Inferring answers to queries

William I. Gasarch, Andrew C. Y. Lee
1997 Proceedings of the tenth annual conference on Computational learning theory - COLT '97  
One focus of inductive inference is to infer a program for a function f from observations or queries about f . We propose a new line of research which examines the question of inferring the answers to queries. For a given class of computable functions, we consider the learning (in the limit) of properties of these functions that can be captured by queries formulated in a logical language L. We study the inference types that arise in this context. Of particular interest is a comparison between
more » ... e learning of properties and the learning of programs. Our results suggest that these two types of learning are incomparable. In addition, our techniques can be used to prove a general lemma about query inference [W. Gasarch, C. Smith, Learning via queries, J. ACM 39 (1992) 649-676]. We show that I ⊂ J ⇒ QI(L) ⊂ QJ (L) for many standard inference types I, J and many query languages L. Hence any separation that holds between these inference types also holds between the corresponding query inference types. One interesting consequence is that [24, 49] QEX 0 [Succ, <] 2 − [2, 4] QEX 0 [Succ, <] 2 = ∅. Published by Elsevier Inc.
doi:10.1145/267460.267512 dblp:conf/colt/GasarchL97 fatcat:frsqw5fc3bbuxfi5ezxufdxgui