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Synthese

, Volume 190, Supplement 1, pp 103–134 | Cite as

On axiomatizations of public announcement logic

  • Yanjing Wang
  • Qinxiang Cao
Article

Abstract

In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL  without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the core set. Moreover, we also propose and advocate an alternative yet meaningful axiomatization of PAL  without the reduction axioms. The completeness is proved directly by a detour method using the canonical model where announcements are treated as merely labels for modalities as in normal modal logics. This new axiomatization and its completeness proof may sharpen our understanding of PAL  and can be adapted to other dynamic epistemic logics.

Keywords

Public announcement logic Reduction axioms Composition axiom Dynamic epistemic logic Completeness Epistemic temporal logic 

Notes

Acknowledgments

The first author is supported by SSFC grant 11CZX054 and the Major Program of National Social Science Foundation of China (No. 12&ZD119). The authors would like to thank Johan van Benthem, Hans van Ditmarsch, Meiyun Guo, Wesley Holliday, Fenrong Liu, Ram Ramanujam, Tomoyuki Yamada and anonymous reviewers of this journal for their insightful comments on earlier versions of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of PhilosophyPeking UniversityBeijingChina

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