ABSTRACT
In this chapter, the authors formally define many variants of inferring a class of functions. They emphasize those variants where the learner can ask questions as well as see data. The authors also emphasis the types of mathematical techniques used in proofs. They include proof sketches but very few actual proofs. The term ‘proof sketch’ is somewhat ambiguous; however, suffice it to say that some of sketches are are sketchier than others. The authors use standard notation from recursion theory and review concepts from inductive inference. Inductive inference has revealed many intuitions concerning machine learning by example. Inductive inference has also served as a rich application area for recursion theory and many other subareas of mathematical logic. The authors surveyed the area of learning via queries to highlight since this shows off many of these areas.
