The non-alethic systems N₁ of da Costa and A of Grana are both paraconsistent and paracomplete. Based on them, a multi-agent doxastic logic N_ADK can be obtained by logical expansion. The soundness and completeness of N_ADK are proved and its special theorems are also presented. In this logic, the belief version of the laws of contradiction and excluded middle, as well as the principle of explosion are all invalid. Therefore, it may provide a reliable logical basis for any theory which has paraconsistent or paracomplete epistemic conflicts, such as true contradictions, true contrarieties, and belief paradoxes. We also explain in detail how a non-alethic doxastic logic provides a reliable logical basis for tolerating these three types of epistemic conflicts. The present paper is the deepening and development of system N₁ and A.

非真势系统Ñ ₁达科斯塔和甲基粒的都是并行相容性和paracomplete。基于它们，多剂doxastic逻辑Ñ_甲DK可以通过逻辑扩展而获得。N _A的健全性和完整性证明了DK并给出了它的特殊定理。按照这种逻辑，矛盾定律和排除中间律的信念版本以及爆炸原理都是无效的。因此，它可以为任何具有超一致或超完全认识论冲突的理论提供可靠的逻辑基础，例如真正的矛盾，真正的矛盾和信仰悖论。我们还将详细解释非种族主义的十二进制逻辑如何为容忍这三种类型的认知冲突提供可靠的逻辑基础。本文是对系统N ₁和A的深化和发展。