Re: Godel's Incompleteness and Nonmonotonic Logic

From: Stephan Lehmke (Stephan.Lehmke_at_ls1.cs.uni-dortmund.de)
Date: 08/23/04 

Date: 23 Aug 2004 09:54:47 GMT

In article <edc21089.0408201124.2850d5cb@posting.google.com>,
        hgtohybtml@mailinator.com (Student) writes:
> I have recently read a few papers, web pages, and parts of a text on
> nonmonotonic logic, Answer Set programming, and AnsProlog in
> particular. I find it interesting that nobody addresses the issue of
> Godel's incompleteness theorems because these "logics" force
> completeness by making any formula "A" or its negation "not A"
> provable.

Small confusion of two distinct concepts of "completeness" here.

What you're referring to here is what I know under the name "Hilbert
completeness", namely the property that for every (atomic? ground?)
Formula F, either F or -F is provable (from a given axiom system, as
generally this is clearly not the case for classical logics).

In fact, from my experience, this property doesn't play any important
role in logical considerations, as it is almost nerver fulfilled under
normal circumstances.

The only exception are, as you noticed, certain non-monotonic calculi
of the "closed world assumption" variety.

The incompleteness theorems of Goedel, however, refer to a completely
unrelated concept of completeness meaning "whatever follows is also
provable".

regards
Stephan 

-- 
  Stephan Lehmke     		 Stephan.Lehmke@cs.uni-dortmund.de
  Fachbereich Informatik, LS I	 Tel. +49 231 755 6434 
  Universitaet Dortmund		 FAX 		  6555
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