The logic behind desirable sets of things, and its filter representation

TL;DR

This paper explores the logical foundations of desirable sets of things, linking them to filter representations, and provides new representation results for coherent models in decision theory.

Contribution

It identifies the filter-based logic behind coherent sets of desirable things and establishes new representation theorems for these models.

Findings

Established a logical framework for desirable sets of things.

Connected coherent models to filter representations.

Provided new representation theorems for decision models.

Abstract

We identify the (filter representation of the) logic behind the recent theory of coherent sets of desirable (sets of) things, which generalise coherent sets of desirable (sets of) gambles as well as coherent choice functions, and show that this identification allows us to establish various representation results for such coherent models in terms of simpler ones.