Distances and limits on Herbrand interpretations

  • Shan-Hwei Nienhuys-Cheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1446)


A notion of distances between Herbrand interpretations enables us to measure how good a certain program, learned from examples, approximates some target program. The distance introduced in [10] has the disadvantage that it does not fit the notion of “identification in the limit”. We use a distance defined by a level mapping [5] to overcome this problem, and study in particular the mapping TII induced by a definite program 11 on the metric space. Continuity of TII holds under certain conditions, and we give a concrete level mapping that satisfies these conditions, based on [10]. This allows us to prove the existence of fixed points without using the Banach Fixed Point Theorem.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Shan-Hwei Nienhuys-Cheng
    • 1
    • 2
  1. 1.Department of Computer ScienceKatholieke Universiteit LeuvenLeuven
  2. 2.Erasmus Unniversiteit RotterdamRotterdam

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