This paper presents a model for how people ask goal-oriented questions and update their beliefs from answers. They work in the context of a battleship game, where the set of questions that a person can ask are pre-defined, as are the answers (e.g. the color on a given board cell, or whether the ship of a given color is horizontal or vertical). The hypothesis space $\mathcal{H}$ of boards is bounded ($\approx 1.6 million$), so it's feasible to have an oracle that answers questions deterministically.
The novelty in this paper is considering that questions are asked with a goal in mind, not to figure out the state of the board. A goal defines a projection of the board space. For example, the goal of "finding out which ships are touching the left border" corresponds to the power set of ships: the possible answers for the target question. Each such answer is associated with a set of boards for which that answer is true.
Under this modelling, you can be Bayesian and maximize expected information gain to reduce uncertainty for the particular goal in mind. The user computes the probability of a certain answer by using a uniform prior over all boards for which the answer would be consistent. This model seems to explain people's behavior quite well. The model's scores correlates strongly ($r = 0.84$) with people's performance. If the goal is inverted for the model, its performance correlates negatively ($r = -0.14$) with the person's performance (with flipped goals), showing that the goal is in fact a very significant component of this question-asking procedure. It also predicts well the follow-up questions a person asks.
This is an interesting scenario that can be used to model how people pick questions when they have a goal in mind. It turns out that the intuitive explanations work in practice. An extra challenge for building systems that interact with people is, of course, how to formulate questions and interpret free-form answers, and how to work with massive or unbounded hypothesis spaces (e.g. natural language answers), which are out of the scope of the proposed model, but remain as practical challenges.