Frege systems for extensible modal logics

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.

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: Emil Jerábek
• Keywords: APAL 2006, Classical Propositional Calculus, Frege Systems, Propositional Calculus