>  all logics are at best r.e., so it is not a decideable subset of a
>>  decideable logic. So on this view, J-OWL-Lite ceases to be a
>>  description logic, or at any rate its not a sub-DL of OWL-Lite.
>>
>>  Taking sublanguages of description logics is a different game than
>>  for ordinary logics, because DLs come with higher expectations about
>>  the questions they can answer. (Think of a DL as a pair of normal
>>  logics, one for answering YES questions and one for answering NO
>>  questions. Subsetting a DL requires one to have sublanguages both
>>  ways round; sublang-ing a normal logic gives you the first of these
>>  but gets the second one backwards, in general.)
>>
>>  All of which, for me, is yet more evidence that DLs are more trouble
>>  than they are worth, but I guess I shouldn't keep on saying that.
>
>I don't pretend to understand Pat's bizarre obsession with DLs. DLs
>are (sigh!) just one of *many* decidable fragments of FOL - others
>include many modal, dynamic and temporal logics, as well as fluted
>logics, the guarded fragments, the two variable fragment, etc., etc.

OK, I didnt mean to start this old argument up again, but just to set 
the record straight. I have no problem with DLs as such, and I agree 
that seen as a decideable subset of logic they are interesting and 
useful, though I still detest the 'class/property' way of thinking 
that they have engendered. I guess what I should have said is that I 
wish that the entire thrust of all SW languages were not based on 
this idiosyncratic subset of logic ands its even more idiosyncratic 
langauge and terminology, but were instead based on logic. It just 
seems to make more sense to base something this large-scale on 
foundations that go back 60 years than ones that go back about a 
decade and start in Bell Labs. The syntactic and semantic advantages 
are overwhelming; the resulting simplicity would make 'layering' a 
trivial exercise. IN fact, we will almost certainly, eventually, get 
back to the calm waters of logic; but starting in the way that we 
have done is going to cause a 5-year hiatus. The computational 
advantages of DLs can stand on their own ground and justify a focus, 
within that overall logical effort, on DL reasoners and DL-oriented 
syntactic subsets.

>Nor do I understand the notion that "yes" answers have greater
>importance than "no" answers, and that logics with decision procedures
>that can give "no" answers with equal certainty to "yes" answers are
>"more trouble than they are worth"; the energy devoted to the study of
>decidable logics in general suggests that many logicians believe in
>the importance of logics supporting "higher expectations about the
>questions they can answer".

I agree that being decideable is very nice when you can get it, but I 
don't think that is centrally important.  In practice, being in a 
decideable subset of logic with an unknown complexity is 
indistinguishable from being in full logic. I also think that being 
in a known decideable subcase is a property that is not worth the 
resulting syntactic warping and meta-theoretic complexity of SW 
languages that we have had to endure; particularly when taken in the 
small, said decideability is likely to happen more or less by 
accident most of the time in any case, and taken in the large, the 
sizes of the data-sets are likely to be so big that decideability as 
such isn't going to be a useful property in any case: we will need 
sublinear complexity to survive.

>
>Perhaps this is because, in practice, "don't know" answers *will* be
>treated as "no" answers (this was the clear intention of Jeremy's
>proposal, even if it was inadvertent in this case). Welcome to the
>real world!

But Jeremy's proposal made perfect sense within a logical framework. 
The language defined by his restricted semantics is indeed a true 
sublanguage of OWLLite *in a conventional logical sense*. There is no 
confusion there, inadvertent or otherwise. The confusion arises when 
you confuse a logic with a description logic, so that the notion of 
'sublanguage' takes on a curiously strong meaning and has to be 
treated in unusual ways. I didn't read Jeremy as saying that he 
planned to treat "don't know" as "no" anywhere; that must have been 
something that YOU were assuming he would do.

Pat
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Received on Tuesday, 10 December 2002 10:34:40 GMT

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