In Statistical Relational Artificial Intelligence, a branch of AI and machine learning which combines the logical and statistical schools of AI, one uses the concept {\em para\-metrized probabilistic graphical model (PPGM)} to model (conditional) dependencies between random variables and to make probabilistic inferences about events on a space of "possible worlds". The set of possible worlds with underlying domain $D$ (a set of objects) can be represented by the set $\mathbf{W}_D$ of all first-order structures (for a suitable signature) with domain $D$. Using a formal logic we can describe events on $\mathbf{W}_D$. By combining a logic and a PPGM we can also define a probability distribution $\mathbb{P}_D$ on $\mathbf{W}_D$ and use it to compute the probability of an event. We consider a logic, denoted $PLA$, with truth values in the unit interval, which uses aggregation functions, such as arithmetic mean, geometric mean, maximum and minimum instead of quantifiers. However we face the problem of computational efficiency and this problem is an obstacle to the wider use of methods from Statistical Relational AI in practical applications. We address this problem by proving that the described probability will, under certain assumptions on the PPGM and the sentence $\varphi$, converge as the size of $D$ tends to infinity. The convergence result is obtained by showing that every formula $\varphi(x_1, \ldots, x_k)$ which contains only "admissible" aggregation functions (e.g. arithmetic and geometric mean, max and min) is asymptotically equivalent to a formula $\psi(x_1, \ldots, x_k)$ without aggregation functions.

翻译：在统计再进化智能中, AI 和机器学习的分支, 将AI 的逻辑和统计学混合在一起, 人们使用概念 $ para\ metricized 概率图形模型( PPGM) 来模拟随机变量之间的( 有条件) 依赖性, 并对“ 可能的世界” 空间上的事件进行概率推论。 一组具有基本域$D( 一组对象) 的可能世界可以通过一套 $\ mathbf{W ⁇ D$ 和 机器学习 来代表 AI 的逻辑集成( 适合的签名) 和 域$D$ 。 使用一种正式逻辑来描述 $\ may\ maybl drobal a mortal, max max max dalvalation etimational divil_ dividates the prealational poligal, legal, legal dreal drealdal_ deal dal dal dal_ deal magistration preal magistrations exal dism dismal dism disml) as a a promaislate.