# Conservative Inference Rule for Uncertain Reasoning under Incompleteness

arXiv: https://arxiv.org/abs/1401.3471 · HTML: https://mlsanity.com/paper/1401.3471/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2014.

## Built on by (most cited first, 3 of 3)

- [Bounding Counterfactuals under Selection Bias](https://mlsanity.com/paper/2208.01417/) (2022)
- [Conformal Prediction with Partially Labeled Data](https://mlsanity.com/paper/2306.01191/) (2023)
- [Interval POMDP Shielding for Imperfect-Perception Agents](https://mlsanity.com/paper/2604.20728/) (2026)

## Abstract (arXiv)

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process behaviour to be partly unknown. Then we use Walleys theory of coherent lower previsions, a generalisation of the Bayesian theory to imprecision, to derive the rule to update beliefs under incompleteness that logically follows from our assumptions, and that we call conservative inference rule. This rule has some remarkable properties: it is an abstract rule to update beliefs that can be applied in any situation or domain; it gives us the opportunity to be neither too optimistic nor too pessimistic about the incompleteness process, which is a necessary condition to draw reliable while strong enough conclusions; and it is a coherent rule, in the sense that it cannot lead to inconsistencies. We give examples to show how the new rule can be applied in expert systems, in parametric statistical inference, and in pattern classification, and discuss more generally the view of incompleteness processes defended here as well as some of its consequences.