Generation and Use of Hints and Feedback in a Hilbert-Style Axiomatic Proof Tutor

Publication Information


  • Josje Lodder, Open University of the Netherlands
  • Bastiaan Heeren, Open Universiteit Nederland
  • Johan Jeuring, Utrecht University & Open Universieit Nederland
  • Wendy Neijenhuis, Open University of the Netherlands


  • 99-133


  • Propositional logic, Axiomatic proofs, Hilbert axiom system, Feedback, Intelligent tutoring


  • This paper describes LOGAX, an interactive tutoring tool that gives hints and feedback to a student who stepwise constructs a Hilbert-style axiomatic proof in propositional logic. LOGAX generates proofs to calculate hints and feedback. We compare these generated proofs with expert proofs 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. Even if a student diverges from the generated solution, LOGAX still provides hints, including next steps or reachable subgoals, and feedback. With a few improvements in the design of the set of buggy rules, LOGAX will cover about 80% of the mistakes made by students by buggy rules. The hints help students to complete the exercises.