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Persistence notions in possibility semantics

Investigate and formalize notions of persistence of modal formulas from possibility frames to their associated full possibility frames, and determine conditions under which validity is preserved by the associated full-frame construction.

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Background

The paper introduces associated full frames and shows many preservation results via morphisms, but notes that a systematic theory of when validity persists from arbitrary possibility frames to their associated full frames remains to be developed.

A framework for such persistence would clarify the behavior of validity under canonical and associated constructions in possibility semantics and may yield new preservation theorems paralleling those in Kripke semantics.

References

We leave it to future work to study various notions of persistence in the context of possibility semantics.

— Possibility Frames and Forcing for Modal Logic (2501.11768 - Holliday, 20 Jan 2025) in Section Completeness for Canonical Possibility Frames (end of \S~\ref{Canonical})