On Urquhart's C logic

Abstract

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