Cut-elimination in a sequents-of-relations calculus for Godel logic

Abstract

Previously, the analytic calculus RG/sub /spl infin// for Godel logic has been introduced. RG/sub /spl infin// operates on "sequents of relations". We show constructively how to eliminate cuts from RG/sub /spl infin//-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 G/sub /spl infin//. Moreover, we give an explicit description of all the axioms of RG/sub /spl infin// and prove their completeness.