论文标题
超越定量代数推理中的非专业操作
Beyond Nonexpansive Operations in Quantitative Algebraic Reasoning
论文作者
论文摘要
定量方程逻辑的框架已成功地应用于代数的理由，其载体是度量空间，并且操作不存在。我们将此框架扩展到两个正交方向：具有广义度量空间结构的代数，并且运行直至提升。我们将结果应用于概率分布的lukaszyk-karmowski距离的代数公理化，该距离最近在马尔可夫过程中发现了在表示领域的应用。
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.
