互模拟逻辑特征的不可证明性
Unprovability of the Logical Characterization of Bisimulation
摘要：
我们快速审查标记马尔可夫过程（LMP），并提供了一个反例表明，在一般的可测空间，事件双相似性和状态双相似性不同的LMP。这表明，Desharnais [*]中的逻辑在非解析可测空间中不刻画状态互模拟。此外，我们表明，根据目前的数学基础，这样的逻辑特征是不可证明的空间，是一个协分析集的投影。在这个结构的基础上，证明了一般可测空间上的平稳马尔可夫过程不具有半拉回。[1] J. Desharnais，Labelled Markov Processes。计算机科学学院。蒙特利尔麦吉尔大学（1999年）
英文摘要：
We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in Desharnais [*] does not characterize state bisimulation in non-analytic measurable spaces. Furthermore we show that, under current foundations of Mathematics, such logical characterization is unprovable for spaces that are projections of a coanalytic set. Underlying this construction there is a proof that stationary Markov processes over general measurable spaces do not have semi-pullbacks. ([*] J. Desharnais, Labelled Markov Processes. School of Computer Science. McGill University, Montréal (1999))
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