P_1 is a paracomplete logic system, in which the law of excluded middle is generally invalid. Based on P_1, a paracomplete multi-agent epistemic logic systems P_1E_mK 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.