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  1. Learning via queries and oracles.Frank Stephan - 1998 - Annals of Pure and Applied Logic 94 (1-3):273-296.
    Inductive inference considers two types of queries: Queries to a teacher about the function to be learned and queries to a non-recursive oracle. This paper combines these two types — it considers three basic models of queries to a teacher (QEX[Succ], QEX[ The results for each of these three models of query-inference are the same: If an oracle is omniscient for query-inference then it is already omniscient for EX. There is an oracle of trivial EX-degree, which allows nontrivial query-inference. Furthermore, (...)
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  • Extremes in the degrees of inferability.Lance Fortnow, William Gasarch, Sanjay Jain, Efim Kinber, Martin Kummer, Stuart Kurtz, Mark Pleszkovich, Theodore Slaman, Robert Solovay & Frank Stephan - 1994 - Annals of Pure and Applied Logic 66 (3):231-276.
    Most theories of learning consider inferring a function f from either observations about f or, questions about f. We consider a scenario whereby the learner observes f and asks queries to some set A. If I is a notion of learning then I[A] is the set of concept classes I-learnable by an inductive inference machine with oracle A. A and B are I-equivalent if I[A] = I[B]. The equivalence classes induced are the degrees of inferability. We prove several results about (...)
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