In this paper we present a solver for a first-order logic language where sets and binary relations can be freely and naturally combined. The language can express, at least, any full set relation algebra on finite sets. It provides untyped, hereditarily finite sets, whose elements can be variables, and basically all the classic set and relational operators used in formal languages such as B and Z. Sets are first-class entities in the language, thus they are not encoded in lower level theories. Relations are just sets of ordered pairs. The solver exploits set unification and set constraint solving as primitive features. The solver is proved to be a sound semi-decision procedure for the accepted language. A Prolog implementation is presented and an extensive empirical evaluation provides evidence of its usefulness.

中文翻译：

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解决有限集和二元关系上的无量词一阶约束

在本文中，我们提出了一种一阶逻辑语言的求解器，其中集合和二元关系可以自由自然地组合。该语言至少可以表达有限集上的任何完整集关系代数。它提供了无类型的、遗传性有限的集合，其元素可以是变量，并且基本上提供了 B 和 Z 等形式语言中使用的所有经典集合和关系运算符。 集合是语言中的一等实体，因此它们不会被编码为较低的水平理论。关系只是有序对的集合。求解器利用集合统一和集合约束求解作为原始特征。求解器被证明是公认语言的一个健全的半决策过程。介绍了 Prolog 实现，广泛的经验评估提供了其有用性的证据。