Frege systems for extensible modal logics

Emil Jeřábek
2006 Annals of Pure and Applied Logic  
By a well-known result of Cook and Reckhow [4, 12] , all Frege systems for the Classical Propositional Calculus (CPC ) are polynomially equivalent. Mints and Kojevnikov [11] have recently shown p-equivalence of Frege systems for the Intuitionistic Propositional Calculus (IPC ) in the standard language, building on a description of admissible rules of IPC by Iemhoff [8] . We prove a similar result for an infinite family of normal modal logics, including K4, GL, S4, and S4Grz .
doi:10.1016/j.apal.2006.04.001 fatcat:mqjlbj4g7zbqbony6yobwfq7o4