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Re: OWL Lite semantics

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 9 Dec 2002 17:38:31 -0600
Message-Id: <p05111b29ba1ad5bf38e0@[]>
To: Ian Horrocks <horrocks@cs.man.ac.uk>, jjc@hplb.hpl.hp.com
Cc: www-webont-wg@w3.org

>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.


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Received on Monday, 9 December 2002 18:39:04 GMT

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