Isomorphism Theorems between Models of Mixed Choice (Revised)

TL;DR

This paper establishes isomorphisms between powercone models of mixed choice and models of previsions using topological and functional analytic methods, correcting previous proof errors.

Contribution

It provides a corrected and slightly less general proof of the isomorphism between these models, connecting powercone models with prevision models under certain conditions.

Findings

Powercone models are isomorphic to prevision models under specific topological assumptions.

The paper corrects a previous proof error in the 2017 version.

Uses advanced functional analysis and cone theory to establish the results.

Abstract

We relate the so-called powercone models of mixed non-deterministic and probabilistic choice proposed by Tix, Keimel, Plotkin, Mislove, Ouaknine, Worrell, Morgan, and McIver, to our own models of previsions. Under suitable topological assumptions, we show that they are isomorphic. We rely on Keimel's cone-theoretic variants of the classical Hahn-Banach separation theorems, using functional analytic methods, and on the Schr\"oder-Simpson Theorem. Lemma 3.4 in the original 2017 version, published at MSCS, had a wrong proof, and we prove a repaired, albeit slightly less general version here.