Composing Local Contexts

An expression's presuppositions must be satisfied by its local context, that is, by the utterance context updated with the content of expressions that have already been evaluated. Traditional dynamic approaches track local context by remaking clause denotations into context update functions. This requires crafting for each semantic operator an update recipe that is not fully determined by its truth conditions, failing to capture how local contexts depend only on truth conditions and order of evaluation. In other theories, computing local contexts involves reasoning about the set of all possible grammatical syntactic completions, which relocates local contexts outside of the semantics. I show how to build local contexts systematically and uniformly as part of the composition of ordinary truth conditions. The result is a minimalist dynamic semantics in which the only thing that is dynamically tracked is the semantic content of what has already been said.