Forschungsberichte Mathematische Logik Learning via Queries and Oracles Universitt at Heidelberg Mathematisches Institut 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 (QEXXSucc], QEXX<] 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 can not overcome diierences between oracles and the query-inference degrees are a proper reenement of the EX-degrees. In the case of nite learning, the query-inference degrees coincide with the Turing-degrees. Furthermore oracles can not close the gap between the diierent types of queries to a teacher.