We investigate, in a logical setting, the expressivist proposal that assertion primarily functions to express and coordinate doxastic states and that ‘might’ fundamentally expresses lack of belief. We provide a formal model of an agent’s doxastic state and novel assertability conditions for an associated formal language. We thereby prove that an arbitrary assertion (including a complex of ‘might’ and ‘factual’ claims) always succeeds in expressing a well-defined (partial) doxastic state, and propose a fully general and intuitive update operation as a model of an agent coming to accept an arbitrary assertion. Leaving a comprehensive philosophical and linguistic defense for elsewhere, we explore technical aspects of our framework, providing, for instance, a complete logic of assertability and reduction axioms for the novel update operations related to our proposal. Finally, we contrast our work with related proposals in the logic literature.