  In recent years, the effort to formalize erotetic inferences---i.e.,
inferences to and from questions---has become a central concern for those
working in erotetic logic. However, few have sought to formulate a proof theory
for these inferences. To fill this lacuna, we construct a calculus for (classes
of) sequents that are sound and complete for two species of erotetic inferences
studied by Inferential Erotetic Logic (IEL): erotetic evocation and erotetic
implication. While an effort has been made to axiomatize the former in a
sequent system, there is currently no proof theory for the latter. Moreover,
the extant axiomatization of erotetic evocation fails to capture its defeasible
character and provides no rules for introducing or eliminating question-forming
operators. In contrast, our calculus encodes defeasibility conditions on
sequents and provides rules governing the introduction and elimination of
erotetic formulas. We demonstrate that an elimination theorem holds for a
version of the cut rule that applies to both declarative and erotetic formulas
and that the rules for the axiomatic account of question evocation in IEL are
admissible in our system.
