Re: Why must the web be monotonic ?

> 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.

Well, this is the usual trick of using a monotonic logic to encode a
theory (i.e., a KB) from a nonmonotonic logic. However, the original
logic *remains* nonmonotonic, otherwise the encoding would be
incorrect. So, if the original theory is nonmonotonic, then it stays
nonmonotonic. That is, if I infer something on the ground that there
is no patient (just because I did not find any record), then when a
new patient is inserted the original inference becomes invalid. The
crucial point is that the encoding of the first theory (the one
without any patient) is NOT included in the encoding of the second
theory (the one with a patient). So, the deductive closure of the
first theory is not included in the deductive closure of the second
theory: you loose exactly the inferences that came form the assumption
that no explicit record means no existing record.

So, your observation should be read as follows: a monotonic logic can
be used to reason with a fixed KB which is (contextually)
nonmonotonic; at each update of the nonmonotonic KB, we should
nonmonotonically change the encoding in the monotonic logic. The
overall reasoning remains nonmonotonic.

> Right now, DAML+OIL and RDF have not entered into this area, but 
> 'rules' languages need to consider it seriously, in my view.

It is quite interesting to notice that the closed world assumption
(together with the domain closure assumption, which is also important)
can be encoded in standard Description Logics, if nominals with the
Unique Name Assumption are expressible. I know little of DAML+OIL, but
I believe that it can express nominals with UNA.

cheers
-- e.

Enrico Franconi                     - franconi@cs.man.ac.uk
University of Manchester            - http://www.cs.man.ac.uk/~franconi/
Department of Computer Science      - Phone: +44 (161) 275 6170
Manchester M13 9PL, UK              - Fax:   +44 (161) 275 6204

Received on Wednesday, 25 July 2001 02:17:52 UTC