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Logic and Logical Philosophy

Logics for Knowability
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Logics for Knowability

Authors

  • Mo Liu CNRS, LORIA, University of Lorraine https://orcid.org/0000-0001-6033-8212
  • Jie Fan Institute of Philosophy, Chinese Academy of Sciences; School of Humanities, University of Chinese Academy of Sciences, Beijing https://orcid.org/0000-0003-2441-5019
  • Hans van Ditmarsch Open University of the Netherlands https://orcid.org/0000-0003-4526-8687
  • Louwe B. Kuijer University of Liverpool https://orcid.org/0000-0001-6696-9023

DOI:

https://doi.org/10.12775/LLP.2021.018

Keywords

knowability, public announcement logic, arbitrary public announcement logic, expressivity, axiomatizations, decidability

Abstract

In this paper, we propose three knowability logics LK, LK−, and LK=. In the single-agent case, LK is equally expressive as arbitrary public announcement logic APAL and public announcement logic PAL, whereas in the multi-agent case, LK is more expressive than PAL. In contrast, both LK− and LK= are equally expressive as classical propositional logic PL. We present the axiomatizations of the three knowability logics and show their soundness and completeness. We show that all three knowability logics possess the properties of Church-Rosser and McKinsey. Although LK is undecidable when at least three agents are involved, LK− and LK= are both decidable.

References

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Logic and Logical Philosophy

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Published

2021-12-08

How to Cite

1.
LIU, Mo, FAN, Jie, VAN DITMARSCH, Hans & KUIJER, Louwe B. Logics for Knowability. Logic and Logical Philosophy [online]. 8 December 2021, T. 31, nr 3, s. 385–426. [accessed 28.3.2023]. DOI 10.12775/LLP.2021.018.
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Vol. 31 No. 3 (2022): September

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