八卦逻辑中的常识

K. Apt, D. Wojtczak
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引用次数: 8

摘要

八卦协议旨在通过点对点或群体通信的方式,达到一种所有特工都知道彼此秘密的状态。最近,许多作者研究了分布式认知八卦协议。这些协议使用来自简单认知逻辑的保护公式,这使得它们的分析和验证更加容易。我们在这里研究这种逻辑背景下的常识。首先,我们分析了它何时可以被简化为迭代知识。然后证明了没有嵌套公共知识算子的公式的语义和真值是可判定的。这意味着使用非嵌套公共知识算子的分布式知识八卦协议的可实现性、部分正确性和终止性也是可确定的。鉴于共同知识等同于嵌套知识的无限结合,这些结果是对(Apt & Wojtczak, 2016)中建立的原始认知逻辑的相应可判定性结果的非平凡推广。K. R. Apt & D. Wojtczak(2016):论八卦逻辑的可决性。中国生物医学工程学报,2016,pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Common Knowledge in a Logic of Gossips
Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. We study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable. This implies that implementability, partial correctness and termination of distributed epistemic gossip protocols that use non-nested common knowledge operator is decidable, as well. Given that common knowledge is equivalent to an infinite conjunction of nested knowledge, these results are non-trivial generalizations of the corresponding decidability results for the original epistemic logic, established in (Apt & Wojtczak, 2016). K. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.
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