Proceedings 31st IEEE International Symposium on Multiple-Valued Logic (2001)
May 22, 2001 to May 24, 2001
Matthias Baaz , Technische Universit?t Wien
Agata Ciabattoni , Technische Universit?t Wien
Christian G. Fermüller , Technische Universit?t Wien
In  the analytic calculus RG1 for G?del logic has been introduced. RG1 operates on "sequents of relations". We show constructively how to eliminate cuts from RG1-derivations. The version of the cut rule we consider allows to derive other forms of cut as well as a rule corresponding to the "communication rule" of Avron's hypersequent calculus for G1. Moreover, we give an explicit description of all the axioms of RG1 and prove their completeness.
M. Baaz, C. G. Fermüller and A. Ciabattoni, "Cut-Elimination in a Sequents-of-Relations Calculus for G?del Logic," Proceedings 31st IEEE International Symposium on Multiple-Valued Logic(ISMVL), Warsaw, Poland, 2001, pp. 0181.