Commonly Knowing Whether

Jie Fan; Davide Grossi; Barteld Kooi; Xingchi Su; Rineke Verbrugge

doi:10.48550/arXiv.2001.03945

Commonly Knowing Whether

Jie Fan^*, Davide Grossi, Barteld Kooi, Xingchi Su, Rineke Verbrugge

^*Corresponding author for this work

Research output: Working paper › Academic

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Abstract

This paper introduces `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'. After giving five possible definitions of this concept, we explore the logical relations among them both in the multi-agent case and in the single-agent case. We focus on one definition and treat it as a modal operator. It is found that the expressivity of this operator is incomparable with the classical common knowledge operator. Moreover, some special properties of it over binary-tree models and KD45-models are investigated.

Original language	English
Publisher	arXiv
Number of pages	13
DOIs	https://doi.org/10.48550/arXiv.2001.03945
Publication status	Submitted - 14-Jan-2020

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cs.LO

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AB - This paper introduces `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'. After giving five possible definitions of this concept, we explore the logical relations among them both in the multi-agent case and in the single-agent case. We focus on one definition and treat it as a modal operator. It is found that the expressivity of this operator is incomparable with the classical common knowledge operator. Moreover, some special properties of it over binary-tree models and KD45-models are investigated.

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Commonly Knowing Whether

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