The present paper aims at developing a theory of logical entropy for p-preserving systems (L, p, ψ), where p is a Bayesian gs-map on a bounded lattice L and ψ is a p-preserving lattice homomorphism. Having proved several desirable properties, we construct a Rokhlin-type metric involving logical conditional entropy of p-partitions of a Bayesian gs-space (L,p), and use it to establish a logical entropy version of Kolmogorov–Sinai theorem in the context. A formal mathematical foundation for the corresponding information theory is also presented in the end.

中文翻译：

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用于广义同时测量的 Kolmogorov-Sinai 型逻辑熵

本论文旨在为保p系统 ( L, p, ψ )开发一种逻辑熵理论，其中p是有界格L上的贝叶斯gs映射，而ψ是保p格同态。在证明了几个理想的属性后，我们构建了一个 Rokhlin 型度量，它涉及贝叶斯gs空间 ( L,p )的p分区的逻辑条件熵，并使用它来建立上下文中 Kolmogorov-Sinai 定理的逻辑熵版本. 最后还给出了相应信息论的正式数学基础。