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.

Yes, I think this is  very accurate.
With respect to the Semantic Web, this problem can be very serious.
People who have training in different fields might use (or misuse) the same
formalisms differently.


> 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.

*Classical* logic has nothing to say about it. This doesn't mean that you
can't define a logic in which meta-info is treated differently from
"regular" data. F-logic does this. It defines what it means to conform to
the meta-data (although not completely satisfactorily from the point of
view of programming languages).
There is also Typed Predicate Calculus (LICS-91), which espouses the same
idea (which later went into F-logic).

The basic idea is that there is a notion of well-typed interpretations and only
those things are acceptable as models. So, you are not supposed to derive
things that violate the meta-data.

This notion is weaker than what is acceptable in programming languages,
but it is acceptable in the DB world.


	--michael

Received on Wednesday, 21 January 2004 15:51:02 UTC