Only Knowing Meets Common Knowledge
Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence. Special Track on Knowledge Representation and Reasoning. 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.
@inproceedings{ijcai2015p390,
title = {Only Knowing Meets Common Knowledge},
author = {Belle, Vaishak and Lakemeyer, Gerhard},
booktitle = {Proceedings of the Twenty-Fourth International Joint Conference on
Artificial Intelligence, {IJCAI-15}},
publisher = {International Joint Conferences on Artificial Intelligence},
editor = {Qiang Yang and Michael Wooldridge},
pages = {2755--2760},
year = {2015},
month = {7},
note = {Special Track on Knowledge Representation and Reasoning},
url = {https://ijcai.org/proceedings/2015/390},
}
TY - CPAPER TI - Only Knowing Meets Common Knowledge AU - Belle, Vaishak AU - Lakemeyer, Gerhard T2 - Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-15 PB - International Joint Conferences on Artificial Intelligence PY - 2015 SP - 2755 EP - 2760 UR - https://ijcai.org/proceedings/2015/390 ER -Copied
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