Generating hints and feedback for Hilbert-style axiomatic proofs

Abstract

This paper describes an algorithm to generate Hilbert-style axiomatic proofs. Based on this algorithm we develop logax, a new interactive tutoring tool that provides hints and feedback to a student who stepwise constructs an axiomatic proof. We compare the generated proofs with expert and student solutions, and conclude that the quality of the generated proofs is comparable to that of expert proofs. logax recognizes most steps that students take when constructing a proof. If a student diverges from the generated solution, logax can still provide hints and feedback.