Abstract
A paradefinite logic is a logic that can serve as the underlying logic
for theories that are inconsistent or incomplete.
A well-known paradefinite logic is Belnap-Dunn logic.
Various expansions of Belnap-Dunn logic have been studied in the
literature.
In this note, it is argued that the most natural paradefinite logic
relative to classical logic is the expansion of Belnap-Dunn logic with
a falsity connective and an implication connective for which the
standard deduction theorem holds.