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From: minton@ptolemy.arc.nasa.gov
Subject: New Article, Random Worlds and Maximum Entropy
Message-ID: <1994Aug22.192915.6266@ptolemy-ethernet.arc.nasa.gov>
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Date: Mon, 22 Aug 1994 19:29:15 GMT
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JAIR is pleased to announce publication of the following article:

Grove, A.J., Halpern, J.Y. and Koller, D. (1994)
  "Random Worlds and Maximum Entropy", Volume 2, pages 33-88.
   Postscript: volume2/grove94a.ps (624K)
	       compressed, volume2/grove94a.ps.Z (243K)

   Abstract: Given a knowledge base KB containing first-order and
   statistical facts, we consider a principled method, called the
   random-worlds method, for computing a degree of belief that some
   formula Phi holds given KB.  If we are reasoning about a world or
   system consisting of N individuals, then we can consider all possible
   worlds, or first-order models, with domain {1,...,N} that satisfy KB,
   and compute the fraction of them in which Phi is true. We define the
   degree of belief to be the asymptotic value of this fraction as N
   grows large.  We show that when the vocabulary underlying Phi and KB
   uses constants and unary predicates only, we can naturally associate
   an entropy with each world. As N grows larger, there are many more
   worlds with higher entropy.  Therefore, we can use a maximum-entropy
   computation to compute the degree of belief.  This result is in a
   similar spirit to previous work in physics and artificial
   intelligence, but is far more general.  Of equal interest to the
   result itself are the limitations on its scope.  Most importantly, the
   restriction to unary predicates seems necessary.  Although the
   random-worlds method makes sense in general, the connection to maximum
   entropy seems to disappear in the non-unary case.  These observations
   suggest unexpected limitations to the applicability of maximum-entropy 
   methods.

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