Communications of the ACM
Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Learning via queries to an oracle
COLT '89 Proceedings of the second annual workshop on Computational learning theory
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Journal of the ACM (JACM)
Machine Learning
Machine Learning
On the structure of degrees of inferability
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
On the amount of nonconstructivity in learning recursive functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
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Most theories of learning consider inferring a functionf from either (1) observations aboutf or, (2) questions aboutf. We consider a scenario whereby thelearner observes f and asks queriesto some set A.EX[A] is the set of concept classesEX-learnable by an inductiveinference machine with oracle A.A andF areEX-equivalent ifEX[A] = EX[B]. The equivalenceclasses induced are the degrees ofinferability. We prove several results about thesedegrees: (1) There are an uncountable number of degrees. (2) ForA r.e., REC &egr; BC[A] iff &0slash;&huml; ≤TA´, and there is evidence thisholds for all sets A. (3) ForA, B r.e.,A ≡T BiffEX[A] = EX[B]. (4) There existsA, B low2 r.e.,A|RB,EX[A] = EX[B]. (hence (3) isoptimal).