Logics for Knowability

Mo Liu; Jie Fan; Hans van Ditmarsch; Louwe B. Kuijer

doi:10.12775/LLP.2021.018

Logics for Knowability

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	385-426
Number of pages	42
Journal	Logic and Logical Philosophy
Volume	31
Issue number	3
DOIs	https://doi.org/10.12775/LLP.2021.018
Publication status	Published - Sept 2022

Keywords

arbitrary public announcement logic
axiomatizations
decidability
expressivity
knowability
public announcement logic

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10.12775/LLP.2021.018Licence: CC BY-ND

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@article{ea8722faa441412e84b34ce2ad662bb5,

title = "Logics for Knowability",

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.",

keywords = "arbitrary public announcement logic, axiomatizations, decidability, expressivity, knowability, public announcement logic",

author = "Mo Liu and Jie Fan and \{van Ditmarsch\}, Hans and Kuijer, \{Louwe B.\}",

note = "Funding Information: Mo Liu holds a China Scholarship Council studentship. Jie Fan is supported by the project 17CZX053 of National Social Science Fund of China. We thank an anonymous referee of this journal for insightful comments. Funding Information: Acknowledgements. Mo Liu holds a China Scholarship Council studentship. Jie Fan is supported by the project 17CZX053 of National Social Science Fund of China. We thank an anonymous referee of this journal for insightful comments. Publisher Copyright: {\textcopyright} The Author(s), 2021.",

year = "2022",

month = sep,

doi = "10.12775/LLP.2021.018",

language = "English",

volume = "31",

pages = "385--426",

journal = "Logic and Logical Philosophy",

issn = "1425-3305",

publisher = "Nicolaus Copernicus University",

number = "3",

}

TY - JOUR

T1 - Logics for Knowability

AU - Liu, Mo

AU - Fan, Jie

AU - van Ditmarsch, Hans

AU - Kuijer, Louwe B.

N1 - Funding Information: Mo Liu holds a China Scholarship Council studentship. Jie Fan is supported by the project 17CZX053 of National Social Science Fund of China. We thank an anonymous referee of this journal for insightful comments. Funding Information: Acknowledgements. Mo Liu holds a China Scholarship Council studentship. Jie Fan is supported by the project 17CZX053 of National Social Science Fund of China. We thank an anonymous referee of this journal for insightful comments. Publisher Copyright: © The Author(s), 2021.

PY - 2022/9

Y1 - 2022/9

N2 - 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.

AB - 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.

KW - arbitrary public announcement logic

KW - axiomatizations

KW - decidability

KW - expressivity

KW - knowability

KW - public announcement logic

U2 - 10.12775/LLP.2021.018

DO - 10.12775/LLP.2021.018

M3 - Article

AN - SCOPUS:85137612096

SN - 1425-3305

VL - 31

SP - 385

EP - 426

JO - Logic and Logical Philosophy

JF - Logic and Logical Philosophy

IS - 3

ER -

Logics for Knowability

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Keywords

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