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Curried least general generalization: A framework for higher order concept learning

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Learning and Reasoning with Complex Representations (PRICAI 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1359))

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Abstract

Continued progress with research in inductive logic programming relies on further extensions of their underlying logics. The standard tactics for extending expressivity include a generalization to higher order logics, which immediately forces attention to the computational complexity of higher order reasoning.

A major thread of inductive logic programming research has focussed on the identification of preferred hypothesis sets, initiated by Plotkin's work on least general generalizations (LGGs). Within higher order frameworks, a relevant extension of LGG is Furukawa's hyper least general generalization (HLGG) [FIG97].

We present a relevant higher order extension of Furukawa's HLGG based on currying, which we call Curried Least General Generalization (CLGG). The idea is that the formal difficulties with the reasoning complexity of a higher order language can be controlled by forming new hypothetical terms restricted to those obtainable by Currying. This technique subsumes the inductive generalization power of HLGG, provides a basis for a significant extension of first order ILP, and is theoretically justified within a well understood formal foundation.

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Author information

Authors and Affiliations

  1. Department of Computing Science, University of Alberta, T6G 2H1, Edmonton, Alberta, Canada

    Srinivas Padmanabhuni & Randy Goebel

  2. Graduate School of Media and Governance, Keio University, 5322 Endo, Fujisawa, 252, Kanagawa, Japan

    Koichi Furukawa

Authors
  1. Srinivas Padmanabhuni
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  2. Randy Goebel
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  3. Koichi Furukawa
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Editor information

Grigoris Antoniou Aditya K. Ghose Mirosław Truszczyński

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© 1998 Springer-Verlag Berlin Heidelberg

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Padmanabhuni, S., Goebel, R., Furukawa, K. (1998). Curried least general generalization: A framework for higher order concept learning. In: Antoniou, G., Ghose, A.K., Truszczyński, M. (eds) Learning and Reasoning with Complex Representations. PRICAI 1996. Lecture Notes in Computer Science, vol 1359. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-64413-X_27

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  • DOI: https://doi.org/10.1007/3-540-64413-X_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64413-2

  • Online ISBN: 978-3-540-69780-0

  • eBook Packages: Springer Book Archive

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