Open AccessLogics for Knowability
Author(s) -
Mo Liu,
Jie Fan,
Hans van Ditmarsch,
Louwe B. Kuijer
Publication year - 2021
Publication title -
logic and logical philosophy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.416
H-Index - 10
eISSN - 2300-9802
pISSN - 1425-3305
DOI - 10.12775/llp.2021.018
Subject(s) - soundness , undecidable problem , decidability , completeness (order theory) , mathematics , discrete mathematics , fragment (logic) , computer science , calculus (dental) , programming language , algorithm , medicine , mathematical analysis , dentistry
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.