Multiplicity of consistent tabular logics with decidable coincidence problems

Determine whether there exists more than one consistent tabular logic in the lattice of extensions of tense Grz or in the lattice of bi-superintuitionistic logics whose coincidence problem is decidable.

Background

The paper establishes one tabular logic in the lattice of extensions of tense Grz with a decidable coincidence problem and refers to a corresponding example for bi-superintuitionistic logics. It leaves unresolved whether either lattice contains any additional consistent tabular logic with this property.

References

We also leave it open whether there is more than one consistent tabular logic $L$ in $ #1{Grz}$ or $ #1{biIPC}$ with a decidable coincidence problem.

— 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