Abstract   Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic objects, for admissibility, the basic objects are sequent rules. Proof systems are defined here for admissible rules of classes of modal logics, including  K4 ,  S4 , and  GL , and also Intuitionistic Logic  IPC . With minor restrictions, proof search in these systems terminates, giving decision procedures for admissibility in the logics.
['Rosalie Iemhoff', 'George Metcalfe']
Proof theory for admissible rules