Revising a Labelled Sequent Calculus for Public Announcement Logic

Chapter
Part of the Logic in Asia: Studia Logica Library book series (LIAA)

Abstract

We first show that a labelled sequent calculus \(\mathbf {G3PAL}\) for Public Announcement Logic (PAL) by Maffezioli and Negri (2011) has been lacking rules for deriving an axiom of Hilbert-style axiomatization of PAL. Then, we provide our revised calculus \(\mathbf {GPAL}\) to show that all the formulas provable in Hilbert-style axiomatization of PAL are also provable in \(\mathbf {GPAL}\) together with the cut rule. We also establish that our calculus enjoys cut elimination theorem. Moreover, we show the soundness of our calculus for Kripke semantics with the notion of surviveness of possible worlds in a restricted domain. Finally, we provide a direct proof of the semantic completeness of \(\mathbf {GPAL}\) for the link-cutting semantics of PAL.

Notes

Acknowledgments

We would like to thank an anonymous reviewer for his/her constructive comments to our manuscript. We also would like to thank the audiences in the Second Taiwan Philosophical Logic Colloquium (TPLC 2014) in Taiwan and the 49th MLG meeting at Kaga, Japan, particularly Makoto Kanazawa for a helpful comment on the link-cutting semantics at the MLG meeting. The second author would like to thank Didier Galmiche for a discussion on the topic of this paper. Finally, we are grateful to Sean Arn for his proofreading of the final version of the paper. This work of the first author was supported by Grant-in-Aid for JSPS Fellows, and that of the second author was supported by JSPS KAKENHI, Grant-in-Aid for Young Scientists (B) 24700146 and 15K21025. This work was conducted also by JSPS Core-to-Core Program (A. Advanced Research Networks).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan

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