Complementary Proof Nets for Classical Logic

Abstract A complementary system for a given logic is proof whose theorems are exactly the formulas that not valid according to in question. This article contribution theory of classical propositional logic. In particular, we present proof-net system, $$\textsf{CPN}$$ CPN , sound and complete with respect set all classically invalid (one-side) sequents. We also show cut elimination enjoys strong normalization along confluence (and, hence, uniqueness normal forms).