Belnap-Dunn逻辑扩张的相互可定义性
The interdefinability of expansions of Belnap-Dunn logic
AI总结：
本文研究Belnap-Dunn逻辑的非经典连接词扩张是否与仅含经典连接词的扩张相互可定义，基于被遗忘的连接词可定义性一般概念，并探讨其与经典逻辑版本的关联。
摘要：
Belnap-Dunn逻辑，也称为一阶蕴含逻辑，是一种可作为不一致或不完备理论底层逻辑的逻辑。出于各种原因，人们已经研究了用非经典连接词对Belnap-Dunn逻辑进行的不同扩张。本文研究这些扩张是否与连接词仅包含经典连接词的扩张相互可定义。令人惊讶的是，这一相关问题在已发表的研究中未在任何地方被提及。所使用的逻辑相互可定义性概念，基于一个似乎已被遗忘的关于逻辑中连接词可定义性的一般概念。本文还关注连接词仅包含经典连接词的扩张在多大程度上与具有相同连接词的经典逻辑版本相关联。
英文摘要：
Belnap-Dunn logic, also knows as the logic of First-Degree Entailment, is a logic that can serve as the underlying logic of theories that are inconsistent or incomplete. For various reasons, different expansions of Belnap-Dunn logic with non-classical connectives have been studied. This paper investigates the question whether those expansions are interdefinable with an expansion whose connectives include only classical connectives. Surprisingly, this relevant question is not addressed anywhere in the published studies. The notion of interdefinability of logics used is based on a general notion of definability of a connective in a logic that seems to have been forgotten. Attention is also paid to the extent to which the expansion whose connectives include only classical connectives is related to the version of classical logic with the same connectives.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
