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

Josje Lodder*, Bastiaan Heeren, Johan Jeuring, Wendy Neijenhuis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)99-133
Number of pages35
JournalInternational Journal of Artificial Intelligence in Education
Issue number1
Early online date6 Nov 2020
Publication statusPublished - Mar 2021


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


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