This paper concerns an expansion of first-order Belnap-Dunn logic which is called $\mathrm{BD}^{\supset,\mathsf{F}}$. Its connectives and quantifiers are all familiar from classical logic and its logical consequence relation is very closely connected to the one of classical logic. Results that convey this close connection are established. Fifteen classical laws of logical equivalence are used to distinguish $\mathrm{BD}^{\supset,\mathsf{F}}$ from all other four-valued logics with the same connectives and quantifiers whose logical consequence relation is as closely connected to the logical consequence relation of classical logic. It is shown that several interesting non-classical connectives added to Belnap-Dunn logic in its expansions that have been studied earlier are definable in $\mathrm{BD}^{\supset,\mathsf{F}}$. It is also established that $\mathrm{BD}^{\supset,\mathsf{F}}$ is both paraconsistent and paracomplete. Moreover, a sequent calculus proof system that is sound and complete with respect to the logical consequence relation of $\mathrm{BD}^{\supset,\mathsf{F}}$ is presented.

翻译：本文研究一种名为$\mathrm{BD}^{\supset,\mathsf{F}}$的一阶Belnap-Dunn逻辑的扩张。其联结词与量词均源于经典逻辑，且其逻辑后承关系与经典逻辑的逻辑后承关系紧密关联。本文建立了若干体现这种紧密关联的结论。通过十五个经典逻辑等价律，将$\mathrm{BD}^{\supset,\mathsf{F}}$与所有具有相同联结词和量词、且其逻辑后承关系与经典逻辑同样紧密关联的四值逻辑区分开来。研究表明，先前在Belnap-Dunn逻辑扩张中研究的若干有趣的非经典联结词可在$\mathrm{BD}^{\supset,\mathsf{F}}$中定义。此外，本文证实$\mathrm{BD}^{\supset,\mathsf{F}}$兼具悖论容忍性与悖论完备性。最后，本文给出一个关于$\mathrm{BD}^{\supset,\mathsf{F}}$逻辑后承关系而言既可靠又完备的矢列演算证明系统。