Possibility and probability expressions, like possibly or prob-ably, are frequently assumed to communicate that the proba-bility of a proposition is above a certain threshold. Most pre-vious empirical research on these expressions has focused oncases of known objective chance: if the true objective proba-bility is given, would a speaker use possibly, probably or oneof their kin? Here, we investigate the use of probability expres-sions when speakers have subjective uncertainty about objec-tive chance, i.e., higher-order uncertainty. Experimental datasuggest that speakers’ choices of a probability expression is acomplex function of their state of higher-order uncertainty. Weformulate a computational probabilistic model of pragmaticspeaker behavior that explains the experimental data.

Complex uncertainty expressions such as probably likely andcertainly possible naturally occur in everyday conversations.However, they received much less attention in the literaturethan simple ones. We propose a probabilistic model of the useand interpretation of complex uncertainty expressions based onthe assumption that their predominant function is to communi-cate factual information about the world, and that further layersof uncertainty are pragmatically inferred. We collected empir-ical data on the use and interpretation of these expressions anduse it for detailed model criticism.