Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

25 Pages Posted: 18 Jul 2006

See all articles by Shan-Hwei Nienhuys-Cheng

Shan-Hwei Nienhuys-Cheng

Erasmus Research Institute of Management (ERIM)

Wim van Laer

Catholic University of Louvain (UCL)

Jan Ramon

Catholic University of Louvain (UCL)

Luc de Raedt

University of Freiburg

Date Written: 16 2000, 11

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, substitutions, refinement, learning, completeness

JEL Classification: M, M11, R4, C61

Suggested Citation

Nienhuys-Cheng, Shan-Hwei and van Laer, Wim and Ramon, Jan and de Raedt, Luc, Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms (16 2000, 11). ERIM Report Series Reference No. ERS-2000-39-LIS, Available at SSRN: https://ssrn.com/abstract=370849

Shan-Hwei Nienhuys-Cheng (Contact Author)

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Wim Van Laer

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

Jan Ramon

Catholic University of Louvain (UCL) ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

Luc De Raedt

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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