P₁是一個弗完全邏輯系統，在其中排中律在一般意義上是無效的。基於P₁通過邏輯擴充的方法，可以構造出弗完全多主體認知邏輯系統P₁EₘK。本研究證明了這種系統的可靠性和完全性，並給出了表徵其特徵的內定理。在這種邏輯系統中，排中律和爆炸原理的認識論版本是無效的。本研究將弗完全邏輯的邏輯技術應用於認知邏輯，構建了一種新的哲學邏輯系統，即弗完全認知邏輯系統；本研究不僅進一步推動了弗完全邏輯的進一步發展，而且還充分表明了弗完全邏輯可以作為解決認知悖論底層邏輯的價值。

P₁ is a paracomplete logic system, in which the law of excluded middle is generally invalid. Based on P₁, a paracomplete multi-agent epistemic logic systems P₁EₘK can be constructed by logical expansion. The soundness and completeness of these systems are proved, and their special theorems are also presented in this study. In this type of system, the epistemic version of the law of excluded middle and the principle of explosion are invalid. This study applies the logical technique of paracomplete logic to epistemic logic, constructs a new philosophical logic system, i.e. a paracomplete epistemic logic system. This study not only promotes the further development of paracomplete logic, but also fully demonstrates the value of paracomplete logic as a solution to the underlying logic of epistemic paradox.