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

arXiv: https://arxiv.org/abs/2302.08176 · HTML: https://mlsanity.com/paper/2302.08176/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making](https://mlsanity.com/paper/2002.05196/) (2020)
- [A Desirability-Based Axiomatisation for Coherent Choice Functions](https://mlsanity.com/paper/1806.01044/) (2018)
- [Coherent and Archimedean choice in general Banach spaces](https://mlsanity.com/paper/2002.05461/) (2020)
- [A theory of desirable things](https://mlsanity.com/paper/2302.07412/) (2023)
- [Nonlinear desirability theory](https://mlsanity.com/paper/2209.00686/) (2022)
- [On a notion of independence proposed by Teddy Seidenfeld](https://mlsanity.com/paper/2102.10342/) (2021)

## Abstract (arXiv)

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.