Prevision domains and convex powercones

Abstract

Two recent semantic families of models for mixed probabilistic and non-deterministic choice over a space X are the convex powercone models, due independently to Mislove, and to Tix, Keimel, and Plotkin, and the continuous prevision model of the author. We show that, up to some minor details, these models are isomorphic whenever X is a continuous, coherent cpo, and whether the particular brand of non-determinism we focus on is demonic, angelic, or chaotic. The construction also exhibits domains of continuous previsions as retracts of well-known continuous cpos, providing simple bases for the various continuous cpos of continuous previsions. This has practical relevance to computing approximations of operations on previsions. © 2008 Springer-Verlag Berlin Heidelberg.