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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… (More)

In this paper we present a framework for automated learning within mathematical reasoning systems. In particular, this framework 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 framework consists of a representation formalism for… (More)

We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to provide a full proof of correctness of the answer. To guarantee… (More)

In this contribution we address two related questions. Firstly, we want to shed light on the question how to use a representation formalism to represent a given problem. Secondly, we want to find out how different formalizations are related and in particular how it is possible to check that one formalization entails another. The latter question is a tough… (More)