On Proof Normalization in Linear Logic

We present a proof-theoretic foundation for automated deduction in linear logic. At rst, 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 possibilities of proof normalization which depend on the proof search strategy and the fragment we consider. Thus, we can deene the concept of normal proof that might be the basis of works about automatic proof construction and design of logic programming languages based on linear logic.