软约束的留数：字典序和近似技术
Residuation for Soft Constraints: Lexicographic Orders and Approximation Techniques
摘要：
剩余理论关注偏序代数结构的研究，最常见的是monoid，配备了monoidal算子的弱逆。它的应用领域之一是约束编程，其关键要求是存在一个聚合器运算符来组合偏好。给定一个偏好的剩余幺半群，本文首先展示了如何建立一个新的（可能是无限的）元组的剩余幺半群，这是基于字典序。其次，它引入了一种近似技术（称为迷你桶），利用弱逆的存在。
英文摘要：
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key requirement is the presence of an aggregator operator for combining preferences. Given a residuated monoid of preferences, the paper first shows how to build a new residuated monoid of (possibly infinite) tuples, which is based on the lexicographic order. Second, it introduces a variant of an approximation technique (known as Mini-bucket) that exploits the presence of the weak inverse.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
