Abstract

Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cut-elimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof objects for intuitionistic linear logic with the connectives ⊗, ⊸, � and! 1; in particular we can interpret the simply typed lambda calculus, with or without product types. We call these proof nets essential nets. We will formulate a correctness criterion for them: there is an intrinsic property that characterizes the essential nets that do come from proofs in the sequent calculus; it turns out that every such (correct) essential net represents a large number of sequent proofs that differ by inessential details. Thus essential nets, as should be the case for proof nets in general, have the power of eliminating a lot of the bureaucracy in the sequent calculus. We will give a cut-elimination procedure for essential nets which is based on that correctness criterion. That procedure is not one that can be said to be

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