In this paper, we propose and consider the problem of cooperative language acquisition as a particular form of the ad hoc team play problem. We then present a probabilistic model for inferring a speaker's intentions and a listener's semantics from observing communications between a team of language-users. This model builds on the assumptions that speakers are engaged in positive signalling and listeners are exhibiting positive listening, which is to say the messages convey hidden information from the listener, that then causes them to change their behaviour. Further, it accounts for potential sub-optimality in the speaker's ability to convey the right information (according to the given task). Finally, we discuss further work for testing and developing this framework.