Within our introduction we mainly want to clarify the subject of Algorithmic Learning Theory. We focus our attention in partially answering of what machine learning is supposed to mean. Clearly, it would be nice to start with a general definition of learning, not necessarily done by machines. Unfortunately, there is no generally accepted definition of learning. Thus, finding out what learning really is must be considered as one of the major goals of all sciences that deal with learning.
Answering what machine learning is all about includes both developing mathematical models of machine learning and deriving results within the models developed. Both parts deserve special attention. In general, a model should capture at least significant applications. However, the state of the art in modeling learning is still much less satisfactory than in other areas of theoretical computer science.
For example, around 60 years ago computability theory emerged. Initially, many different models have been introduced, e.g., Turing machines, partial recursive functions, Markov algorithms, Church' lambda-calculus. Nevertheless, later on, all those models have been proved to be equivalent. Subsequently, researchers focused their attention to obtaining results within the model.
The situation in algorithmic learning theory is however, quite different. Numerous mathematical models of learning have been proposed during the last three decades. Nevertheless, different models give often vastly different results concerning the learnability and non-learnability of objects one wants to learn. Hence, finding an appropriate definition of learning which covers most aspects of learning is also part of the goals aimed at in algorithmic learning theory. Therefore we continue our introduction with a general approach explaining which aspects every learning model has to specify.