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以作为不一致或不完备理论之基础逻辑的逻辑。著名的准确定义逻辑包括贝尔纳普-邓恩逻辑。文献中已对贝尔纳普-邓恩逻辑的多种扩展进行了研究。本文论证指出，相对于经典逻辑最自然的准确定义逻辑，是在贝尔纳普-邓恩逻辑基础上扩展了虚假性联结词与满足标准演绎定理的蕴涵联结词所形成的逻辑系统。