Paraconsistent logics constitute an important class of formalisms dealing with non-trivial reasoning from inconsistent premisses. In this paper, we introduce uniform axiomatisations for a family of nonmonotonic paraconsistent logics based on minimal inconsistency in terms of sequent-type proof systems. The latter are prominent and widely-used forms of calculi well-suited for analysing proof search. In particular, we provide sequent-type calculi for Priest's three-valued minimally inconsistent logic of paradox, and for four-valued paraconsistent inference relations due to Arieli and Avron. Our calculi follow the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti and Olivetti, whose distinguishing feature is the use of a so-called rejection calculus for axiomatising invalid formulas. In fact, we present a general method to obtain sequent systems for any many-valued logic based on minimal inconsistency, yielding the calculi for the logics of Priest and of Arieli and Avron as special instances.

中文翻译：

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非单调次协调逻辑系统的序列型演算

超一致逻辑构成了一类重要的形式主义，处理来自不一致前提的非平凡推理。在本文中，我们介绍了基于序列类型证明系统中最小不一致性的一系列非单调次协调逻辑的统一公理化。后者是突出且广泛使用的演算形式，非常适合分析证明搜索。特别是，我们为 Priest 的三值最小不一致悖论逻辑以及由于 Arieli 和 Avron 引起的四值超一致推理关系提供了连续型演算。我们的演算遵循由 Bonatti 和 Olivetti 在非单调推理背景下首次引入的序列方法，其显着特征是使用所谓的拒绝演算来公理化无效公式。实际上，