Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what statements and questions can be expressed in InqBQ about the number of individuals satisfying a given predicate. As special cases, we show that several variants of the question how many individuals satisfy $\alpha (x)$ are not expressible in InqBQ, both in the general case and in restriction to finite models.

好奇的一阶逻辑，查询BQ, 是一个用表达问题的公式扩展经典一阶逻辑的系统。从数学的角度来看，该逻辑中的公式表达了关系结构集的属性。本文对这一逻辑的研究做出了两个贡献。首先，我们描述了一个 Ehrenfeucht–Fraïssé 博弈查询BQ并表明它表征了逻辑的区分能力。其次，我们使用游戏来研究好奇设置中的基数量词。也就是说，我们研究可以用什么语句和问题来表达查询BQ关于满足给定谓词的个体数量。作为特例，我们展示了多少个人满足 $\alpha (x)$ 的问题的几个变体无法表达 查询BQ，无论是在一般情况下还是在有限模型的限制下。