NDLI: Numberings and learnability

Content Provider	Springer Nature Link
Author	Ambos Spies, K.
Copyright Year	2014
Abstract	For a computable family A of computably enumerable sets there are two properties that indicate that the sets in A can be sufficiently easily distinguished: first, learnability of the class A where two models of learning may be considered, explanatory learning (EX) and behaviorally correct learning (BC); and, second, equivalence of all computable numberings of the family A under computable functions (computable equivalence) or under functions computable relative to the halting problem (∅′-equivalence). Ambos-Spies, Badaev and Goncharov (2011) have studied the relations among these properties. They have shown that EX-learnability of A implies that all computable numberings of A are ∅′-equivalent but that the converse is not true in general, and that the properties of BC-learnability of A and of ∅′-equivalence of the computable numberings of A are independent. They left open the question whether there is a computable family A of c.e. sets such that all computable numberings of A are computably equivalent and A is not BC-learnable. Such a family has been recently constructed by Ambos-Spies and Badaev. The above results are presented in this paper.
Starting Page	302
Ending Page	303
Page Count	2
File Format	PDF
ISSN	19950802
Journal	Lobachevskii Journal of Mathematics
Volume Number	35
Issue Number	4
e-ISSN	18189962
Language	English
Publisher	Pleiades Publishing
Publisher Date	2014-12-04
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computably enumerable sets Computable numberings Inductive inference Mathematics Algebra Analysis Geometry Mathematical Logic and Foundations Probability Theory and Stochastic Processes
Content Type	Text
Resource Type	Article
Subject	Mathematics

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