A paradefinite logic is a logic that can serve as the underlying logic for theories that are inconsistent or incomplete. A well-known paradefinite logic is Belnap-Dunn logic. Various expansions of Belnap-Dunn logic have been studied in the literature. In this note, it is argued that the most natural paradefinite logic relative to classical logic is the expansion of Belnap-Dunn logic with a falsity connective and an implication connective for which the standard deduction theorem holds.

翻译：准确定义逻辑是一种可作为不一致或不完备理论之基础逻辑的逻辑。Belnap-Dunn 逻辑是著名的准确定义逻辑。文献中已研究了 Belnap-Dunn 逻辑的多种扩展形式。本文论证指出：相对于经典逻辑最自然的准确定义逻辑，是在 Belnap-Dunn 逻辑基础上扩展了假值连接词及满足标准演绎定理的蕴涵连接词所形成的逻辑系统。