Abstract
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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© 1998 Springer-Verlag Berlin Heidelberg
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Nienhuys-Cheng, SH. (1998). Distances and limits on Herbrand interpretations. In: Page, D. (eds) Inductive Logic Programming. ILP 1998. Lecture Notes in Computer Science, vol 1446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027329
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DOI: https://doi.org/10.1007/BFb0027329
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