Using a Cognitive Architecture to Plan Dialogs for the Adaptive Explanation of Proofs

Abstract

In order to generate high quality expl anations in technical or mathematical domains , th e presentation must be adapted to the knowledge of th e intended audience. C urr e nt proof presentation systems only communicate proofs on a fixed degr ee of abstraction indepe nd ent ly of the addressee's knowledge. In this paper we propose an architecture for an interactive proof expl anation system, ca ll ed Prex . Based on the theory of human cognition ACT-R , its dialog plann er exploits a cognitive mod e l, in which both the user 's knowledge and his cognitive processes are mod eled. By this means , his cognitive states are traced during the explanation. Th e explicit represe ntation of the user 's cognitive states in ACT-R allows the dialog planner to choose a degr ee of abstraction tailored to the user for each proof step to be explained. Moreover, the system can rev is e its assumptions about the user's knowledge and react to his intera ct ions.