Re: A Problem With The Semantics of DAML+OIL Restrictions

On July 23, pat hayes writes:
> Tim Berners-Lee:
> >Having just caught up on this thread I feel the basic diconnect is in
> >the question, "How do we know what is the sufficient condition to
> >be a member of restriction R"?
> >
> >You never do know.  You are only given some *necessary* conditions.
> 

Pat,

> Well, that doesn't seem to be the case in DAML+OIL, where the 
> conditions *can* be stated to be necessary and sufficient. 

This is certainly the case. If you say:

(sameClassAs WhiteWine (intersectionOf Wine (Restriction (onProperty
colour) (hasValue White))))

then being a wine with color White is both a necessary and sufficient
condition for being a WhiteWine. Moreover, adding further axioms (or
even RDF triples) to the ontology can never change this (otherwise we
would be non-monotonic).

> Obviously, 
> there are cases where one wants to be able to say this, to be able to 
> give necessary and sufficient conditions. We do this when we say two 
> names are equivalent, for example, in effect. But I think your point 
> arises in the form: how can we adopt this open-ended attitude, and 
> state necessary conditions on restrictions *without* saying they are 
> sufficient? That would be easy to characterise semantically, but I 
> suspect might place a burden on a DAML+OIL reasoner which would break 
> decideability.  (? Any DL expert care to comment?)

I'm not sure I understand your concern here. If C is an arbitrary
class and R is a restriction, then In DAML+OIL we can state any or all
of C -> R, R -> C, or C <-> R (i.e., subClassOf C R, subClassOf R C,
sameClassAs C R). This does not have an adverse effect on
decidability, and modern DL reasoners (such as FaCT) can easily cope
with this.

> >You have to replace the question "is this consistent with the
> >restriction R?" with "is this consistent with the document D?".
> >
> >As you point out, R is just an abstract thing, a class.  And
> >anyone can say anything about anything, you don't know
> >whether there are any other constraints on it.
> 
> Sure, but that's a different question. If you state N&S conditions on 
> something and I also state N&S conditions on the same thing, then 
> taken together we will have said that our N&S conditions are 
> equivalent (even if we didnt intend to :-) . But that doesn't remove 
> our freedom to state the conditions independently.

In fact the initial "problem" was exactly this one: using multiple
properties and/or restriction types in a single restriction has the
effect of asserting multiple sets of N&S conditions, all of which
would then be implicitly equivalent. This is clear from the formal
semantics, but was incorrectly described in the reference document. The
semantics are defined this way in order maintain monotonicity in the
face of the freedom RDF gives to add arbitrary terms to a restriction.

Ian

> 
> Pat
> 
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Received on Tuesday, 24 July 2001 02:27:11 UTC