Likely Events and Possible States

This paper provides a recipe to generate definitions of possibility, which is equivalent to the standard approach of deriving possibility from belief/knowledge. Savage's notion of nonnullity is therefore an example that fits into our framework. The recipe is used to create a new definition of possibility, which is logically coherent for all weakly monotonic preferences. For various nonexpected utility models of preference, our new definition improves nonnullity and its existing alternatives.