Re: Why must the web be monotonic ?

>From: "pat hayes" <phayes@ai.uwf.edu>
>
> > Right now, DAML+OIL and RDF have not entered into this area, but
> > 'rules' languages need to consider it seriously, in my view. The
> > global advantages of monotonicity should not be casually tossed
> > aside, but at the same time the computational advantages of
> > nonmonotonic reasoning modes is hard to deny, and they are widely
> > used in the current state of the art. We need ways for them to
> > co-exist smoothly.
>
>How about just stating that a given context is monotonic like the following?
>
>[1] {TheGroup containsMembers Pat, Tim, exp(membersOf  RDFLogic). }
>instanceOf MonotonicContext.

The issue is how do we do reasoning in the global context, however. 
There really isnt anything useful to be gained from being told that a 
small subworld is monotonic, since the need for monotonicity arises 
when one wants to make inferences which will stay correct even in 
some larger context.  (That is the definition of monotonic inference: 
if you can validly infer something from Q, then you can validly infer 
it from Q plus anything else; the extra information can't invalidate 
your earlier conclusion.) If we were restricted to some TheGroup 
which is listed explicitly, or whose boundaries we can compute at a 
reasonable cost, then we can use nonmonotonic inferences freely, 
knowing that we are talking about this limited domain. But if we want 
to publish our conclusions to a broader audience, it would be 
irresponsible (IMHO*) to fail to indicate that they were derived from 
this narrowly defined context, and rely on the nonmonotonic powers of 
our listeners to rescue themselves from any errors into which they 
might be led by relying on our conclusions in areas where they are no 
longer valid. If, however,  we publish them with an explicit 
indication that they are derived from, and claimed to be valid only 
with respect to, this narrower context, then our published claims 
(including this rider) can be used monotonically by other reasoners 
with perfect safety. If they are willing to accept the limits of the 
context, they can continue to reason within the closed world. If they 
do not, they can insert this rider as an explicit condition on any 
further conclusions they might wish to draw from what we tell them. 
Either way, this enables them to have the same confidence in what we 
publish as we have ourselves, which is the best that one can do.

Pat Hayes

* PS. I became convinced of the importance of monotonicity for the 
semantic web after trying, and failing, to persuade Tim B-L that 
nonmonotonic reasoning was the proper way to go. He insisted that web 
logic had to be monotonic, and he was right.

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Received on Tuesday, 24 July 2001 19:02:32 UTC