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.

An Extensible Domain-Specific Language for Describing Problem-Solving Procedures

“…We have exemplified the DSL approach and its feasibility by describing three tutors for di↵erent task domains that are based on this language. Other domains for which the DSL was used are proposition logic, logical equivalence, axiomatic proofs [15], evaluating expressions, and microcontroller programming. The DSL provides an explicit representation for problem-solving procedures, which is missing in other ITS paradigms.…”

Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction

“…This section describes LogInd, a tool that supports students with constructing inductive proofs. Experience with other intelligent tutoring systems for logic (LogEx for rewriting propositional formulae [19], and LogAx for Hilbert-style axiomatic proofs [18]) shows that students benefit from a system where they can enter solutions stepwise, get feedback after each step, and can ask for a hint or next step at any moment, or receive a worked-out solution. The possibility to add proof steps both backwards and forwards in these systems resembles the way an exercise is solved with pen and paper.…”