Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindstr\"om and developed as a substantial topic application of logic, especially model theory, to linguistics with work by Barwise, Cooper, Keenan. In this paper, we mainly study the proof theory of some non-standard quantifiers as second order formulae . Our first example is the usual pair of first order quantifiers (for all / there exists) when individuals are viewed as individual concepts handled by second order deductive rules. Our second example is the study of a second order translation of the simplest branching quantifier: ``A member of each team and a member of each board of directors know each other", for which we propose a second order treatment.

翻译：广义量词（包括Henkin的分支量词）由Mostowski和Lindström提出，并经由Barwise、Cooper、Keenan等人的工作发展成为逻辑（特别是模型论）在语言学中的重要应用领域。本文主要研究某些非标准量词作为二阶公式的证明论性质。第一个示例是将通常的一阶量词对（全称/存在）在个体被视为由二阶演绎规则处理的个体概念时的情形。第二个示例研究最简单分支量词（"每个团队的某成员与每个董事会的某成员相互认识"）的二阶翻译，并为此提出相应的二阶处理方法。