Use of filtration to prove decidability for several logics

Ascertain whether the filtration method can be employed to prove decidability of the membership problems in the logics Lfc, Lbc, Ldc, Lfbc, Lfdc, Lbdc, and Lfbdc.

Background

Filtration is a standard finite-model construction technique used to establish decidability, and the paper adapts it to certain intuitionistic modal logics. For several other systems (notably those tied to various confluence combinations), the applicability of filtration remains uncertain.