Natural language contains a variety of means for expressing possibilities consistent with what is known. Particularly well-studied among them are the epistemic modal auxiliaries "might" and "must": (1) a. Ann: "Where is Peter?" b. Mary: "He {might/must} be in his office." There is broad agreement that "might" and "must" relate a body of premises -- things that are known and/or assumed by the relevant agent -- to a conclusion (e.g., in 1b, the proposition expressed by "Peter is in his office," the 'prejacent' of the modal). "Might" conveys more uncertainty than does "must"; that is, "might" expresses a comparatively weaker link between the premises and the conclusion expressed within the prejacent. This dissertation follows Roberts (2023) in "assum[ing] a central thesis about modal auxiliaries due to Angelika Kratzer" (Roberts, 2023: 1219): (2) THE MODAL BASE PRESUPPOSITION: Natural language expressions that contain a modal component in their meaning, including all English modal auxiliaries and EMAs [epistemic modal auxiliaries] in particular, presuppose a modal base, a function that draws from context a relevant set of propositions which contribute to a premise-semantics for the modal (Roberts, 2023: 1220). Roberts (2023) notes that among theorists who generally assume (2), there are live matters of theoretical debate, including disagreement over how to answer the following two questions: 1. What constraints, if any, are there on the character of the premise set for an EMA [epistemic modal auxiliary], and how can this be reliably retrieved in the context of utterance? (Roberts, 2023: 1220). 2. What is the nature of the relationship between premises and conclusion that is required for truth of the EMA statement? (ibid). This dissertation addresses Roberts' questions for the epistemic modal auxiliaries and for a range of other epistemic modal operators. The formal machinery of probability theory plays a central role in this work in two main respects: Probabilistic semantics for epistemic modals: Probability theory -- in particular, Bayesian probability theory -- provides a formal characterization of how a rational agent updates their beliefs under persistent uncertainty via observation of data ('evidence') which speaks for/against the agent's competing hypotheses regarding what the world is like. Building on past efforts to apply probability theory to the formal study of epistemic modal meaning, I show that a Bayesian formulation of evidential reasoning also provides the basis of a semantics for epistemic "must/might" which addresses a number of challenges that have vexed linguistic semanticists and philosophers of language. These challenges include: How do we specify a formal framework that verifies entailment relations between the modal auxiliaries and other epistemic operators (e.g., "possible, certain")? How do we specify a formal framework that verifies entailment from "must p" to 'the relevant agent has a high degree of confidence in "p"'? How can we account for the observation that "must p" (cf. other epistemic operators, including "possible" and "must's" putative dual "might") is often infelicitous without contextually-salient evidence for "p"? How can we account for the observation that "must p" is infelicitous in contexts where the relevant agent has direct evidence for "p"? [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]