Re: Nonmonotonic rules

>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).

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. 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)? 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.  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.

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. 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.

Pat


>Cheers,
>Bijan Parsia.


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Received on Wednesday, 21 January 2004 14:12:02 UTC