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RE: Non-monotonic

From: Stephane Fellah <fellah@pcigeomatics.com>
Date: Fri, 14 Nov 2003 15:58:42 -0500
Message-ID: <8ED21571324EB145933ACCD22B86AC363C3DDE@bach.ncr.pcigeomatics.com>
To: "Drew McDermott" <drew.mcdermott@yale.edu>, <sean@smo.uhi.ac.uk>
Cc: <adrianw@snet.net>, <minsu@etri.re.kr>, <www-rdf-rules@w3.org>, <www-rdf-interest@w3.org>


I think I've heard that the web must be monotonic. The monotonic aspect
of the semantic web is an interesting issue. I am claiming that some
operations in the logic layer of the semantic stack cannot be executed
while at the same time respecting monotonicity. The engines handling the
logic layer of the semantic web stack should take into account the
specificity of the World Wide Web. One of the properties of the web is
the fact that sets are not closed. This implies that not all elements of
a set are known. Reasoning then has to happen in an open world. 

Some operations in the logic layer of the semantic stack cannot be
executed while at the same time respecting monotonicity.

Here an example will illustrate my thought:

Let suppose I have a series of purchasable items with a price property
expressed as triples by:


and a query is done asking for the lowest price.

Then some more items are added in the knowledge base:


and again the query is done asking for the lowest price.

It seems natural that the answer can now be different from the first
answer. Monotonicity would require the first answer to remain in the set
of solutions, this obviously does not make any sense.
It is clear that a Semantic Web that is not able to perform such an
operation cannot be satisfactory. Such non-monotonic reasoning
capabilities seem crucial for systems with incomplete information about
their environment, however I read across multiple document that the
semantic web requires to be monotonic. Can anyone explain why ?

Best regards
Stephane Fellah
Senior Software Engineer
PCI Geomatics
490, Boulevard St Joseph
Hull, Quebec
Canada J8Y 3Y7
Tel: 1 819 770 0022 Ext. 223
Fax 1 819 770 0098
Visit our web site:  www.pcigeomatics.com

-----Original Message-----
From: Drew McDermott [mailto:drew.mcdermott@yale.edu] 
Sent: Friday, November 14, 2003 11:52 AM
To: sean@smo.uhi.ac.uk
Cc: adrianw@snet.net; minsu@etri.re.kr; www-rdf-rules@w3.org;
Subject: Re: Non-monotonic

   [Minsu Jang]
   Non-monotonic reasoning is about the ability to retract previous
   conclusions and coming up with new conclusions, as the world
   is changing and facts we are given are changing.

   [Sean Mehan]
   Nonmonotonic reasoning is the ability to mkae assertions about the=20
   domain (push new facts on the stack) which may later be modified
   retracted (pop the facts).

Both of these don't quite state correctly what nonmonotonicity is. A
reasoning algorithm (or logic) is nonmonotonic if there are premise sets
P and Q such that P is a subset of Q, but the algorithm draws (or the
logic licenses) a conclusion C given P that it does not draw or permit
given Q.  In other words, some conclusions can cease to be inferrable in
the presence of more information.

In practical situations, this ability also requires the ability to
retract previous conclusions.  But monotonic systems also require that
ability.  If some of the premises are retracted (by some other agent),
then some of your conclusions may have to be retracted.

   [Sean Mehan]
   The  question I have is how often do we need open world? In other=20
   words, how often would a closed world assumption supporting logic
   good enough?

I hope you realize that a world assumed to be closed is the nonmonotonic
case, in other words, the harder case according to many web gurus.  By
their lights, your query is like asking, Do we really need to explore
the solar system?  Wouldn't exploring the galaxy be good enough?

However, I tend to agree with you.  Closed-world assumptions work quite
well in practice and are well understood.  It's the purely monotonic
case that's difficult.  

                                             -- Drew McDermott
                                                Yale University CS Dept.
Received on Friday, 14 November 2003 16:00:13 UTC

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