定量代数推理中的超越非扩张运算
Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning
摘要：
定量方程逻辑的框架已成功地应用于推理的载体是度量空间和操作是非扩张的代数。我们在两个正交的方向扩展这个框架：代数赋予广义度量空间结构，和操作是非扩张的提升。我们将我们的结果的代数公理化的Eukaszyk-Karmowski距离的概率分布，最近发现的应用领域的表示学习马尔可夫过程。
英文摘要：
The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed with generalised metric space structures, and operations being nonexpansive up to a lifting. We apply our results to the algebraic axiomatisation of the Łukaszyk--Karmowski distance on probability distributions, which has recently found application in the field of representation learning on Markov processes.
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