4 problems

Let $L$ be an intermediate logic which is hereditarily structurally complete. Hereditary admissibility conjecture. Hereditary admissibility is equivalent to admissibility over $L$.…

Non-necessity conjecture. Distributivity is not a necessary condition for validating the Split axiom even over finite classical frames; equivalently, there should be a finite class…

Consider the hypersequent rules obtained from geometric frame axioms by the translation method described in the source, together with the linearity rule. Cut-admissibility conjectu…

Let the method in Definition translate geometric frame axioms into hypersequent rules, and let $\mathrm{HG3ipm}$-like calculi be augmented with the $\mathrm{lin}$ rule. Cut-admissi…