Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

Shan-Hwei Nienhuys-Cheng, W. van Laer, Jandry Ramon () and L. de Raedt

ERIM Report Series Research in Management from Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam

Abstract: Inductive Logic Programming considers almost exclusively universally quantied theories. To add expressiveness, prenex conjunctive normal forms (PCNF) with existential variables should also be considered. ILP mostly uses learning with refinement operators. To extend refinement operators to PCNF, we should first do so with substitutions. However, applying a classic substitution to a PCNF with existential variables, one often obtains a generalization rather than a specialization. In this article we define substitutions that specialize a given PCNF and a weakly complete downward refinement operator. Moreover, we analyze the complexities of this operator in different types of languages and search spaces. In this way we lay a foundation for learning systems on PCNF. Based on this operator, we have implemented a simple learning system PCL on some type of PCNF.

Keywords: PCNF; completeness; learning; refinement; substitutions (search for similar items in EconPapers)
JEL-codes: C61 M M11 R4 (search for similar items in EconPapers)
Date: 2000-11-16
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