Thesis: Ph. D., Massachusetts Institute of Technology, Department of Brain and Cognitive Sciences, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 205-211).A number of recent proposals have used techniques from game theory and Bayesian cognitive science to formalize Gricean pragmatic reasoning [29, 28, 36, 51]. In the first part of this work, we discuss several phenomena which pose a challenge to these accounts of pragmatics: M-implicatures [45] and embedded implicatures which violate Hurford's constraint [49, 16]. While techniques have been developed for deriving M-implicatures, Hurford-violating embedded implicatures pose a more fundamental challenge to the models' architecture. In order to explain these phenomena, we propose that the semantic content of an utterance is not fixed independent of pragmatic inference; rather, pragmatic inference partially determines an utterance's semantic content. We show how semantic inference can be realized as an extension to the Rational Speech Acts framework [36]. The addition of lexical uncertainty derives both M-implicatures and the relevant embedded implicatures. This principle explains a novel class of implicature, non-convex disjunctive implicatures. These implicatures can be preserved in downward-entailing contexts in the absence of accenting, a property which is predicted by lexical uncertainty, but which violates prior generalizations in the literature [46, 27] In the second part of the thesis, we combine these pragmatic models with another recent probabilistic approach to natural language understanding, exploring the formal pragmatics of communication on a noisy channel. We extend a model of rational communication between a speaker and listener, to allow for the possibility that messages are corrupted by noise. Prosodic stress is modeled as the choice to intentionally reduce the noise rate on a word. We show that the model derives several well-known changes in meaning associated with stress, including exhaustive interpretations, scalar implicature strengthening, the association between stress and disagreement, and the interpretation of the focus-sensitive adverbs. We then show that it can account for several phenomena which are outside of the scope of previous accounts of stress interpretation: the effects of stress on quantifier domain inferences, the intensification of gradable adjective interpretation, and the strengthening of hyperbolic utterances. The account avoids the use of syntactic or semantic representations of stress; the interpretive effects of stress are derived from general-purpose pragmatic reasoning.by Leon Bergen.Ph. D.