A Sequent Systems without Improper Derivations

In the natural deduction system for classical propositional logic given by G. Gentzen, there are some inference rules with assumptions discharged rule. D. Prawitz calls such improper, and others proper. Improper more complicated often harder to understand than proper ones. present paper, we distinguish between improper derivations using sequent systems. Specifically, introduce a \(\vdash_{\bf Sc}\) only structural rules, prove that does not allow in general. For instance, \(\Rightarrow p \to q\) cannot be derived from \(p \Rightarrow Sc}\). order failure of derivations, modify usual notion truth valuation, modified completeness We also consider whether an derivation can described generally