Herbrand Methods in Sequent Calculi: Unification in LL

We propose a reformulation of quantiiers rules in sequent calculi which allows to replace blind existential instantiation with uniication, thereby reducing non-determinism and complexity in proof-search. Our method, based on some ideas underlying the proof of Herbrand theorem for classical logic, may be applied to any \reasonable" non-classical sequent calculus, but here we focus on sequent calculus for linear logic, in view of an application to linear logic programming. We prove that the new linear proof-system which we propose, the so called system LLH, is equivalent to standard linear sequent calculus LL.