TL;DR
This paper completes the classification of certain modal logic extensions, proving Craig interpolation for six open cases using a novel approach with Fine's frame formulas.
Contribution
It provides a complete classification of S4 extensions with interpolation and proves Craig interpolation for previously unresolved cases using a new method.
Findings
Proves Craig interpolation for six S4 extensions.
Completes Maksimova's classification of S4 extensions with interpolation.
Introduces a novel proof approach using Fine's frame formulas.
Abstract
We complete Maksimova's classification of the normal extensions of S4 with interpolation. In particular, we prove Craig interpolation for the six extensions of S4 for which Craig interpolation was still open. The proof strategy builds upon the ideas of Smory\'nski, but employs a novel approach using Fine's frame formulas for splitting clusters.
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