Non-deterministic distributions

Most models of uncertainty change a precise value in some formal space to some other kind of value, function or a set, in another formal space. We define a new representation, called non-deterministic distributions, which allow us to integrate ignorance with probability models, and prove several theorems relating them to information theory and denotational semantics. The model integration problem is very difficult in general; we, like many others, have solved it only in very special cases. Our approach to integrating ignorance with probability, using non-deterministic distributions, shows a way to integrate ignorance with other uncertainty measures.