一句话：通过 effect monoid 刻画实数单位区间，说明其结构可由少量合理假设自然导出。
本文试图解释为何在量子计算等非标准计算模型中，尽管“谓词”等概率论基本概念差异很大，实数单位区间却始终是唯一有用的概率代数。作者研究 effect monoid：它抽象实数单位区间的代数结构，具有仅在 x+y≤1 时定义的部分加法，以及补运算 x↦1-x 构成 effect algebra，并配有结合的（可能非交换的）乘法。有序环的单位区间与布尔代数均为其例子。论文证明，在若干合理假设下，实数单位区间的结构会自然出现，从而给出有序抽象概率的一种代数刻画。
In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of an algebra of probabilities is the real unit interval. In this paper we try to explain this phenomenon. We will show that the structure of the real unit interval naturally arises from a few reasonable assumptions. We do this by studying effect monoids, an abstraction of the algebraic structure of the real unit interval: it has an addition x + y which is only defined when x + y ≤ 1 and an involution x~1 -- x which make it an effect algebra, in combination with an associative (possibly non-commutative) multiplication. Examples include the unit intervals of ordered rings and Boolean algebras.