This paper addresses the integration of epistemic entrenchment into paraconsistent belief revision systems based on Logics of Formal Inconsistency (LFIs). While systems like AGMp and AGMo adapt AGM principles to paraconsistency, they lack mechanisms to rank beliefs, primarily due to the absence of properties such as the replacement property in the underlying logics. We introduce two novel logics, Cbr and RCBr, with the latter extending the former to fully address these limitations given that it is self-extensional. Using RCBr, we define contraction operations via epistemic entrenchment, adhering to key rationality principles. Our framework leverages non-deterministic matrix semantics (Nmatrices) and Boolean algebras with LFI operators (BALFIs), providing a robust foundation for paraconsistent reasoning. These contributions advance the theory of paraconsistent belief revision and pave the way for applications in domains such as multi-agent systems and inconsistent knowledge bases.

翻译：本文探讨了将认知固守性整合到基于形式不一致性逻辑（LFIs）的次协调信念修正系统中的问题。虽然AGMp和AGMo等系统将AGM原则适配于次协调性，但由于底层逻辑缺乏替换性等性质，它们缺少对信念进行排序的机制。我们引入了两种新颖的逻辑Cbr和RCBr，其中RCBr作为自外延逻辑扩展了Cbr，从而全面解决了这些局限性。利用RCBr，我们通过认知固守性定义了收缩操作，并遵循关键理性原则。我们的框架采用非确定性矩阵语义（Nmatrices）和带有LFI算子的布尔代数（BALFIs），为次协调推理提供了坚实基础。这些贡献推进了次协调信念修正理论的发展，并为多智能体系统和不一致知识库等领域的应用铺平了道路。