Presenting mathematical concepts as an example for inference-rich domains

Abstract

Presenting machine-stored information in human-adequate terms is a challenge in all kinds of domains and applications. Especially in inference-rich domains, this task proves to be difficult, because presentations directly reflecting the organization of the information stored in some knowledge or data base differ significantly from comparable presentations produced by human authors. Motivated by the associated discrepancies, we have developed presentation techniques for machine-stored information in inference-rich domains, and we have elaborated these techniques for mathematical concepts. The presentations obtained are fundamentally reorganized, compared to the uniform representation of domain objects, and they can be produced in varying forms, geared by evidence about the domain knowledge, inferential capabilities, and information intentions of the audience. These techniques prove relevant to assist the inspection of standardized information repositories, and they contribute significantly to the adaptation of interactive teaching material in formal, inference-rich domains.