Epistemic Vs. Deontic Modality
Epistemic modals are used to indicate the possibility or necessity of some piece of knowledge. In the epistemic use, modals can be interpreted as indicating inference or some other process of reasoning involved in coming to the conclusion stated in the sentence containing the modal. However, epistemic modals do not necessarily require inference, reasoning, or evidence. One effect of using an epistemic modal (as opposed to not using one) is a general weakening of the speaker's commitment to the truth of the sentence containing the modal. However, it is disputed whether the function of modals is to indicate this weakening of commitment, or whether the weakening is a by-product of some other aspect of the modal's meaning.
Examples of the expression of epistemic modality in English are: he might be there (low probability, substantial doubt), He may be there (possibility), He should be there by now (high probability), and He must be there by now (very high probability, little doubt).
In contrast, deontic modality is concerned with possibility and necessity in terms of freedom to act (including ability, permission, and duty). English examples include She can go (ability), You may go (permission), You should go (obligation), and You must go (strong obligation). In English as in many other languages, some of the same words are used for deontic modality as for epistemic modality, and the meaning is distinguished from context: He must be there by now (epistemic) versus He must be there tomorrow at noon (deontic).