DAG Sequent Proofs with a Substitution Rule

In this paper we study an extension to classical sequent calculus with a substitution rule, which is normally admissible in classical logic. The structure of proofs is also extended to permit DAG shaped proofs. We analyse several properties of this system, such as the complexity of cut-elimination, and propose an extended tableau proof system, called s-tableau, that corresponds to the DAGsequent calculus. We show how the pigeon hole principle can be solved linearly solved in s-tableaux.