Some cognitively-motivated learning paradigms in algorithmic learning theory

This thesis pertains to the field of Gold-style Algorithmic Learning Theory. We present results on three classes of learning paradigms motivated by Cognitive Science. Chapter 2 investigates the necessity---for full learning power---of U-shaped learning (i.e., semantically returning to a previously abandoned correct conjecture) in the context of Vacillatory Learning (when the learner stabilizes in the limit to up to a finite number of correct conjectures). These results are joint work with John Case, Sanjay Jain and Frank Stephan. Chapter 3 answers the question of the necessity---for full learning power---of returning to previously abandoned wrong conjectures during the learning process. A complete answer to this question is given for four variants of the latter concept and with respect to the most prominent learning paradigms: Explanatory, Behaviourally Correct and Vacillatory Learning. These results are joint work with Sanjay Jain, Efim Kinber and Frank Stephan. Chapter 4 presents results on a new learning paradigm, learning correction grammars. This paradigm explores the possibility that the description of the language that a learner uses is not in terms of a single grammar but, instead, in terms of a set of grammars, each one used to edit corrections to the previous ones. We extend this concept into the transfinite and prove a general Hierarchy Result. These results are joint work with John Case and Sanjay Jain.