# Visions of a generalized probability theory

arXiv: https://arxiv.org/abs/1810.10341 · HTML: https://mlsanity.com/paper/1810.10341/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2018.

## Built on by (most cited first, 13 of 13)

- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)
- [Uncertainty measures: The big picture](https://mlsanity.com/paper/2104.06839/) (2021)
- [Random-Set Large Language Models](https://mlsanity.com/paper/2504.18085/) (2025)
- [The intersection probability: betting with probability intervals](https://mlsanity.com/paper/2201.01729/) (2022)
- [Reasoning with random sets: An agenda for the future](https://mlsanity.com/paper/2401.09435/) (2023)
- [Generalising realisability in statistical learning theory under epistemic uncertainty](https://mlsanity.com/paper/2402.14759/) (2024)
- [Epistemic Generative Adversarial Networks](https://mlsanity.com/paper/2603.18348/) (2026)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Statistical inference with belief functions: A survey](https://mlsanity.com/paper/2605.07908/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [A geometric approach to conditioning belief functions](https://mlsanity.com/paper/2104.10651/) (2021)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)

## Abstract (arXiv)

In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the geometric and algebraic properties of belief functions as mathematical objects are illustrated and discussed in Part II, with a focus on both a perspective 'geometric approach' to uncertainty and an algebraic solution to the issue of conflicting evidence. In Part III we show how these theoretical developments arise from important computer vision problems (such as articulated object tracking, data association and object pose estimation) to which, in turn, the evidential formalism is able to provide interesting new solutions. Finally, some initial steps towards a generalization of the notion of total probability to belief functions are taken, in the perspective of endowing the theory of evidence with a complete battery of estimation and inference tools to the benefit of all scientists and practitioners.