---
title: "How Hard to Tell? Complexity of Belief Manipulation Through Propositional Announcements"
authors:
  - "Thomas Eiter"
  - "Aaron Hunter"
  - "Francois Schwarzentruber"
doi: "10.24963/ijcai.2021/257"
url: "https://ijcai.org/proceedings/2021/257"
pdf: "https://ijcai.org/proceedings/2021/0257.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "1866-1872"
track: "Main Track"
keywords:
  - "Knowledge Representation and Reasoning: Belief Change"
  - "Knowledge Representation and Reasoning: Reasoning about Knowledge and Belief"
---

# How Hard to Tell? Complexity of Belief Manipulation Through Propositional Announcements

Thomas Eiter, Aaron Hunter, Francois Schwarzentruber

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 1866-1872. DOI: [10.24963/ijcai.2021/257](https://doi.org/10.24963/ijcai.2021/257)

## Abstract

Consider a set of agents with initial beliefs and a formal operator for incorporating new information. Now suppose that, for each agent, we have a formula that we would like them to believe.  Does there exist a single announcement that will lead all agents to believe the corresponding formula? This paper studies the problem of the existence of such an announcement in the context of model-preference definable revision operators. First, we provide two characterisation theorems for the existence of announcements: one in the general case, the other for total partial orderings. Second, we exploit the characterisation theorems to provide upper bound complexity results. Finally, we also provide matching optimal lower bounds for the Dalal and Ginsberg operators.