Bilattices have proven again and again to be extremely rich structures from a logical point of view. As a matter of fact, even if we fix the canonical notion of many-valued entailment and consider the smallest non-trivial bilattice, distinct logics may be defined according to the chosen ontological or epistemological reading of the underlying truth-values. This note will explore the consequence relations of two variants of Belnap’s well-known 4-valued logic, and delve into their interrelationship. The strategy will be that of reformulating those logics using only two ‘logical values’, by way of uniform classic-like semantical and proof-theoretical frameworks, with the help of which such logics can be more easily compared to each other. For a different reading of Belnap’s logic, it will also be proposed a combination mechanism from which it would result in a very natural way.