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Mind Change Complexity of Learning Logic Programs

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Computational Learning Theory (EuroCOLT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1572))

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Abstract

The present paper motivates the study of mind change complexity for learning minimal models of length-bounded logic programs. It establishes ordinal mind change complexity bounds for learnability of these classes both from positive facts and from positive and negative facts.

Building on Angluin’s notion of finite thickness and Wright’s work on finite elasticity, Shinohara defined the property of bounded finite thickness to give a sufficient condition for learnability of indexed families of computable languages from positive data. This paper shows that an effective version of Shinohara’s notion of bounded finite thickness gives sufficient conditions for learnability with ordinal mind change bound, both in the context of learnability from positive data and for learnability from complete (both positive and negative) data.

More precisely, it is shown that if a language defining framework yields a uniformly decidable family of languages and has effective bounded finite thickness, then for each natural number m > 0, the class of languages defined by formal systems of length ≤ m:

  • is identifiable in the limit from positive data with a mind change bound of ωm;

  • is identifiable in the limit from both positive and negative data with an ordinal mind change bound of ω × m.

The above sufficient conditions are employed to give an ordinal mind change bound for learnability of minimal models of various classes of length-bounded Prolog programs, including Shapiro’s linear programs, Arimura and Shinohara’s depth-bounded linearly-covering programs, and Krishna Rao’s depth-bounded linearly-moded programs. It is also noted that the bound for learning from positive data is tight for the example classes considered.

The research of Arun Sharma is supported by Australian Research Council Grant A49803051.

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Author information

Authors and Affiliations

  1. School of Computing, National University of Singapore, Singapore, 119260, Republic of Singapore

    Sanjay Jain

  2. School of Computer Science and Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Arun Sharma

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  1. Sanjay Jain
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Informatik II, Universität Dortmund, D-44221, Dortmund, Germany

    Paul Fischer

  2. Fakultät für Mathematik, Ruhr Universität Bochum, D-44780, Bochum, Germany

    Hans Ulrich Simon

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Jain, S., Sharma, A. (1999). Mind Change Complexity of Learning Logic Programs. In: Fischer, P., Simon, H.U. (eds) Computational Learning Theory. EuroCOLT 1999. Lecture Notes in Computer Science(), vol 1572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49097-3_16

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  • DOI: https://doi.org/10.1007/3-540-49097-3_16

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  • Print ISBN: 978-3-540-65701-9

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