Decidability of membership problems for Lutra and Ldtra

Determine whether the membership problems for the logics Lutra and Ldtra are decidable, where Lutra=Lmin+(Autra) corresponds to up-transitive frames and Ldtra=Lmin+(Adtra) corresponds to down-transitive frames.

Background

The paper establishes decidability for the base logic Lmin and for several other systems via filtration-based finite model properties. For the systems tied to up- and down-transitivity (Lutra and Ldtra), the decidability of membership remains unresolved.