This article presents a theoretical foundation for approaching the problem of how a learner can infer what a teacher wants it to do through strongly ambigu-ous interaction or observation. The article groups the in-terpretation of a broad range of information sources un-der the same theoretical framework. A teacher's motion demonstration, eye gaze during a reproduction attempt, pushes of "good"/"bad" buttons and speech comment are all treated as specific instances of the same general class of information sources. These sources all provide (partially and ambiguously) information about what the teacher wants the learner to do, and all need to be interpreted con-currently. We introduce a formalism to address this chal-lenge, which allows us to consider various strands of pre-vious research as different related facets of a single gener-alized problem. In turn, this allows us to identify impor-tant new avenues for research. To sketch these new direc-tions, several learning setups are introduced, and algorith-mic structures are introduced to illustrate some of the prac-tical problems that must be overcome.