The basic question about admissible rules of a given logic is whether the set of all admissible rules is decidable. Note that the problem is nontrivial even if the logic itself (i.e., its set of theorems) is decidable: the definition of admissibility of a rule "A"/"B" involves an unbounded universal quantifier over all propositional substitutions, hence "a priori" we only know that admissibility of rule in a decidable logic is formula_25 (i.e., its complement is recursively enumerable). For instance, it is known that admissibility in the bimodal logics "K""u" and "K"4"u" (the extensions of "K" or "K"4 with the universal modality) is undecidable. Remarkably, decidability of admissibility in the basic modal logic "K" is a major open problem.