Information Processing Letters
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Journal of Computer and System Sciences
Generalized teaching dimensions and the query complexity of learning
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
How many queries are needed to learn?
Journal of the ACM (JACM)
Logical settings for concept-learning
Artificial Intelligence
Learning Function-Free Horn Expressions
Machine Learning - The Eleventh Annual Conference on computational Learning Theory
Algorithmic Program DeBugging
Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Learning closed horn expressions
Information and Computation
Learning Logical Definitions from Relations
Machine Learning
Machine Learning
Machine Learning
Ideal Theory Refinement under Object Identity
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Learning Acyclic First-Order Horn Sentences from Entailment
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
ALT '01 Proceedings of the 12th International Conference on Algorithmic Learning Theory
Learning Horn Definitions with Equivalence and Membership Queries
ILP '97 Proceedings of the 7th International Workshop on Inductive Logic Programming
Learning First-Order Acyclic Horn Programs from Entailment
ILP '98 Proceedings of the 8th International Workshop on Inductive Logic Programming
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The paper identifies several new properties of the lattice induced by the subsumption relation over first-order clauses and derives implications of these for learnability. In particular, it is shown that the length of subsumption chains of function free clauses with bounded size can be exponential in the size. This suggests that simple algorithmic approaches that rely on repeating minimal subsumption-based refinements may require a long time to converge. It is also shown that with bounded size clauses the subsumption lattice has a large branching factor. This is used to show that the class of first-order length-bounded monotone clauses is not properly learnable from membership queries alone. Finally, the paper studies pairing, a generalization operation that takes two clauses and returns a number of possible generalizations. It is shown that there are clauses with an exponential number of pairing results which are not related to each other by subsumption. This is used to show that recent pairing-based algorithms can make exponentially many queries on some learning problems.