Learning via queries and oracles

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[<] and QEX[+]) together with membership qu...

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Bibliographic Details
Published in:Annals of pure and applied logic Vol. 94; no. 1; pp. 273 - 296
Main Author: Stephan, Frank
Format: Journal Article
Language:English
Published: Elsevier B.V 05.10.1998
Subjects:
Inductive inference
Logical queries
Oracles inference degrees
Turing degrees
Inductive inference
03D30
03D80
Oracles inference degrees
03D25
Logical queries
Turing degrees
ISSN:0168-0072
Online Access:Get full text
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Summary: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[<] and QEX[+]) together with membership queries to some oracle. 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, queries to a teacher cannot overcome differences between oracles and the query-inference degrees are a proper refinement of the EX-degrees. In the case of finite learning, the query-inference degrees coincide with the Turing degrees. Furthermore oracles can not close the gap between the different types of queries to a teacher.
ISSN:0168-0072
DOI:10.1016/S0168-0072(97)00077-8