Re: Why must the web be monotonic ?

pat hayes wrote:
> 
> >From: "Ian Horrocks" <horrocks@cs.man.ac.uk>
> >
> > > 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).
> >
> >I think I've heard it said that the web must be monotonic.  Have I misheard?
> >If not, then why must the web be monotonic?
> 
> Good question. The answer is controversial, but seems to me to be
> clear. First, its not the Web that is monotonic (whatever that would
> mean) but the reasoning from Web resources that must be monotonic.
> And the reason is that it - the reasoning - needs to always take
> place in a potentially open-ended situation: there is always the
> possibility that new information might arise from some other source,
> so one is never justified in assuming that one has 'all' the facts
> about some topic (unless you have been explicitly told that you
> have.)  Nonmonotonic reasoning is therefore inherently unsafe on the
> Web. In fact, nonmonotonic reasoning is inherently unsafe anywhere,
> which is why all classical reasoning is monotonic; this isn't
> anything particuarly new. But the open-ended assumption that seems to
> underlie much thinking about reasoning on the semantic web makes the
> issue a little more acute than it often is in many of the situations
> where logic has been put to use in computer science.
> 
> For example, if you are reasoning with a particular database of
> information, it is often assumed that the dbase is complete, in the
> sense that if some item is missing, then it is assumed to be false:
> if a hospital's databanks do not contain any record of a certain
> patient, you can conclude that they weren't a patient at the hospital
> (because if they had been, their record would be there.) Nonmonotonic
> inference modes such as this (often called negation-as-failure, ie if
> you fail to find P in the database, assume P is false) are widely
> used because they are efficient and because closed worlds are so
> common. It is used in Prolog, where it is often exactly what one
> wants because the domains being described are recursively enumerable
> and failure to prove amounts to knowing that no proof can exist. But
> open-ended domains are not like this, and it is very dangerous to
> rely on this kind of reasoning when one has no licence to assume that
> the world is closed in the appropriate way. If there were ever an
> open-ended domain it is surely the semantic web.
> 
> There is a way to combine the global security of monotonic reasoning
> with the local advantages of nonmonotonic reasoning (eg when working
> with hospital records on a website, say), which is to provide a way
> to state the closed world assumptions explicitly. Take the
> hospital-records example again, where you fail to find any record of
> a patient and conclude that the person never was a patient.  That is
> a non-monotonic inference from just the patient records, but it is
> monotonic from the patient records PLUS an explict statement of the
> closed-world assumption, ie the statement that the set of records is
> exhaustive. So if we have a way to refer to a set of assertions -
> say, all those at a certain URL, or all those which use a certain
> namespace, or by some other means - and a way to state the
> closed-world assumptions that are being made about this set of
> assertions - say, they they are exhaustive with respect to all
> queries of a certain form - then the overall reasoning can be
> considered monotonic, even though it proceeds locally by using
> efficient nonmonotonic methods.

This idea of refering to a set of assertions ("say, all those at a
certain URL, or all those which use a certain namespace, or by some
other means") ties in with a comment that I've made on 2 different
threads, in connection with DAML-S expressiveness issues.  I won't go
into detail here, but in considering some things we've wanted to
express, it has come up that it would be very useful to be able to state
a restriction with respect to "a set of assertions".  For instance, it
would be useful to be able to say that, within a given namespace, a
property has cardinality 1 (without saying anything about property
instances outside of the namespace).  (I suppose there's an issue about
what namespace a property instance belongs to, but for present purposes,
I don't think that needs to be dealt with here.)

- David

 
> 
> 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.
> 
> Pat Hayes
> 
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Received on Wednesday, 25 July 2001 01:08:30 UTC