Journal of Symbolic Logic

Anomalous Vacillatory Learning

Achilles A. Beros

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In 1986, Osherson, Stob and Weinstein asked whether two variants of anomalous vacillatory learning, TxtFex$^*_*$ and TxtFext$^*_*$, could be distinguished [3]. In both, a machine is permitted to vacillate between a finite number of hypotheses and to make a finite number of errors. TxtFext$^*_*$-learning requires that hypotheses output infinitely often must describe the same finite variant of the correct set, while TxtFex$^*_*$-learning permits the learner to vacillate between finitely many different finite variants of the correct set. In this paper we show that TxtFex$^*_*$ $\neq$ TxtFext$^*_*$, thereby answering the question posed by Osherson, et al. We prove this in a strong way by exhibiting a family in TxtFex$^*_2 \setminus \mbox{TxtFext}^*_*$.

Article information

J. Symbolic Logic Volume 78, Issue 4 (2013), 1183-1188.

First available in Project Euclid: 5 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Inductive Inference Learning Theory Vacillatory Learning


Beros, Achilles A. Anomalous Vacillatory Learning. J. Symbolic Logic 78 (2013), no. 4, 1183--1188. doi:10.2178/jsl.7804090.

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