Counting extensional differences in BC-learning

Abstract

Let BC be the model of behaviourally correct function learning as introduced by Bārzdins [Theory of Algorithms and Programs, vol. 1, Latvian State University, 1974, p. 82-88] and Case and Smith [Theoret. Comput. Sci. 25 (1983) 193-220]. We introduce a mind change hierarchy for BC, counting the number of extensional differences in the hypotheses of a learner. We compare the resulting models BC n to models from the literature and discuss confidence, team learning, and finitely defective hypotheses. Among other things, we prove that there is a trade-off between the number of semantic mind changes and the number of anomalies in the hypotheses. We also discuss consequences for language learning. In particular we show that, in contrast to the case of function learning, the family of classes that are confidently BC-learnable from text is not closed under finite unions. © 2003 Elsevier Inc. All rights reserved.