  Bi-intuitionistic logic is the conservative extension of intuitionistic logic
with a connective dual to implication. It is sometimes presented as a symmetric
constructive subsystem of classical logic.
  In this paper, we compare three sequent calculi for bi-intuitionistic
propositional logic: (1) a basic standard-style sequent calculus that restricts
the premises of implication-right and exclusion-left inferences to be
single-conclusion resp. single-assumption and is incomplete without the cut
rule, (2) the calculus with nested sequents by Gore et al., where a complete
class of cuts is encapsulated into special "unnest" rules and (3) a cut-free
labelled sequent calculus derived from the Kripke semantics of the logic. We
show that these calculi can be translated into each other and discuss the
ineliminable cuts of the standard-style sequent calculus.
