On Urquhart´s C logic

In this paper we investigate the basic many-valued logics introduced by Urquhart (1986), here referred to as C and C_new, respectively. We define a cut-free hyper-sequent calculus for C_new and show the following results: (1) C and C _new are distinct versions of Godel logic without contraction. (2) C_new is decidable. (3) In C_new the family of axioms ((A^k→C)∧(B^k→C))→((AVB) ^k→C), with k⩾2, is in fact redundant