Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property
This paper considers the class of normal modal logics containing K4 and intermediate logics having the finite model property and satisfying two rather complicated conditions (one of them is related to the possibility of constructing a frame for a logic L by adding a root to the disjoint union of finite frames for L, the other one to the possibility of effectively estimating the cardinality of finite frames separating a given formula from L). It is shown that the admissibility problem for logics in this class is decidable; more precisely, an inference rule with \(n\) variables is admissible in a logic L in this class iff it cannot be disproved in the \(n\)-universal frame for L, which can be checked effectively. This result covers a wide variety of modal and intermediate logics known in the literature (K4.1, K4.2, K4.3, GL2, etc.).
scientific article; zbMATH DE number 590919
scientific article