Re: Nonmonotonic rules

On Jan 21, 2004, at 2:04 PM, pat hayes wrote:

>> On Jan 21, 2004, at 3:15 AM, Michael Kifer wrote:
>> [snip]
>>>> Indeed. There may be no differences, given my newer understanding of
>>>> how you intend that nonmon rules are to be used. I think we may have
>>>> been viewing the world from  different metalevels, as it were.
>>>
>>> Suddenly the difference of opinion became fuzzy ...
>>>
>>> Unfortunately, nobody had the patience to read this far to find out 
>>> that we
>>> actually agree :-)
>> [snip]
>>
>> I have, FWIW, but I'm not sure what to make of this agreement. Once 
>> more, it may be at the level of nuts and bolts that the blood will 
>> start to flow :)
>
> Actually, I don't think so. Getting a bit closer to the nuts and bolts 
> makes things clearer (for me, at least).

Oh good.

> Its interesting that this disagreement/misunderstanding can be rooted 
> in the differences between two world-views of what class-based 
> reasoning is really *for*, one based on DL's evolution from logic, the 
> other based on schemas considered as data descriptions.

Yes. Stefan Decker and I hit this clash last march in Japan.

> This difference of perspectives keeps coming up and seems to be very 
> important: for example, does one think of range assertions as 
> constraints (datatype) or simply as assertions (logic)?

Yep. It seems particularly critical in the service realm, as Stefan 
again drove home forcefully in Florida last fall. If you describe an 
input's type using an OWL class, at invocation time, what information 
must you know, and know to send? If the class is Person and person 
restricted onProperty childOf someValuesFrom Person...do you have to 
send all the information about the parents as well? What if the 
individual happens to be  a member of parent and soccerCoach (where 
neither is a subclass of the other)? Do you send all you know? What if 
you're knowledge is incomplete, i.e., you know its a parent but don't 
know any further details about the children? For some services that 
might matter, others not. This difference isn't usefully expressed by 
the simple declaration of type. (Stefan, feel free to jump in if I'm 
mangling your point.)

It seems to me to be a severe problem: You are likely to often have too 
much *and* too little information.

> How about datatyping? And so on. We keep running into cases where 
> people have divergent intuitions which can be traced back to the 
> differences in attitude arising from these two world-views.  Clearly 
> at some level they are similar: Codd's Relational model and the DL 
> logic-based semantics all agree on the ultimate nature of relations 
> and classes; but the ways that the two communities think seem often to 
> be sharply different.  Im not sure how to characterize the difference, 
> exactly, but it seems to be that the DB world-view sees a sharp 
> distinction between different kinds of information, and tends to treat 
> general facts as conditions imposed on concrete facts: meta-data as 
> opposed to data.

Also, as is apropos, the handling of incomplete information, and thus 
the kind of (and efficiency) of the sort of reasoning you can do.

>  Distinctions like this may be operationally important but have no 
> natural place in a logic-based perspective which historically has been 
> largely motivated by the desire to unify divergent sources of 
> information as far as possible into one uniform framework.

I tend to think of this as a consequence of the expressivity of the 
formalism. TBoxs and ABoxs can be pretty distinct, at least until you 
reach a certain level of expressivity.

> If one thinks of a universally quantifier assertion as really being 
> meta-data, i.e. as being about the ground facts rather than just 
> another fact about the world, then this lends itself immediately to a 
> host of what seem to someone coming from the logical tradition to be 
> basically errors: things like considering Herbrand interpretations to 
> be a fully adequate semantic theory; like finding various nonmonotonic 
> techniques natural (even obvious) and thinking of quantifiers are 
> essentially substitutional, all of which are anathema to logicians.

Oh come! Substiutional quantification rules! :)

> And if you think that the more general assertion's chief purpose is to 
> control, select or check the internal coherence of a body of ground 
> data, then the purely logical account of quantification is inadequate 
> or at any rate incomplete, since a combination like
> (forall (x) (R x x))
> (not (R a a ))
> is of course inconsistent, but inconsistent in a special way: the 
> second item is wrong, or should be rejected, as it fails to conform to 
> the schema. The schema has more assertional force than the mere data 
> in a DB world, since the schema is a kind of filter or guardian of the 
> data. Logic has nothing to say about intuitions like this.
>
> Anyway, just rambling. It might be fun to try to get this divergence 
> between world-views stated clearly, though, as the SW world seems to 
> require DB folk and logic folk to be able to get along with one 
> another.

Yes.

Cheers,
Bijan Parsia.

Received on Thursday, 22 January 2004 08:12:32 UTC