Learning via queries

The power of various query languages is compared along two dimensions, namely the inherent power of the language and the number of alternations of quantizers. Learning by asking questions is compared to learning by passively reading data. It is found that the extent of what can be learned by queries is largely dependent on the language used by the inference mechanism to formulate questions to ask of its trainer. It is proved that inference machines that are allowed to ask first-order questions with plus and times can be used to solve the halting problem and therefore can learn all the recursive functions. Learning languages are also considered.<>