On logic of paradox
Zuoquan Lin, Wei Li · 2002
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/sub m/ is nonmonotonic in the sense that inconsistency is minimal. The problem of proof theory of logic LP/sub m/ left open because the base logic LP is paraconsistent so that syntactic formulations of nonmonotonic logic are not available for LP/sub m/, though LP/sub m/ is well characterized by minimal semantics. In this paper, we provide a minimal tableaus as a satisfactory proof theory for LP/sub m/. We first present a signed tableaux for LP. Then minimal tableaux for LP/sub m/ is obtained by revising signed tableaux for LP to fit LP/sub 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/sub m/ are proved, respectively.