Unbelievable formulas in KD and KD5 beyond the BK paradox

Investigate whether formulas other than the Brandenburger–Keisler paradox are already unbelievable in KD or KD5, and identify the distinct mechanisms responsible for their unknowability and unbelievability.

Background

The paper characterizes unknowability and unbelievability in several modal frame classes and analyzes the Brandenburger–Keisler paradox as an example of a formula that is unbelievable because of Russell-style diagonalization rather than solely because of introspection principles. It remains unresolved whether other formulas exhibit analogous mechanisms in the weaker classes KD or KD5. Finding such examples could expand the taxonomy of sources of unknowability and unbelievability developed in the paper.

References

First, there might be formulas other than the BK paradox that are already unbelievable in KD or KD5. Finding such formulas would reveal further distinct mechanisms for unknowability and unbelievability.

— 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