  Paraconsistent logics constitute an important class of formalisms dealing
with non-trivial reasoning from inconsistent premisses. In this paper, we
introduce uniform axiomatisations for a family of nonmonotonic paraconsistent
logics based on minimal inconsistency in terms of sequent-type proof systems.
The latter are prominent and widely-used forms of calculi well-suited for
analysing proof search. In particular, we provide sequent-type calculi for
Priest's three-valued minimally inconsistent logic of paradox, and for
four-valued paraconsistent inference relations due to Arieli and Avron. Our
calculi follow the sequent method first introduced in the context of
nonmonotonic reasoning by Bonatti and Olivetti, whose distinguishing feature is
the use of a so-called rejection calculus for axiomatising invalid formulas. In
fact, we present a general method to obtain sequent systems for any many-valued
logic based on minimal inconsistency, yielding the calculi for the logics of
Priest and of Arieli and Avron as special instances.
