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.