Mathematical domain reasoning tasks in natural language tutorial dialog on proofs

We study challenges that are imposed to mathematical domain reasoning in the context of natural language tutorial dialog on mathematical proofs. The focus is on proof step evaluation: (i) How can mathematical domain reasoning support the resolution of ambiguities and underspecified parts in proof steps uttered by a student? (ii) How can mathematical domain reasoning support the evaluation of a proof step with respect to the criteria soundness, granularity, and relevance?