一句话：提出 Riesz 模态逻辑，用 Riesz 空间建立概率转移系统性质的对偶理论，并给出可靠完备公理化与概率互模拟刻画。
本文面向概率转移系统，提出一种新的实值内生逻辑——Riesz 模态逻辑，用于表达其性质。其语法与语义受 Riesz 空间理论启发，该理论位于泛代数与泛函分析的交叉处。作者利用 Riesz 空间的强结果建立该逻辑的对偶理论，形式为代数到余代数的对应。由此得到若干结论：可靠且完备的公理化，该逻辑刻画概率互模拟，以及完备化定理等便利结果。该工作旨在为后续加入不动点算子的 Riesz 模态逻辑扩展奠定基础。
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of universal algebra and functional analysis. By using powerful results from this theory, we develop the duality theory of the Riesz modal logic in the form of an algebra-to-coalgebra correspondence. This has a number of consequences including: a sound and complete axiomatization, the proof that the logic characterizes probabilistic bisimulation and other convenient results such as completion theorems. This work is intended to be the basis for subsequent research on extensions of Riesz modal logic with fixed-point operators.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{FurberMM19,
title = {Probabilistic logics based on Riesz spaces},
author = {Robert Furber and Radu Mardare and Matteo Mio},
journal = {Logical Methods in Computer Science},
volume = {Volume 16, Issue 1},
year = {2020},
doi = {10.23638/lmcs-16(1:6)2020}
}