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In this paper rejection systems for the "nonsense-logic" W and the k-valued implicational-negational sentential calculi of Sobociński are given. Considered systems consist of computable sets of rejected axioms and only one rejection rule: the rejection version of detachment rule. Keywords: rejected axioms, the logic W, the k-valued sentential calculi of Sobociński.doi:10.12775/llp.2008.018 fatcat:glafwwgju5bl3mkpfnc7itrhry