On logic of paradox

G. Priest introduced nonmonotonicity into a paraconsistent logic, so-called logic of paradox LP, that yields a solution to the weakness of paraconsistent logic. The resulting logic (of minimal parades) LP_m is nonmonotonic in the sense that inconsistency is minimal. The problem of proof theory of logic LP_m left open because the base logic LP is paraconsistent so that syntactic formulations of nonmonotonic logic are not available for LP_m, though LP_m is well characterized by minimal semantics. In this paper, we provide a minimal tableaus as a satisfactory proof theory for LP_m . We first present a signed tableaux for LP. Then minimal tableaux for LP_m is obtained by revising signed tableaux for LP to fit LP_m in which the branches of non-minimally-inconsistent models of the tableaux are eliminated. The soundness and completeness theorems of the tableaux with respect to the semantics of LP and LP_m are proved, respectively