Coming up with a good question is not easy: A proof

Abstract

Abstract-Ability to ask good questions is an important part of learning skills. Coming up with a good question, a question that can really improve one's understanding of the topic, is not easy. In this paper, we prove -on the example of probabilistic and fuzzy uncertainty -that the problem of selecting of a good question is indeed hard. I. FORMULATION OF THE PROBLEMAsking good questions is important. Even after a very good lecture, some parts of the material remain not perfectly clear. A natural way to clarify these parts is to ask questions to the lecturer.Ideally, we should be able to ask a question that immediately clarifies the desired part of the material. Coming up with such good questions is an important part of learning process, it is a skill that takes a long time to master.Coming up with good questions is not easy: an empirical fact. Even for experienced people, it is not easy to come up with a good question, i.e., with a question that will maximally decrease uncertainty.What we do in this paper. In this paper, we prove that the problem of designing a good question is indeed computationally difficult (NP-hard).We will show this both for probabilistic and for fuzzy uncertainty. Specifically, we will prove NP-hardness for the simplest types of questions -for "yes"-"no" questions for which the answer is "yes" or "no". Since already designing such simple questions is NP-hard, any more general problem (allowing more complex problems) is NP-hard as well. II. TOWARDS DESCRIBING THE PROBLEM IN PRECISETERMS: GENERAL CASE