Abstract The so-called gossip problem is a formal model of peer-to-peer communication. In order to perform such communication efficiently, it is important to keep track of what agents know about who holds what information at a given point in time. The knowledge that the agents possess depends strongly on the particular type of communication that is used. Here, we formally define a large number of different variants of the gossip problem, that differ in the extent to which communication is private (observable, synchronous or asynchronous), the direction of the flow of information (caller to callee, callee to caller or both) and whether the agents become aware of the exact set of information possessed by their communication partner. We consider a number of formulas that represent interesting properties that a gossip situation may or may not enjoy, and show for which variants they are valid. Additionally, we show that the model checking and validity checking problems for each variant are decidable, and we introduce sound and complete proof systems for them.

中文翻译：

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八卦的逻辑

摘要 所谓八卦问题是一种形式化的点对点通信模型。为了有效地执行此类通信，重要的是要跟踪代理知道谁在给定时间点持有哪些信息。代理拥有的知识在很大程度上取决于所使用的特定通信类型。在这里，我们正式定义了八卦问题的大量不同变体，它们的不同之处在于通信的私密程度（可观察的、同步的或异步的）、信息流的方向（调用者到被调用者、被调用者到调用者或两者）以及代理是否意识到其通信伙伴拥有的确切信息集。我们考虑了许多代表八卦情况可能会或可能不会喜欢的有趣特性的公式，并显示它们对哪些变体有效。此外，我们表明每个变体的模型检查和有效性检查问题都是可判定的，并且我们为它们引入了健全和完整的证明系统。