Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport's happened-before relation. To this end, we introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results state that (i) every first-order sentence can be transformed into an equivalent star-free PDL sentence (and conversely), and (ii) every star-free PDL sentence can be translated into an equivalent CFM. This answers an open question and settles the exact relation between CFMs and fragments of monadic second-order logic. As a byproduct, we show that first-order logic over MSCs has the three-variable property.

消息序列图（MSC）自然是作为通信有限状态机（CFM）的执行而出现的，其中有限状态进程通过无限制的FIFO通道交换消息。我们研究了以兰伯特的事前关系为特征的MSC的一阶逻辑。为此，我们介绍了具有循环和逆向功能的命题动态逻辑（PDL）的无星星版本。我们的主要结果表明，（i）每个一阶句子都可以转换为等效的无星星PDL句子（反之亦然），并且（ii）每个无星星的PDL句子都可以转换为等效的CFM。这回答了一个悬而未决的问题，并解决了CFM与单子二阶逻辑片段之间的确切关系。作为副产品，我们表明MSC上的一阶逻辑具有三变量属性。