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Least generalizations under implication

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Inductive Logic Programming (ILP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1314))

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Abstract

One of the most prominent approaches in Inductive Logic Programming is the use of least generalizations under subsumption of given clauses. However, subsumption is weaker than logical implication, and not very well suited for handling recursive clauses. Therefore an important open question in this area concerns the existence of least generalizations under implication (LGIs). Our main new result in this paper is the existence and computability of such an LGI for any finite set of clauses which contains at least one non-tautologous function-free clause. We can also define implication relative to background knowledge. In this case, least generalizations only exist in a very limited case.

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Authors and Affiliations

  1. Department of Computer Science, H4-19, Erasmus University of Rotterdam, P.O. Box 1738, 3000, DR Rotterdam, the Netherlands

    Shan-Hwei Nienhuys-Cheng & Ronald de Wolf

Authors
  1. Shan-Hwei Nienhuys-Cheng
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  2. Ronald de Wolf
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Stephen Muggleton

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© 1997 Springer-Verlag Berlin Heidelberg

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Nienhuys-Cheng, SH., de Wolf, R. (1997). Least generalizations under implication. In: Muggleton, S. (eds) Inductive Logic Programming. ILP 1996. Lecture Notes in Computer Science, vol 1314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63494-0_61

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  • DOI: https://doi.org/10.1007/3-540-63494-0_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63494-2

  • Online ISBN: 978-3-540-69583-7

  • eBook Packages: Springer Book Archive

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