A conventional expansion of first-order Belnap-Dunn logic

Abstract: This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers are all familiar from classical logic. The language and logical consequence relation of the logic are defined, a proof system for the defined logic is presented, and the soundness and completeness of the presented proof system is established. The close relationship between the logical consequence relations of the defined logic and the version of classical logic with the same language is illustrated by the minor differences between the presented proof system and a sound and complete proof system for the version of classical logic with the same language. Moreover, fifteen classical laws of logical equivalence are given by which the logical equivalence relation of the defined logic distinguishes itself from the logical equivalence relation of many logics that are closely related at first glance.