Proof theory for admissible rules

Rosalie Iemhoff, George Metcalfe
2009 Annals of Pure and Applied Logic  
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
more » ... IPC. With minor restrictions, proof search in these systems terminates, giving decision procedures for admissibility in the logics. Preliminaries We treat a logic L as a consequence relation based upon a propositional language with binary connectives ∧, ∨, →, a constant ⊥, and sometimes also a modal con-
doi:10.1016/j.apal.2008.10.011 fatcat:7z7trrc4gjg3vo2z76ppxksd2e