5 problems

Let ${\bf GL}$ be Gödel–Löb provability logic, let … and define Solovay's logic by … Let ${\bf S5}$ denote the modal logic of equivalence frames, and let $\rightthreetimes$ denote…

Let $n$ be finite, and let ${\operatorname{ILog}}(\omega^n,\preceq)$ denote the intermediate logic of the frame $(\omega^n,\preceq)$. Local finiteness claim. For all finite $n$, ……

Disjunctive-binding decidability conjecture. The fragment $db$ enjoys a decidable satisfiability problem.

Conjunctive-binding positive-properties conjecture. The fragment $cb$ enjoys the finite-model property and has a decidable satisfiability problem.

Extension-preservation conjecture. Some of these extensions preserve the same model-theoretic and algorithmic properties.