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A Simple Logic of the Hide and Seek Game

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Abstract

We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion with respect to such a language extension, and we add a new modal variant to that class. We discuss the relative expressive power of the proposed logic in comparison to the standard modal counterparts. We prove that the model checking problem for the resulting logic is \(\textsf{P}\)-complete. In addition, by exploring the connection with related product logics, we gain more insight towards having a better understanding of the subtleties of the proposed framework.

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Acknowledgements

We thank Johan van Benthem for his inspiring suggestions. We wish to thank the anonymous reviewers for their helpful comments for improvements. Sujata Ghosh acknowledges Department of Science and Technology, Government of India for financial support vide Reference No DST/CSRI/2018/202 under Cognitive Science Research Initiative (CSRI) to carry out this work. Dazhu Li is supported by the National Social Science Foundation of China [22CZX063], Fenrong Liu and Yaxin Tu are supported by Tsinghua University Initiative Scientific Research Program.

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Authors and Affiliations

  1. Institute of Philosophy, Chinese Academy of Sciences, Beijing, China

    Dazhu Li

  2. Department of Philosophy, University of Chinese Academy of Sciences, Beijing, China

    Dazhu Li

  3. Indian Statistical Institute, Chennai, India

    Sujata Ghosh

  4. The Tsinghua–UvA JRC for Logic, Department of Philosophy, Tsinghua University, Beijing, China

    Fenrong Liu

  5. Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China

    Yaxin Tu

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  1. Dazhu Li
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Correspondence to Sujata Ghosh.

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Li, D., Ghosh, S., Liu, F. et al. A Simple Logic of the Hide and Seek Game. Stud Logica 111, 821–853 (2023). https://doi.org/10.1007/s11225-023-10039-4

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