---
title: "Probabilistic Reasoning with Inconsistent Beliefs Using Inconsistency Measures"
authors:
  - "Nico Potyka"
  - "Matthias Thimm"
doi: ""
url: "https://ijcai.org/proceedings/2015/445"
pdf: "https://ijcai.org/proceedings/2015/0445.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "3156-3162"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

# Probabilistic Reasoning with Inconsistent Beliefs Using Inconsistency Measures

Nico Potyka, Matthias Thimm

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 3156-3162.

## Abstract

The classical probabilistic entailment problem is to determine upper and lower bounds on the probability of formulas, given a consistent set of probabilistic assertions. We generalize this problem by omitting the consistency assumption and, thus, provide a general framework for probabilistic reasoning under inconsistency. To do so, we utilize inconsistency measures to determine probability functions that are closest to satisfying the knowledge base. We illustrate our approach on several examples and show that it has both nice formal and computational properties.