Generalization of Clauses under Implication

نویسنده

  • Peter Idestam-Almquist
چکیده

In the area of inductive learning, generalization is a main operation, and the usual deenition 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-subsumption instead of implication. The main reason is that there is a well-known and simple technique to compute least general generalizations under-subsumption, but not under implication. However generalization under-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 nite 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-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-subsumption of the expansion.

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عنوان ژورنال:
  • J. Artif. Intell. Res.

دوره 3  شماره 

صفحات  -

تاریخ انتشار 1995