Author:
Pulcini Gabriele,Varzi Achille C.
Abstract
AbstractA complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$
CPN
, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$
CPN
enjoys strong normalization along with strong confluence (and, hence, uniqueness of normal forms).
Funder
Università degli Studi di Roma Tor Vergata
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Logic
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