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From: jair-ed@ptolemy.arc.nasa.gov
Subject: New Article, Generalization of Clauses under ...
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Date: Thu, 21 Dec 1995 10:46:20 GMT
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JAIR is pleased to announce the publication of the following article:

Idestam-Almquist, P. (1995)
  "Generalization of Clauses under Implication", 
   Volume 3, pages 467-489.
   PostScript: volume3/idestam95a.ps (277K)
	       compressed, volume3/idestam95a.ps.Z (94K)


   Abstract: In the area of inductive learning, generalization is a main
   operation, and the usual definition of induction is based on logical
   implication.  Recently there has been a rising interest in clausal
   representation of knowledge in machine learning. Almost all inductive
   learning systems that perform generalization of clauses use the
   relation theta-subsumption instead of implication. The main reason is
   that there is a well-known and simple technique to compute least
   general generalizations under theta-subsumption, but not under
   implication.  However generalization under theta-subsumption is
   inappropriate for learning recursive clauses, which is a crucial
   problem since recursion is the basic program structure of logic
   programs.
   
   We note that implication between clauses is undecidable, and we
   therefore introduce a stronger form of implication, called
   T-implication, which is decidable between clauses. We show that for
   every finite set of clauses there exists a least general
   generalization under T-implication.  We describe a technique to reduce
   generalizations under implication of a clause to generalizations under
   theta-subsumption of what we call an expansion of the original
   clause. Moreover we show that for every non-tautological clause there
   exists a T-complete expansion, which means that every generalization
   under T-implication of the clause is reduced to a generalization under
   theta-subsumption of the expansion.

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