6 problems

Completeness conjecture. The completeness of non-classical variants of $\mathsf{S4}$ may be proved by combining the methods of Balbiani et al. and Baltag et al.

Full-completeness conjecture. The full-completeness results should be extendable to all proofs of a formula, rather than only to the factorised ones.

Combinatorial proof equivalence conjecture. As in the intuitionistic combinatorial proofs for the logic $\mathsf{LI}$, the combinatorial proofs presented in this paper should captu…

The paper considers constructive predicate logic involving strong negation and its cut elimination theorem. Unrestricted cut-elimination conjecture. The new cut elimination theorem…

Strict-weakness conjecture. $\mathsf{MP}_\mathsf{L}$ is strictly weaker than $\mathsf{MP}$.

Proof-theoretic semantics studies logical validity through the deductive use of logical constants, as expressed by their introduction and elimination rules. In a verificationist ap…