中文摘要：

Extended IF逻辑是一阶逻辑的扩张，其主要特点是可表达量词间的相互依赖和独立关系，但其命题部分至今没有得到公理化．基于Cirquent演算方法，给出了一个关于Cirquent语义（命题水平）可靠完备的形式系统．该系统能够很好地解释和表达命题联结词间的相互依赖和独立关系，从而使Extended IF逻辑在命题水平得到了真正意义上的公理化．

英文摘要：

Extended independence-friendly （IF） logic is an extension of classical first-order logic. The main characteristic of IF logic is to allowing one to express independence relations between quantifiers. However, its propositional level has never been successfully axiomatized. Based on Cirquent calculus, this paper axiomatically constructs a formal system, which is sound and complete w.r.t, the propositional fragment of Cirquent-based semantics, for propositional extended IF logic. Such a system can account for independence relations between propositional connectives, and can thus be considered an axiomatization of purely propositional extended IF logic in its full generality.