Completeness via Correspondence for Extensions of the Logic of Paradox

Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (L P). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to L P by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for L P . Third, we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics. §