Proof nets with explicit negation for multiplicative linear logic

Abstract

Multiplicative linear logic MLL was introduced in Gi as a onesided sequent calculus linear negation is a notion that is dened via De Morgan identities One obtains proof nets for MLL by identifying derivations in the onesided calculus that are equal up to a permutation of inference rules In this paper we consider a similar quotient for the formulation of MLL as a two-sided sequent calculus to the usual set of links we add links also for the left rules As a consequence negation need no longer be dened but can be treated as a basic connective We develop the fundamental theory substructures empires and sequentialization for this variation on the notion of proof net and show how to obtain Girards sequentialization theorem for the standard proof nets in onesided sequent calculus as a corollar