Minimally inconsistent LP (MiLP) is a nonmonotonic paraconsistent logic based on Graham Priest’s logic of paradox (LP). Unlike LP, MiLP purports to recover, in consistent situations, all of classical reasoning. The present paper conducts a proof-theoretic analysis of MiLP. I highlight certain properties of this logic, introduce a simple sequent system for it, and establish soundness and completeness results. In addition, I show how to use my proof system in response to a criticism of this logic put forward by J. C. Beall.

中文翻译：

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一种用于最小不一致LP的简单序列系统

最小不一致 LP (MiLP) 是一种基于 Graham Priest 悖论逻辑 (LP) 的非单调次一致逻辑。与 LP 不同，MiLP 旨在在一致的情况下恢复所有经典推理。本文对 MiLP 进行了证明理论分析。我强调了该逻辑的某些属性，为其引入了一个简单的顺序系统，并建立了健全性和完整性结果。此外，我还展示了如何使用我的证明系统来回应 J. C. Beall 对此逻辑提出的批评。