Communications of the ACM
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Crytographic limitations on learning Boolean formulae and finite automata
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Prediction-preserving reducibility
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Cryptographic lower bounds for learnability of Boolean functions on the uniform distribution
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Learnability of description logics
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
PAC-learnability of determinate logic programs
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Compiling prior knowledge into an explicit basis
ML92 Proceedings of the ninth international workshop on Machine learning
Learning Logical Definitions from Relations
Machine Learning
Some Lower Bounds for the Computational Complexity of Inductive Logic Programming
ECML '93 Proceedings of the European Conference on Machine Learning
Background Knowledge and Declarative Bias in Inductive Concept Learning
AII '92 Proceedings of the International Workshop on Analogical and Inductive Inference
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An active area of research in machine learning is learning logic programs from examples. This paper investigates formally the problem of learning a single Horn clause: we focus on generalizations of the language of constant-depth determinate clauses, which is used by several practical learning systems. We show first that determinate clauses of logarithmic depth are not learnable. Next we show that learning indeterminate clauses with at most k indeterminate variables is equivalent to learning DNF. Finally, we show that recursive constant-depth determinate clauses are not learnable. Our primary technical tool is the method of predictionpreserving reducibilities introduced by Pitt and Warmuth [1990]; as a consequence our results are independent of the representations used by the learning system.