Logics for Knowability

Liu, Mo, Fan, Jie, Van Ditmarsch, Hans and Kuijer, Louwe B ORCID: 0000-0001-6696-9023 (2022) Logics for Knowability. LOGIC AND LOGICAL PHILOSOPHY, 31 (3). pp. 385-426.

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Official URL: http://dx.doi.org/10.12775/llp.2021.018

Abstract

<jats:p>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.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	knowability, public announcement logic, expressivity, arbitrary public announcement logic, axiomatizations, decidability
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	09 Dec 2021 11:25
Last Modified:	18 Jan 2023 21:24
DOI:	10.12775/LLP.2021.018
Open Access URL:	https://apcz.umk.pl/LLP/article/view/33886/30664
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3143018