A note on the system GRW with the intensional contraction rule

Abstract

In Ilić and Boričić (2014, Log. J. IGPL, 22, 673–695), the right-handed cut-free sequent calculus $GRW$ for the contraction-less relevant logic $RW$ is defined. In this paper, we show that the enlargement of the system $GRW$ with the structural rule of intensional contraction (WI) presents the sequent system for the principal relevant logic $R$ but the rule of cut cannot be eliminated in $GRW+$(WI).