Abstract
Belnap-Dunn logic, also knows as the logic of First-Degree Entailment,
is a logic that can serve as the underlying logic of theories that are
inconsistent or incomplete.
For various reasons, different expansions of Belnap-Dunn logic with
non-classical connectives have been studied.
This paper investigates the question whether those expansions are
interdefinable with an expansion whose connectives include only
classical connectives.
Surprisingly, this relevant question is not addressed anywhere in the
published studies.
The notion of interdefinability of logics used is based on a general
notion of definability of a connective in a logic that seems to have
been forgotten.
Attention is also paid to the extent to which the expansion whose
connectives include only classical connectives is related to the
version of classical logic with the same connectives.