Certain content of a linguistic construction can project when the construction is embedded in entailment-canceling environments. For example, the conclusion that John smoked in the past from "John stopped smoking" still holds for "John didn't stop smoking," where the original utterance is embedded under negation. There are two main approaches to account for projection. The semantic approach adds restrictions of the common ground to the conventional meaning. The pragmatic approach tries to derive projection from general conversational principles. In this paper we build a probabilistic model of language understanding in which the listener jointly infers the world state and the common ground the speaker has assumed. We take change-of-state verbs as an example and model its projective content under negation. Under certain assumptions, the model correctly predicts the projective behavior and its interaction with the question under discussion, without any special semantic treatment of projective content.