When communicating, interlocutors negotiate knowledge by proposing propositional content to be added to their shared common ground. The way in which speakers put forward propositional content -- expressing more or less confidence in its truthfulness -- may affect the way in which other interlocutors react to such content. This article examines speakers' production choices and hearers' interpretations of the formulations "believe"/"know"/bare assertion to test how (maximal) certainty is expressed and inferred, whether speakers adjust their production choices depending on their communicative goals and whether hearers are able to adjust their interpretations correspondingly. For this purpose, we created two scenarios -- one with a cooperative interlocutor and one with a potentially uncooperative interlocutor. The results suggest that "know" is epistemically the most powerful formulation -- stronger than the bare assertion -- but that the bare assertion may still be preferred over know for expressing maximal certainty in cooperative scenarios. Our findings also suggest that "believe" is used to hedge the assertive strength of statements in cooperative settings. Whereas speakers and hearers agree in the relative epistemic ordering of the formulations ("believe" < bare assertion < "know"), when inferring the speakers' degrees of belief hearers to not appear to consistently take into account that speakers' communicative goals may shift as a function of context.