论文标题
关于paracissistent逻辑的经典观点
A classical-logic view on a paraconsistent logic
论文作者
论文摘要
本文关注的是一阶逻辑LPQ $^{\ supset，\ Mathsf {f}} $，Priest's LPQ充满了含义的连接和虚假的常数。提出了该逻辑的序列式自然扣除证明系统，对于此证明系统，给出了模型理论的理由和通过嵌入一阶古典逻辑中的逻辑理由。给定的嵌入还提供了对这种副暂停逻辑的经典解释。另外，讨论了它在有关此旁s逻辑的可决定性问题中的使用。 LPQ $^{\ supset，\ Mathsf {f}} $关于其逻辑后果关系及其逻辑等价关系的主要属性也得到了处理。本文强调了LPQ $^{\ supset，\ Mathsf {f}} $与经典逻辑有关的程度。
This paper is concerned with the paraconsistent first-order logic LPQ$^{\supset,\mathsf{F}}$, Priest's LPQ enriched with an implication connective and a falsity constant. A sequent-style natural deduction proof system for this logic is presented and, for this proof system, both a model-theoretic justification and a logical justification by means of an embedding into first-order classical logic is given. The given embedding provides in addition a classical-logic explanation of this paraconsistent logic. As a further matter, its use in decidability issues concerning this paraconsistent logic is discussed. The major properties of LPQ$^{\supset,\mathsf{F}}$ concerning its logical consequence relation and its logical equivalence relation are also treated. The paper emphasizes how closely LPQ$^{\supset,\mathsf{F}}$ is related to classical logic.
