Interpolation above S4
arXiv:2604.220207.3h-index: 5
AI Analysis
For modal logicians, this resolves a long-standing open problem in the classification of S4 extensions with interpolation.
The paper completes the classification of normal extensions of S4 with Craig interpolation by proving interpolation for the six remaining open cases. The result establishes a complete map of which S4 extensions have the interpolation property.
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 Smoryński, but employs a novel approach using Fine's frame formulas for splitting clusters.