---
title: "Only Knowing Meets Common Knowledge"
authors:
  - "Vaishak Belle"
  - "Gerhard Lakemeyer"
doi: ""
url: "https://ijcai.org/proceedings/2015/390"
pdf: "https://ijcai.org/proceedings/2015/0390.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "2755-2760"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

# Only Knowing Meets Common Knowledge

Vaishak Belle, Gerhard Lakemeyer

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 2755-2760.

## Abstract

Only knowing captures the intuitive notion that the beliefs of an agent are precisely those that follow from its knowledge base. While only knowing has a simple possible-world semantics in a single agent setting, the many agent case has turned out to be much more challenging. In a recent paper, we proposed an account which arguably extends only knowing to multiple agents in a natural way. However, the approach was limited in that the semantics cannot deal with infinitary notions such as common knowledge. In this work, we lift that serious limitation to obtain a first-order language with only knowing and common knowledge, allowing us to study the interaction between these notions for the very first time. By adding a simple form of public announcement, we then demonstrate how the muddy children puzzle can be cast in terms of logical implications given what is only known initially.