Complexity and Succinctness of Public Announcement Logic

Carsten LutzCarsten Lutz

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Carsten Lutz
Complexity and Succinctness of Public Announcement Logic
In Peter Stone and Gerhard Weiss, eds., Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS'06), 137-144, 2006. Association for Computing Machinery (ACM)

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KurzfassungAbstract
There is a recent trend of extending epistemic logic (EL) with dynamic operators that allow to express the evolution of knowledge and belief induced by knowledge-changing actions. The most basic such extension is public announcement logic (PAL), which is obtained from EL by adding an operator for truthful public announcements. In this paper, we consider the computational complexity of PAL and show that it coincides with that of EL. This holds in the single- and multi-agent case, and also in the presence of common knowledge operators. We also prove that there are properties that can be expressed exponentially more succinct in PAL than in EL. This shows that, despite the known fact that PAL and EL have the same expressive power, there is a benefit in adding the public announcement operator to EL: it exponentially increases the succinctness of formulas without having negative effects on computational complexity.
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@inproceedings{ Lutz-AAMAS-06,
  author = {C. {Lutz}},
  booktitle = {Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS'06)},
  editor = {Peter {Stone} and Gerhard {Weiss}},
  pages = {137--144},
  publisher = {Association for Computing Machinery (ACM)},
  title = {Complexity and Succinctness of Public Announcement Logic},
  year = {2006},
}