A note on functional relations in a certain class of implicative expansions of FDE related to Brady's 4-valued logic BN4.

The logic E4 is related to Brady's BN4 in a similar way to which Anderson and Belnap's logic of entailment E is related to their logic of the relevant implication R. In 'A companion to Brady's 4-valued relevant logic: the 4-valued logic of entailment E4', quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer's basic logic B, provided some conditions are fulfilled. The aim of this note is to prove (i) BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; (ii) to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely. [ABSTRACT FROM AUTHOR]