A Conventional Expansion of First-Order Belnap-Dunn Logic
A Conventional Expansion of First-Order Belnap-Dunn Logic
复制标题
一阶 Belnap-Dunn 逻辑的常规展开
DOI：
10.48550/arxiv.2301.10555
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
K. Middelburg
中科院分区：
文献类型：
--
作者：
K. Middelburg
本文讨论一阶Belnap-Dunn逻辑的一种扩展，它的连接词和量词都与经典逻辑相似。定义了逻辑的语言和逻辑推理关系，给出了所定义逻辑的证明系统，并证明了该证明系统的可靠性和完备性。定义逻辑的逻辑结果关系与同语言经典逻辑版本之间的密切关系通过所提出的证明系统与同语言经典逻辑版本的健全完整证明系统之间的细微差别来说明。此外，还给出了15条经典的逻辑等价定律，通过这些定律，定义的逻辑的逻辑等价关系有别于许多逻辑的逻辑等价关系，这些逻辑等价关系乍一看是密切相关的。
This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers are all familiar from classical logic. The language and logical consequence relation of the logic are defined, a proof system for the defined logic is presented, and the soundness and completeness of the presented proof system is established. The close relationship between the logical consequence relations of the defined logic and the version of classical logic with the same language is illustrated by the minor differences between the presented proof system and a sound and complete proof system for the version of classical logic with the same language. Moreover, fifteen classical laws of logical equivalence are given by which the logical equivalence relation of the defined logic distinguishes itself from the logical equivalence relation of many logics that are closely related at first glance.
一阶 Belnap-Dunn 逻辑的扩展
DOI：
--
发表时间：
2011
期刊：
影响因子：
--
作者：
Sano;K.;Omori;H.
通讯作者：
H.
Belnap-Dunn 逻辑的扩展
DOI：
--
发表时间：
2011
期刊：
影响因子：
--
作者：
Sano;K.;Omori;H.;大森仁
通讯作者：
大森仁