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On the Inference of Natural Level Mappings

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Program Development in Computational Logic

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3049))

Abstract

Reasoning about termination is a key issue in logic program development. One classic technique for proving termination is to construct a well-founded order on goals that decreases between successive goals in a derivation. In practise, this is achieved with the aid of a level mapping that maps atoms to natural numbers. This paper examines why it can be difficult to base termination proofs on natural level mappings that directly relate to the recursive structure of the program. The notions of bounded-recurrency and bounded-acceptability are introduced to alleviate these problems. These concepts are equivalent to the classic notions of recurrency and acceptability respectively, yet provide practical criteria for constructing termination proofs in terms of natural level mappings for definite logic programs. Moreover, the construction is entirely modular in that termination conditions are derived in a bottom-up fashion by considering, in turn, each the strongly connected components of the program.

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Author information

Authors and Affiliations

  1. University of Kent, Canterbury, CT2 7NF, UK

    Jonathan C. Martin & Andy King

Authors
  1. Jonathan C. Martin
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  2. Andy King
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Editors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Belgium

    Maurice Bruynooghe

  2. School of Computer Science, The University of Manchester, M13 9PL, Manchester, United Kingdom

    Kung-Kiu Lau

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Martin, J.C., King, A. (2004). On the Inference of Natural Level Mappings. In: Bruynooghe, M., Lau, KK. (eds) Program Development in Computational Logic. Lecture Notes in Computer Science, vol 3049. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25951-0_13

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  • DOI: https://doi.org/10.1007/978-3-540-25951-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22152-4

  • Online ISBN: 978-3-540-25951-0

  • eBook Packages: Springer Book Archive

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