Ideas from 'A Completeness Theorem in Modal Logic' by Saul A. Kripke [1959], by Theme Structure

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4. Formal Logic / D. Modal Logic ML / 1. Modal Logic

10163

Propositional modal logic has been proved to be complete [Feferman/Feferman]

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic

10760

With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Rossberg]

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula

16189

The variable domain approach to quantified modal logic invalidates the Barcan Formula [Simchen]

15132

The Barcan formulas fail in models with varying domains [Williamson]