Traditional first-order logic has four definitions for quantifiers, which are defined by universal and existential quantifiers. In L₃-valued (three-valued) first-order logic, there are eight kinds of definitions for quantifiers; and corresponding Gentzen deduction systems will be given and their soundness and completeness theorems will be proved.

中文翻译：

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L3值一阶逻辑中的变量

传统的一阶逻辑对量词有四个定义，它们由通用量词和存在量词定义。在L ₃值（三值）一阶逻辑中，量词有八种定义；第二种是量词。并给出相应的Gentzen演绎系统，并证明其稳健性和完备性定理。