Conversational implicatures are usually described as being licensed by the disobeying or flouting of some principle by the speaker in cooperative dialogue. However, such work has failed to distinguish cases of the speaker flouting such a principle from cases where the speaker is either deceptive or holds a mistaken belief. In this paper, we demonstrate how the three different cases can be distinguished in terms of the beliefs ascribed to the speaker of the utterance. We argue that in the act of distinguishing the speaker's intention and ascribing such beliefs, the intended inference can be made by the hearer. This theory is implemented in ViewGen, a pre-existing belief modelling system used in a medical counselling domain.