 Perhaps the best way of capturing the cognitive nature of assertion is to give a theory of the cognitive features of normal communication by means of assertion. A classic theory is Stalnaker’s (1974, 1978). Stalnaker provides a model of a conversation in which assertion and presupposition dynamically interact. On Stalnaker’s model, propositions are presupposed in a conversation if they are on record as belonging to the common ground between the speakers. When an assertion is made and accepted in the conversation, its content is added to the common ground, and the truth of the proposition in question will be presupposed in later stages. What is presupposed at a given stage has an effect on the interpretation of new utterances made at that stage. For Stalnaker, the common ground is a set of propositions. He models this with the set of worlds in which all common ground propositions are true, the context set.