论文标题
呈现定量不合理理论
Presenting with Quantitative Inequational Theories
论文作者
论文摘要
引起了我自己和（S.，Rozowski，Silva，Rot，2022）的合着者的注意，可以通过代数介绍其指定的过渡系统的分支结构来获得许多过程计算。例如，标记的过渡系统分支为过渡的一组术语，在过渡产生的自由半层次中。在集合类别中解释方程理论具有不良的局限性，我们希望在其他类别中提供更多演示示例。在这篇简短的文章中，我讨论了部分有序集和单调图的类别中的单调演示文稿。我专注于定量的单调，即在有序的半序上进行自由模块，并为其中之一提供足够的条件来提升集合类别的单子。我还提供了有序的半连接的描述，这些半序有助于指定无护理的递归调用。示例包括有序的概率理论和有序的半纹身。
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled transition systems, for example, branch into sets of transitions, terms in the free semilattice generated by the transitions. Interpreting equational theories in the category of sets has undesirable limitations, and we would like to have more examples of presentations in other categories. In this brief article, I discuss monad presentations in the category of partially ordered sets and monotone maps. I focus on quantitative monads, namely free modules over ordered semirings, and give sufficient conditions for one of these to lift a monad on the category of sets. I also give a description of ordered semirings that are useful for specifying unguarded recursive calls. Examples include ordered probability theory and ordered semilattices.
