论文标题
非单调副矛盾逻辑系统的序列型结石
Sequent-Type Calculi for Systems of Nonmonotonic Paraconsistent Logics
论文作者
论文摘要
paracissistent的逻辑构成了一个重要的形式主义类，这些形式主义涉及不一致的前提原因的非平凡推理。在本文中，我们为基于最小的不一致性的非单调副派信任逻辑介绍了统一的公理分解，以序列型预防系统。 后者是突出的且广泛使用的微积分形式，非常适合分析证明搜索。特别是，我们为祭司的三个价值微不足道的悖论以及由于Arieli和Avron引起的四价偏见的推断关系提供了序列型计算。我们的结石遵循Bonatti和Olivetti在非单调推理背景下首次引入的序列方法，其明显的特征是使用所谓的拒绝演算来使无效的公式用于公理。实际上，我们提出了一种一般方法，以获得基于最小不一致的任何多个逻辑的序列系统，从而产生了牧师以及Arieli和Avron作为特殊实例的逻辑的结石。
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.
