The Value of the Two Values

abstract. Bilattices have proven again and again to be extremely rich structures from a logical point of view. As a matter of fact, even if one fixes the canonical notion of many-valued entailment and consider the smallest non-trivial bilattice, distinct logics may be defined accord-ing to the chosen ontological, epistemological or informational reading of the underlying truth-values. This note will explore the consequence relations of two very natural 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 uni-form classic-like semantical and proof-theoretical frameworks, with the help of which such logics may be more easily compared to each other.