Syntactic Cut-elimination for Common Knowledge

We see a cut-free infinitary sequent system for common knowledge. Its sequents are essentially trees and the inference rules apply deeply inside of these trees. This allows to give a syntactic cut-elimination procedure which yields an upper bound of @f"20 on the depth of proofs, where @f is the Veblen function.

[1]  Wolfram Pohlers.  Proof Theory: An Introduction , 1990 .

[2]  Ryo Kashima,et al.  Cut-free sequent calculi for some tense logics , 1994, Stud Logica.

[3]  Evangelia Antonakos.  Justified and Common Knowledge: Limited Conservativity , 2007, LFCS.

[4]  Charles A. Stewart,et al.  A Systematic Proof Theory for Several Modal Logics , 2004, Advances in Modal Logic.

[5]  Kai Brünnler,et al.  Deep sequent systems for modal logic , 2009, Arch. Math. Log..

[6]  W. van der Hoek,et al.  Epistemic logic for AI and computer science , 1995, Cambridge tracts in theoretical computer science.

[7]  K. Schütte.  Schlußweisen-Kalküle der Prädikatenlogik , 1950 .

[8]  S. Buss.  Handbook of proof theory , 1998 .

[9]  Regimantas Pliuskevicius,et al.  Investigation of Finitary Calculus for a Discrete Linear Time Logic by means of Infinitary Calculus , 1991, Baltic Computer Science.

[10]  Dines Bjørner,et al.  Baltic Computer Science: Selected Papers , 1991 .

[11]  Alessio Guglielmi,et al.  A system of interaction and structure , 1999, TOCL.

[12]  Thomas Studer,et al.  Cut-free common knowledge , 2007, J. Appl. Log..

[13]  Kurt Schütte.  Proof theory , 1977 .

[14]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[15]  Thomas Studer,et al.  Deduction chains for common knowledge , 2006, J. Appl. Log..

[16]  Yoshihito Tanaka.  Some Proof Systems for Common Knowledge Predicate , 2003, Reports Math. Log..

[17]  W. Pohlers.  Chapter IV – Subsystems of Set Theory and Second Order Number Theory , 1998 .

[18]  Sergei N. Artëmov.  Justified common knowledge , 2006, Theor. Comput. Sci..

[19]  Gerhard Jäger,et al.  About cut elimination for logics of common knowledge , 2005, Ann. Pure Appl. Log..

[20]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.