Transitivity of Finite Models Constructed from Normal Forms for a Modal Logic Containing K4

By using normal forms for a modal logic L, Moss [3] constructed finite model Cn,m(L) and proved that the model is reflexive if L contains KT, it is serial if L contains KD, and so on. However, concerning to transitivity, he raised the problem: “Is it true that for every logic L containing K4, Cn,m(L) is transitive for almost all n?”. In the present paper, by using another type of normal forms in [4], we prove that the model Cn,m(S4BW2) is not transitive for each n ≥ 2, where S4BW2 is the logic characterized by the class of the reflexive and transitive models of width ≤ 2.