Equivalences of logic programs
Foundations of deductive databases and logic programming
Foundations of deductive databases and logic programming
Logic programs with classical negation
Logic programming
Machine Learning - special issue on inductive logic programming
Logical settings for concept-learning
Artificial Intelligence
Strongly equivalent logic programs
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part I
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part I
Equivalence in Answer Set Programming
LOPSTR '01 Selected papers from the 11th International Workshop on Logic Based Program Synthesis and Transformation
ILP '01 Proceedings of the 11th International Conference on Inductive Logic Programming
On Indefinite Databases and the Closed World Assumption
Proceedings of the 6th Conference on Automated Deduction
Which Hypotheses Can Be Found with Inverse Entailment?
ILP '97 Proceedings of the 7th International Workshop on Inductive Logic Programming
Induction as Consequence Finding
Machine Learning
Induction from answer sets in nonmonotonic logic programs
ACM Transactions on Computational Logic (TOCL)
Equivalence in abductive logic
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
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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.