一句话：借助有效关系统一刻画概率状态与谓词上的度量，并应用于经典和量子概率的 state-and-effect 三角。
本文研究概率分布（状态）与谓词上的多种度量，目标是以统一方式理解这些距离。作者利用状态与谓词之间的有效性（validity）关系来定义和比较度量，并将凸集（状态）与 effect module（谓词）之间的标准伴随限制到凸完备度量空间与有向完备 effect module。由此，该伴随可用于两个 state-and-effect 三角：经典离散概率与量子概率。论文展示该框架能系统组织经典和量子情形下的状态距离与谓词距离，并为概率/量子语义提供范畴学基础。评估主要是理论构造与实例展示，而非实验。
This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard adjunction between convex sets (of states) and effect modules (of predicates) is restricted to convex complete metric spaces and directed complete effect modules. This adjunction is used in two state-and-effect triangles, for classical (discrete) probability and for quantum probability.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{0001W19,
title = {Distances between States and between Predicates},
author = {Bart Jacobs and Abraham Westerbaan},
journal = {Logical Methods in Computer Science},
volume = {Volume 16, Issue 1},
year = {2020},
doi = {10.23638/lmcs-16(1:26)2020}
}