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Expressivity of Some Versions of APAL

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Dynamic Logic. New Trends and Applications (DaLi 2020)

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Abstract

Arbitrary public announcement logic (APAL) is a logic of change of knowledge with modalities representing quantification over announcements. We present two rather different versions of APAL wherein this quantification is restricted to formulas only containing a subset of all propositional variables: FSAPAL and SCAPAL; and another version quantifying over all announcements implied by or implying a given formula: IPAL. We then determine the relative expressivity of these logics and APAL. The IPAL quantifier promises to provide a novel perspective on substructural implication as dynamic consequence.

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Notes

  1. 1.

    For example, state 0 is \(M_3\) is distinguished by \(\hat{K}_b\hat{K}_a\hat{K}_b q \wedge \lnot \hat{K}_a \hat{K}_b q\); 0 is the unique state where we can get with three steps but not with two.

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Acknowledgements

We thank the reviewers for their comments. Hans van Ditmarsch is also affiliated to IMSc, Chennai, India, as a research associate.

Author information

Authors and Affiliations

  1. CNRS, LORIA, University of Lorraine, Nancy, France

    Hans van Ditmarsch & Mo Liu

  2. University of Liverpool, Liverpool, UK

    Louwe B. Kuijer

  3. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Igor Sedlár

Authors
  1. Hans van Ditmarsch
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  2. Mo Liu
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  3. Louwe B. Kuijer
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  4. Igor Sedlár
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Corresponding author

Correspondence to Hans van Ditmarsch .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Manuel A. Martins

  2. Institute of Computer Science, Czech Academy of Sciences, Praha 8, Czech Republic

    Igor Sedlár

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van Ditmarsch, H., Liu, M., Kuijer, L.B., Sedlár, I. (2020). Expressivity of Some Versions of APAL. In: Martins, M.A., Sedlár, I. (eds) Dynamic Logic. New Trends and Applications. DaLi 2020. Lecture Notes in Computer Science(), vol 12569. Springer, Cham. https://doi.org/10.1007/978-3-030-65840-3_8

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  • DOI: https://doi.org/10.1007/978-3-030-65840-3_8

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  • Online ISBN: 978-3-030-65840-3

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