Up to now it has been assumed that the epistemic use of modal auxiliaries such as must is entirely distinct from their deontic use, though the widespread association of the deontic with the epistemic in various languages suggests that they have a common semantic base. A consideration of practical examples of must in English shows that this base can be identified with the deontic notion of 'demand', which is closely related to 'desire' or 'will' (i.e. volition). may expresses the logically related notion of 'permission'. The basically deontic function of must and may is easily detectable in all their uses including the epistemic. The epistemic lies at the extremity of a deontic gradient which also affects associated rules of syntax such as those affecting the scope of not and the use of have + en. The performative analysis is untenable. The notion of 'demand' or 'will' is present in all the deontic-epistemic modals and in will and shall, and the main source of their varied interpretability is the presence of unspecified arguments in the deep structure. © 1982.
Tregidgo, P. S. (1982). Must and may: Demand and permission. Lingua, 56(1), 75–92. https://doi.org/10.1016/0024-3841(82)90051-1