As general purpose robots become more capable, pre-programming of all tasks at the factory will become less practical. We would like for non-technical human owners to be able to communicate, through interaction with their robot, the details of a new task; I call this interaction "task communication". During task communication the robot must infer the details of the task from unstructured human signals, and it must choose actions that facilitate this inference. In this dissertation I propose the use of a partially observable Markov decision process (POMDP) for representing the task communication problem; with the unobservable task details and unobservable intentions of the human teacher captured in the state, with all signals from the human represented as observations, and with the cost function chosen to penalize uncertainty. This dissertation presents the framework, works through an example of framing task communication as a POMDP, and presents results from a user experiment where subjects communicated a task to a POMDP-controlled virtual robot and to a human controlled virtual robot. The task communicated in the experiment consisted of a single object movement and the communication in the experiment was limited to binary approval signals from the teacher. This dissertation makes three contributions: 1) It frames human-robot task communication as a POMDP, a widely used framework. This enables the leveraging of techniques developed for other problems framed as a POMDP. 2) It provides an example of framing a task communication problem as a POMDP. 3) It validates the framework through results from a user experiment. The results suggest that the proposed POMDP framework produces robots that are robust to teacher error, that can accurately infer task details, and that are perceived to be intelligent. / Engineering and Applied Sciences