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RE: Merging Rulesets

From: Gerd Wagner <wagnerg@tu-cottbus.de>
Date: Mon, 29 Aug 2005 23:28:15 +0200
To: "'Sandro Hawke'" <sandro@w3.org>
Cc: <public-rule-workshop-discuss@w3.org>
Message-Id: <20050829212941.823A05081F7@smtp2.TU-Cottbus.De>

> Can you give me a simple example of where you can't merge FOL like
> this, to help me understand the problem (and explain it to others)?
> It seems obvious that FOL merges (I guess it follows from
> And-Introduction [1]), although perhaps there's a subtlety that I'm
> missing?
> 
> Maybe you can phrase it in terms of scenario #2, where several
> organizations are publishing knowledge about drug interactions.  Each
> of them publishes a view of their KB, using a shared ontology.  It
> seems to me that the only time adding another source would cast doubt
> on conclusions derived from conjoining previous sources would be if a
> contradiction arose when the new KB was conjoined.  Does the seeming
> need for non-monotonicity perhaps parallel the need for dealing with
> such possible logical inconsistencies?  

Yes, indeed, handling/resolving inconsistencies does typically
create non-monotonicity when you merge knowledge items such as
rules. Notice that in classical FOL this issue is simply avoided
by the unrealistic principle "ex contradictione sequitur quodlibet"
(or "Law of the Excluded Contradiction"), according to which the
entire KB is meaningless as soon as a single contradiction arises
somewhere in it (which is OK for mathematical logic but not for 
practical knowledge systems).

When you merge rule sets from different (cognitive agent) sources 
you must take into account that there may be inconsistencies in 
the merge result, but they do not invalidate all rules in the merge 
set. Only when you merge rule sets from the same agent, you may 
assume that this agent is sensible enough to avoid any inconsistency.
So, the requiremement for merging rule sets implies nonmonotonicity.

Notice that in an empirical domain such as the "Validating 
Prescriptions" scenario of the charter draft, you will typically
have to reason with positive and negative evidence. And you are
not only interested in drawing 100% safe/monotonic conclusions
(which may mean no conclusion at all in certain cases) but you 
are rather interested in drawing informed (but possibly 
unsafe/nonmonotonic) conclusions that allow you to act 
rationally, simply because not acting at all may also kill 
people.

Coming back to your scenario, I think it's realistic to
have the following kinds of rules:

a) pimozide is contraindicated with macrolides according to a 
   1996 FDA bulletin 

b) pimozide is safe in conjunction with macrolides for men
   over 60 according to a 1999 FDA bulletin

Then b would logically contradict a, and we would need
a nonmonotonic conflict resolution procedure such as
giving higher priority to more specific and/or more 
recent pieces of knowledge.

-Gerd
Received on Monday, 29 August 2005 21:29:46 GMT

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