In this paper, we give a sequent calculus GRW+∘ for the positive contraction‐less relevant logic RW+∘ and we give a proof that it is cut‐free without the use of the truth constant t. Based on GRW+∘, we re‐prove the decidability of the logic RW+∘.

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We describe theorem provers for some decidable propositional substructural logics.

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).