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. This is worth knowing because it is difficult to say how close a logic with non-classical connectives is related to classical logic. 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.

翻译：Belnap-Dunn逻辑，又称一阶蕴涵逻辑，是一种可作为不一致或不完全理论之基础逻辑的逻辑。出于多种原因，研究者对包含非经典联结词的Belnap-Dunn逻辑的不同扩张进行了探讨。本文研究这些扩张是否与仅包含经典联结词的扩张之间存在相互可定义性。这一问题的研究具有重要价值，因为难以断定包含非经典联结词的逻辑与经典逻辑的关联程度。本文采用的逻辑间相互可定义性概念，基于一种似乎已被遗忘的联结词在逻辑中的可定义性一般概念。