| Abstract: | This work deals with the exponential fragment of Girard's linear logic (3]) without the contraction rule, a logical system which has a natural relation with the direct logic (10], 7]). A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism (6]) with respect to the logical system in question. MSC: 03B40, 03F05. |
