Nondeterministic Linear Logic

In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the system is expressed by the process of normalization, not by proof search. Moreover we can incorporate the system into Light Linear Logic and Elementary Linear Logic developed by J.-Y.Girard recently: Nondeterministic Light Linear Logic and Nondeterministic Elementary Linear Logic are defined in a very natural way.