The interdefinability of expansions of Belnap-Dunn logic (2403.04641v2)

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.