On Proof Normalization in Linear Logic

Abstract : We present a proof-theoretic foundation for automated deduction in linear logic. At first, we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a proof. Then we discuss the naturally-arising question of the redundancy reduction and investigate the definition of the normal proof concept. We briefly consider some of the issues related to proof construction mechanization in linear logic and to the design of logic programming languages from linear logic fragments.