Gradable epistemic modals, probability, and scale structure

The epistemic modals possible, probable, likely, and certain require a semantics which explains their behavior both as modal operators and as gradable adjectives. An analysis of these items in terms of Kennedy & McNally's theory of gradability suggests that they are associated with a single, fully closed scale of possibility. An implementation using the standard theory of modality due to Kratzer is shown to make incorrect predictions in several domains. However, if the scale of possibility is identified with standard numerical probability, the facts about gradability are explained and the undesirable predictions of Kratzer's theory are avoided.