When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user- and goal-adaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation that exploits machine learning techniques to extract a model of the specific granularity of proof examples and employs this model for the automated generation of further proofs at an adapted level of granularity.

Learning and reasoning are both aspects of what is considered to be intelligence. Their studies within AI have been separated historically, learning being the topic of machine learning and neural networks, and reasoning falling under classical (or symbolic) AI. However, learning and reasoning are in many ways interdependent. This paper discusses the nature of some of these interdependencies and proposes a general framework called FLARE, that combines inductive learning using prior knowledge together with reasoning in a propositional setting. Several examples that test the framework are presented, including classical induction, many important reasoning protocols and two simple expert systems.