Mathematical learning theory: a formalized, axiomatic, abstract approach

Abstract Completion, Formalized

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new and formalized correctness proofs of abstract completion, both for finite and infinite runs. For the special case of ground completion we present a new proof based on random descent. We moreover extend the results to ordered completion, an impor...

A Mathematical Theory of Learning

In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik’s General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis in response to a given training set. Such hypothesis can, for example, be a decision boundary in classification, a set of centroids in clustering, or a set o...

A mathematical theory of learning

Discussions of the role of mathematics in cognition typically emphasize the application of discrete logic to internal symbolic representations. The traditional assumption is that learning is something like the application of induction to nd patterns or regularities within those representations. In this article the focus is moved back to the world that we cognize. Using results from continuous m...

Quantum Theory. A Mathematical Approach

Mathematical Learning Theory