Logics for Knowability

Mo Liu, Jie Fan*, Hans van Ditmarsch, Louwe B. Kuijer

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)385-426
Number of pages42
JournalLogic and Logical Philosophy
Issue number3
Publication statusPublished - Sept 2022


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


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