一句话：扩展定量等式逻辑以支持广义度量代数与提升意义下的非扩张运算，并公理化概率分布上的Ł–K距离。
定量等式逻辑已被成功用于推理载体为度量空间、运算为非扩张的代数。本文沿两个正交方向扩展该框架：一是代数配备广义度量空间结构，二是运算仅在“提升”意义下满足非扩张性。作者给出相应的等式逻辑与语义基础，使这类代数仍可进行定量推理。作为应用，论文对概率分布上的 Łukaszyk–Karmowski 距离给出代数公理化；该距离近期被用于 Markov 过程上的表示学习。结果扩展了定量代数推理可处理的代数类别，并为概率度量提供公理化工具。
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.