Automatic Learning of Proof Methods in Proof Planning

In this paper we present an approach to automated learning within mathematical reasoning systems. In particular, the approach enables proof planning systems to automatically learn new proof methods from well-chosen examples of proofs which use a similar reasoning pattern to prove related theorems. Our approach consists of an abstract representation for methods and a machine learning technique which can learn methods using this representation formalism. We present an implementation of the approach within the Ωmega proof planning system, which we call LearnΩmatic. We also present the results of the experiments that we ran on this implementation in order to evaluate if and how it improves the power of proof planning systems.