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Several methods for checking admissibility of rules in the modal logic $S4$are presented in [1], [15]. These methods determine admissibility of rules in$S4$, but they don't determine or give substitutions rejecting inadmissiblerules. In this paper, we investigate some relations between one of the abovemethods, based on the reduced normal form rules, and sets of substitutionswhich reject them. We also generalize the method in [1], [15] for one rule toadmissibility of a set of rules.

Rejecting inadmissible rules in reduced normal forms in S4