A Class of Implicative Expansions of Belnap-Dunn Logic in which Boolean Negation is Definable

Abstract Belnap and Dunn’s well-known 4-valued logic FDE is an interesting useful non-classical logic. defined by using conjunction, disjunction negation as the sole propositional connectives. Then question of expanding with implication connective course great interest. In this sense, some implicative expansions have been proposed in literature, among which Brady’s BN4 seems to be preferred option relevant logicians. The aim paper define a class whose elements Boolean definable, whence strong logics such paraconsistent paracomplete PŁ4 itself are addition classical