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Distances and Limits on Herbrand Interpretations
S-H. Nienhuys-Cheng.
In D. Page, editor, Proceedings of the 8th International Conference on
Inductive Logic Programming, volume 1446 of Lecture Notes in
Artificial Intelligence, pages 250--260. Springer-Verlag, 1998.
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 it does
not fit the notion of identification in the limit. We use a distance defined
by level mapping [5] to overcome this prolem, and study in particular the
mapping T_\Pi induce by a definite program \Pi on the metric space.
Continuity of T_\Pi holds under certain conditions, and we give a concrete
level mapping that satisfies these conditions, based on [10]. This allows us
to pove the existence of fixed points without using the Banach fixed point
theorem.
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S-H Nienhuys-Cheng,
cheng@few.eur.nl. Last modified on Wednesday 9 April 2003 at 18:31. © 2003 ILPnet2