Equivalence of static and dynamic notions in other frame classes

Determine whether the equivalences established in Theorems 1 and 2 between static unknowability and unbelievability, Moorean fixed points, and the associated dynamic notions continue to hold in classes of frames other than those treated in the paper.

Background

The paper proves broad equivalences among static and dynamic notions in the single-agent setting over S5 and establishes a static multi-agent analogue in KD45 and S5. It also records only partial implications for other frame classes, including KD4 and S4. The behavior of the remaining equivalence directions outside the principal classes therefore remains unresolved.

References

Second, we leave the discussions of whether the equivalence in Theorems~\ref{Unknowability and unbelievability in KD45 and S5} and \ref{Multi-agent unknowability} holds in other classes of frames as a future work.

— The Sources of Unknowability and Self-refutation in Epistemic and Dynamic Epistemic Logic  (2609.21317 - Yamada, 18 Sep 2026) in Section 6, Conclusion and future directions

The following equivalence is expected to hold in S5 for multi-agent epistemic logic with common knowledge operator $C_G$, with almost the same proof in Proposition 5.7 in. We just leave it for future work: $\varphi$ is always informative $\iff$ $C_G\varphi$ is unsatisfiable $\iff$ $\varphi$ is eventually self-refuting.

— The Sources of Unknowability and Self-refutation in Epistemic and Dynamic Epistemic Logic  (2609.21317 - Yamada, 18 Sep 2026) in Section 4, paragraph immediately following Theorem \ref{Multi-agent unknowability}