The lattice of all 4-valued implicative expansions of Belnap-Dunn logic containing Routley and Meyer's basic logic Bd

The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with Lambda, V and similar to as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer's basic logic B and its useful disjunctive extension B-d. It is to be noted that Boolean negation (so, classical propositional logic) is definable in the strongest element in the said class.