FO-correspondence transfer from full world frames to full possibility frames

Determine whether every modal formula that has a local or global first-order correspondent over full world (Kripke) frames also has a local or global first-order correspondent over full possibility frames.

Background

A core motivation for Kripke semantics is the robust first-order correspondence of many modal axioms (e.g., seriality, reflexivity, transitivity). The paper develops corresponding results for full possibility frames and shows transfer in several cases, but notes that a general transfer result—ensuring that every formula with a Kripke first-order correspondent also has one over possibility frames—has not been established.

Resolving this would unify correspondence theory across Kripke frames and possibility frames and clarify whether possibility semantics preserves all first-order expressivity seen in Kripke semantics.