Re: OWL Lite semantics

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.

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".

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!


> Pat
> -- 
> ---------------------------------------------------------------------
> IHMC					(850)434 8903   home
> 40 South Alcaniz St.			(850)202 4416   office
> Pensacola              			(850)202 4440   fax
> FL 32501           				(850)291 0667    cell
>   for spam

Received on Tuesday, 10 December 2002 06:00:22 UTC