Metainferences, Invalidities and Contraction-Free Sequent Calculi for S5 and Carnap’s C

Abstract This paper develops a sequent calculus framework for representing locally and globally valid metainferences through which contraction-free sequent calculi for the modal logics S5 and the propositional fragment of Carnap’s C are obtained. The sequent calculi allow for strongly terminating and backtracking-free proof search, features which in turn arguably explain why the decision problems for S5 and the propositional fragment of Carnap’s C are reducible to that of propositional classical logic.