Characterization of tabular logics with decidable coincidence problems

Characterize the tabular logics in the lattice of extensions of tense S4 for which the coincidence problem is decidable.

Background

The paper proves that the lattice of extensions of tense S4 contains infinitely many tabular logics with undecidable coincidence problems and infinitely many tabular logics with decidable coincidence problems. It does not provide a criterion distinguishing the two classes, and explicitly identifies a full characterization as unresolved.

References

However, we do not have a full characterization of tabular logics $L$ in $ #1{S4}$ for which the coincidence problem is decidable.

— Most properties are undecidable even in $\mathop{\mathsf{NExt}} \mathsf{Grz}_t$  (2608.30816 - Chen et al., 31 Aug 2026) in Remark following Corollary \ref{cor:undec-prop-S4t-=tab}, Section 3