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Consistent term mappings, term partitions, and inverse resolution

  • Shan Hwei Nienhuys-Cheng
  • Peter A. Flach
Part 5: Inversion Of Resolution
Part of the Lecture Notes in Computer Science book series (LNCS, volume 482)

Abstract

We formalize the notion of inverse substitution, used in the context of inverse resolution, by means of consistent term mappings. An inverse substitution from a clause to a more general clause can also be characterized by means of a term partition. We can generate clauses more general than a given clause by taking an admissible subset of its term occurrences, and constructing a term partition of this subset. We show that these term partitions can be partially ordered. This ordering coincides with the generality of the induced clauses. Similar partitions have been used by Muggleton and Buntine for describing their absorption operator. We show that their absorption algorithm is incomplete, and we give an alternative, complete algorithm, based on our definitions of admissible subset and term partition. We show that under certain conditions, clauses generated by absorption are incomparable with respect to generality. Finally, we relate this to a recent result about least general absorption obtained by Muggleton.

Keywords

Inverse resolution absorption substitution 

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References

  1. Stephen Muggleton. Inductive Logic Programming. First Conference on Algorithmic Learning Theory, Ohmsha, Tokyo, October 1990.Google Scholar
  2. Stephen Muggleton & Wray Buntine. Machine Invention of First-order Predicates by Inverting Resolution. Proceedings of the 5th International Conference on Machine Learning, Morgan Kaufmann, pp. 339–351, 1988.Google Scholar
  3. Shan-Hwei Nienhuys-Cheng. Consequent Functions and Inverse Resolutions. Report Eur-CS-90-03, Erasmus University, Rotterdam, Netherlands, May 1990.Google Scholar
  4. Shan-Hwei Nienhuys-Cheng, Term Partitions and Minimal Generalizations of Clauses. Report, Erasmus University, Rotterdam, Netherlands, 1991.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Shan Hwei Nienhuys-Cheng
    • 1
  • Peter A. Flach
    • 2
  1. 1.Erasmus UniversityRotterdamNetherlands
  2. 2.Tilburg UniversityTilburgNetherlands

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