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Intuitionistic Public Announcement Logic with Distributed Knowledge

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Abstract

We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is not valid for a frame class discussed in [12] but valid for the restricted frame class introduced in [20, 26]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.

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Acknowledgements

We would like to thank the reviewers for their helpful comments. The work of the first author was supported by JSPS KAKENHI Grant-in-Aid for JSPS Fellows Grant Number JP 21J10573. The work of the second author was partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B) Grant Number JP 22H00597 and (C) Grant Number JP 19K12113.

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Authors and Affiliations

  1. Graduate School of Humanities and Human Sciences, Hokkaido University, Nishi 7 Chome, Kita 10 Jo, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan

    Ryo Murai

  2. Faculty of Humanities and Human Sciences, Hokkaido University, Nishi 7 Chome, Kita 10 Jo, Kita-ku, Sapporo, Hokkaido, 060-0810, Japan

    Katsuhiko Sano

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  1. Ryo Murai
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  2. Katsuhiko Sano
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Correspondence to Ryo Murai.

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Murai, R., Sano, K. Intuitionistic Public Announcement Logic with Distributed Knowledge. Stud Logica (2023). https://doi.org/10.1007/s11225-023-10066-1

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