In the paper rejection systems for a system of nonsense-logic are investigated. The first rejection system consists of four rejected axioms and only one rejection rule  the rule of rejection by detachment. The second one consists of one rejected axiom and two rejection rules: the rule of rejection by detachment and the rule of rejection by substitution. The aim of the paper is to present also a proof of Ł-decidability for the considered systems.

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.