  We introduce translations between display calculus proofs and labeled
calculus proofs in the context of tense logics. First, we show that every
derivation in the display calculus for the minimal tense logic Kt extended with
general path axioms can be effectively transformed into a derivation in the
corresponding labeled calculus. Concerning the converse translation, we show
that for Kt extended with path axioms, every derivation in the corresponding
labeled calculus can be put into a special form that is translatable to a
derivation in the associated display calculus. A key insight in this converse
translation is a canonical representation of display sequents as labeled
polytrees. Labeled polytrees, which represent equivalence classes of display
sequents modulo display postulates, also shed light on related correspondence
results for tense logics.
