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Inductive Equivalence of Logic Programs

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Chiaki Sakama and Katsumi Inoue

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Proceedings of the 15th International Conference on
Inductive Logic Programming (ILP'05),
Lecture Notes in Artificial Intelligence 3625,
pages 312-329, Springer-Verlag, 2005.
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## Abstract

This paper studies equivalence issues in inductive logic programming.
A background theory B1 is *inductively equivalent*
to another background theory B2 if B1 and B2 induce the same hypotheses
for any given set of examples.
Inductive equivalence is useful to compare inductive capabilities among agents
having different background theories.
Moreover, it provides conditions for
optimizing background theories through appropriate program transformations.
In this paper, we consider three different classes of background theories:
clausal theories, Horn logic programs, and nonmonotonic extended logic programs.
We show that logical equivalence is the necessary and sufficient
condition for inductive equivalence
in clausal theories and Horn logic programs.
In nonmonotonic extended logic programs, on the other hand,
*strong equivalence* is
necessary and sufficient for inductive equivalence in general.
Interestingly, however, we observe that
several existing induction algorithms require weaker conditions of
equivalence under restricted problem settings.
We also discuss connection to equivalence in abductive logic
and conclude that the notion of strong equivalence is useful to
characterize equivalence of non-deductive reasoning.

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