Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power

Author:

Ågotnes Thomas,Alechina Natasha,Galimullin Rustam

Abstract

AbstractPublic announcement logic (PAL) is an extension of epistemic logic with dynamic operators that model the effects of all agents simultaneously and publicly acquiring the same piece of information. One of the extensions of PAL, group announcement logic (GAL), allows quantification over (possibly joint) announcements made by agents. In GAL, it is possible to reason about what groups can achieve by making such announcements. It seems intuitive that this notion of coalitional ability should be closely related to the notion of distributed knowledge, the implicit knowledge of a group. Thus, we study the extension of GAL with distributed knowledge, and in particular possible interaction properties between GAL operators and distributed knowledge. The perhaps surprising result is that, in fact, there are no interaction properties, contrary to intuition. We make this claim precise by providing a sound and complete axiomatisation of GAL with distributed knowledge. We also consider several natural variants of GAL with distributed knowledge, as well as some other related logic, and compare their expressive power.

Funder

University of Bergen

Publisher

Springer Science and Business Media LLC

Subject

Linguistics and Language,Philosophy,Computer Science (miscellaneous)

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. To be announced;Information and Computation;2023-06

2. Quantifying over information change with common knowledge;Autonomous Agents and Multi-Agent Systems;2023-03-08

3. The Expressivity of Quantified Group Announcements;Journal of Logic and Computation;2022-11-24

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